Anna Rose (00:00:05):
Welcome to zero knowledge. I'm your host, Anna Rose. In this podcast, we will be exploring the latest in zero knowledge research and the decentralized web, as well as new paradigms that promise to change the way we interact and transact online.


Anna Rose (00:00:28):
This week, I share with you a conversation that I had a few months ago with repeat guest Guillermo Angeris. In this conversation, we dive into the topic of math. The history of math collaboration is a key driver, how to bring more people into the space and the potential opportunities and downsides of bringing some kinds of math mainstream. But as a bit of a disclaimer, we decided it would be really smart to pair our conversation with a bottle of sake. And while this one starts very clearheaded, it sort of veered into drunk history territory near the end of the episode. Like I know Pythagoras was from ancient Greece, but for some reason I decided to place him in Alexandria in this episode. And we managed to both mix up astrology and astronomy by the end. Anyway, I digress. I hope you like the episode. I am thinking of doing more like this, where we explore people's relationships to math, cryptography, and engineering in some way.


Anna Rose (00:01:20):
But I am curious to hear if you like it, and if not, let me know that too. We can maybe try to find another place for conversations like this.


Anna Rose (00:01:28):
Now, before we start in, I do wanna let you know that the ZK podcast crew is growing. We are taking on a number of new projects at the moment, and we are looking to hire an additional content producer to join us. I've added the job description for this position to the ZK jobs board, ZK jobs board is a place where you can find lots of jobs from different teams in the ZK space, not just us. So do check that out in general. Now for this particular role, the job really requires that you have at least two years of experience working on regular content production. I won't really be looking at CVs that don't have this, and ideally you would be organized good at project management and somewhat familiar with our field, but no need to be an expert on specifically ZK. If you or someone, you know, fits the bill, please apply. I've added links in the description. I hope to hear from you. Now, Tanya, the podcast producer will share a little bit about this week's sponsor.


Tanya (00:02:21):
Today's episode is sponsored by Anoma. Anoma is a set of protocols that enables self-sovereign coordination. Their unique architecture facilitates sufficiently the simplest forms of economic coordination, such as two parties transferring an asset to each other as well as more sophisticated ones like an asset agnostic bartering system involving multiple parties without direct coincidence of wants, or even more complex ones, such as N-party collective commitments to solve multipolar traps where any interaction can be performed with adjustable zero knowledge privacy. Anoma's first fractal instance Namada is planned for later in 2022, and it focuses on enabling shielded transfers for any assets with a few second transaction latency and near zero fees visit anoma.net for more information. That's anoma.net. So thanks again Anoma. Now here is Anna's interview with Guillermo.


Anna Rose (00:03:18):
Today. I'm here IRL with Guillermo someone who's been on the show a couple times. Welcome back to the show Guillermo.


Guillermo Angeris (00:03:24):
Thank you. It's kind of weird to do it in person actually, I think is the first time we've met IRL to be fair as well for real that's right. That's right. Or not this time, I guess yesterday, but close enough.


Anna Rose (00:03:34):
Right. So right now we're in Amsterdam for the DevConnect week. Like I'm in the middle of two events. So I just did the ZKV Cosmos event and I have the ZKsummit coming up. Guillermmo, you just got in. Yeah. How, how are you doing?


Guillermo Angeris (00:03:48):
Currently subsisting on approximately like five hours of sleep or cumulatively, maybe eight hours of sleep or something like that over the past few days. And along with the sake we're drinking, I'm sure it's gonna lead to a very interesting episode.


Anna Rose (00:04:02):
Definitely. And our combination of Amsterdam and sake is quite random, but we felt like this would be a good combination for today's episode. Weirdly our goal here is to have a conversation about math and this is something that came up, I think a few weeks ago we were talking about math and you, you just started to sort of like tell me this philosophy math. Right. And I was like, maybe this is something worth doing on the show since we often talk about math, but we don't necessarily talk about the metas of math. Like we just talk about actual types of math or you know, math comes up a lot first. Let's take a step back though, even though you've been on the show, what


Guillermo Angeris (00:04:45):
Is it? I guess three times


Anna Rose (00:04:46):
I think, I think is your fourth.


Guillermo Angeris (00:04:48):
I think it's my fourth. That's right.


Anna Rose (00:04:49):
Yeah. Okay. So people may be familiar with you. Some people still believe you're just Tarun's alt, but 


Guillermo Angeris (00:04:56):
You know, it's, I think it's closer to reality than most people would like to believe.


Anna Rose (00:05:00):
All right. But why don't you introduce yourself to the listeners?


Guillermo Angeris (00:05:04):
I'm Guillermo Angeris I guess I have this weird fake made up title called head of research at a VC fund called Bain Capital Crypto. And I mostly, you know, sit in a dark corner and do a bunch of math as I believe as part of my role. So, so I, I unfortunately or, you know, very appropriately we're doing this with alcohol, but you know, to have thought a lot about the metas of math and all that and whatever that entails. Cool.


Anna Rose (00:05:32):
Before you were doing the head of research thing though, and when you've been on the show, you've also been producing a lot of like research papers with our often cohost Tarun tell me what's the repor there? Like what, what were you doing beforeand why does everyone call you Tarun's alt?


Guillermo Angeris (00:05:52):
Yeah. Yeah. So, so I guess the, the quick background that most people don't know is that Tarun is actually my boss in 2016 at a weird company called D. E. Shaw research that did essentially did molecular dynamics essentially kind of trying to simulate protein, folding, essentially it built super computers for, for doing molecular dynamics for chemistry simulations, specifically for protein folding. Anyway, so the point is we became friends then you know, he left then to go for trading at 2017 or something like that. And then, but we just kept on chatting and in, I believe 2018, he comes up to me and he's like, Hey, I'm building this weird company it's called Gauntlet. And you know, we're, we're thinking of doing some stuff with simulating blockchains. Yes. And kind of thinking through originally at the time it was


Anna Rose (00:06:41):
Proof of stake stuff. That's I had him on the show then.


Guillermo Angeris (00:06:44):
Yeah, exactly. So it was, it was, yeah, it was like questions about like L1 security and he's like, look, we have these agents, we have to simulate them. And, and it turns out that, you know, I know you're doing optimization stuff. So maybe like you might find something interesting there. And so I was like, yeah, I like Tarun, I, you know, was a fun person to work with. I've worked with him before. Sure. Why hell not let's do it. And so from there we started looking into some weird thing called Uniswap for some reason or another that came up. We were just very confused as to why some at the time, some 200 line Vyper contract had like, I think 5 million dollars, this was late 2018, like about to be early 2019. And we were like, what, what is going on?


Guillermo Angeris (00:07:28):
Like how has, you know, like $5 million for context at the time was a lot of fucking money in a contract. Yeah. and just it, from there, it kind of devolved into you know, we wrote this paper called analysis of Uniswap markets, which kind of became popular. And then from there we just started coauthoring a crap ton of papers together. And in fact, if I think every single paper that we've written since pretty much barring, like maybe one or two exceptions has been just like with us and then later with Alex in the title. So


Anna Rose (00:08:00):
Did you know Uniswap? Was this like, were you in crypto?


Guillermo Angeris (00:08:04):
No. So I, I was in crypto a little bit. So actually Tarun originally had told me about Ethereum back in back when I was his, his intern in D. E. Shaw research, actually and I had some, but I, you know, I wanted to mess with it, but I never did anything.


Anna Rose (00:08:16):
I don't know if I asked you this already, but what was your opinion about it back then? If you can remember.


Guillermo Angeris (00:08:25):
Let's just say crypto is often used for things in which cash would've probably made the equivalent replacement.


Anna Rose (00:08:35):
Buying drugs?


Guillermo Angeris (00:08:36):
You know? Yeah. That that's one, one of the possibilities or something like that, you know? Yeah. So, so anyway, so that my, my opinion in crypto was, you know, I don't wanna hold this thing for longer than I have to. Maybe that's that's the oh,


Anna Rose (00:08:49):
Kind, like get it away.


Guillermo Angeris (00:08:51):
That's right. That's right. That that's right.


Anna Rose (00:08:52):
Did you think it was illegal? Did you think of it as


Guillermo Angeris (00:08:56):
No. So I didn't think it was illegal. It was just, you know at the time,


Anna Rose (00:08:59):
I mean, it isn't, it wasn't, but it's more like, did you see it as something like, oh, this could be dangerous to me to have or something weird.


Guillermo Angeris (00:09:08):
It wasn't that actually, it was okay. If you, if you remember some amounts of, you know, how these sites worked is you would actually often put like a little extra because of the fact that like crypto would be very volatile. Okay. Right. And so, you know, you needed to do some, you wanted to pay someone, whatever 90 bucks for, you know, any number of things. One could imagine that, like what happened there is you know, the price of Bitcoin would fluctuate enough that you would then have to put an extra in order for you to be able to have the transaction go through and stuff like that. So I was like, if this, you know, I can't even like pay like someone 90 bucks on this thing. Like, why would I wanna hold onto


Anna Rose (00:09:43):
It was almost like, because small value transfers just made no sense.


Guillermo Angeris (00:09:47):
That's right. That's right.


Anna Rose (00:09:48):
Which is still is, I mean, kind of true kind of tricky with the gas fees and stuff to actually, well, at least on Ethereum. Right. I mean, did you just find it unpractical?


Guillermo Angeris (00:09:57):
I found it. Yeah. So I was very confused. When a year later my mom calls me and I, you know, asked me about this thing called she's like, Hey have you heard about this thing called like Bitcoin or Ethereum? And I'm like, oh no. What did my mom find out about what I've been doing? But, but it, it turned out this was right during the 2017 bubble. I was just very confused. Right. Because why the hell my mom be calling me about this system that like, is cool. I mean, it's like, it was very interesting to me and I had some Ethereum because I was interested in writing smart contracts at the time. But you know, it's kind of, not really that usable for me. Like why would my mom know about this thing? So I was worried.


Guillermo Angeris (00:10:36):
It was, for other reasons, it turned out that my mom was simply just like, very interested in like this internet money. Yeah. as she still is weirdly enough. That's cool. But I don't know. I didn't think like anything of it, other than like, as a cool technical curiosity, actually my, my story with this stuff started very early. Like back when I was in like, I guess, late middle school, early high school, I had a really cool graphics card and, you know, I'd played like the coolest games that you could play on this graphics card. And then I realized that like I had nothing better to do. And then one of my friends comes up to me. He's like, you know, you can also do with your graphics card is you can mine Bitcoin,


Anna Rose (00:11:11):
You did mine Bitcoin as well?


Guillermo Angeris (00:11:12):
Mine, Bitcoin, and then it for a little bit.


Anna Rose (00:11:14):
But was it kind of like a thing where you're like, let's mine Bitcoin, you do it. It's kind of worthless at the time.


Guillermo Angeris (00:11:19):
Yeah. It, it was worth nothing. So it was for fun...


Anna Rose (00:11:21):
You just turned it off?


Guillermo Angeris (00:11:23):
Yeah. It was just, so now there's some amount of Bitcoin maybe, cuz this is at the time of, you know, there's some mining pools, but let's just say that amount of money is probably lost to the ether. I have personally never been able to recover it.


Anna Rose (00:11:35):
I see. All right. So the point of this episode is actually not your history with cryptocurrency, but it's rather the <laugh> right.


Guillermo Angeris (00:11:42):
Sorry.


Anna Rose (00:11:43):
It's the, the real question is the question of math. So putting that aside, I almost wanna understand your journey into math and at what point that intersects with what we're talking about?


Guillermo Angeris (00:11:55):
Oh man.


Anna Rose (00:11:56):
So give us a little bit of a story of like, why math, what math, when math?


Guillermo Angeris (00:12:01):
When math, who math? Actually I did not really like math as its own topic for a long time. It's this weird thing of like, you know, you memorize these steps. Yeah. And you memorize these proofs and you memorize, actually wasn't even proofs, whatever techniques I don't. Yeah. I don't wanna call them proofs because they're just like writing some shit on a table and making some equivalents or some stupid thing. So to me that was kind of, you know, what math was, it was at best, in the best of cases, I was interested in physics in the best of cases, it was a tool to do things that you wanted to do. Mm. But it, but it wasn't really like a subject of study. Right. It wasn't that interesting as its own thing. Yeah. So there's a lot of things that kind of develop. One of them actually is I went to, speaking of Tarun is I went to a summer camp with Tarun's brother and a few other people. But there it was, it was this weird summer camp where essentially the only thing you did for about 10 weeks was just start from scratch. Like truly start from like the basics of math, like axioms and prove your way all the way to like very interesting unintuitive results. In number theory,


Anna Rose (00:13:19):
You went to math camp.


Guillermo Angeris (00:13:21):
That's right. I went to math camp.


Anna Rose (00:13:22):
What is math camp?


Guillermo Angeris (00:13:23):
That that's that's this is a whole other topic that probably requires more sake. So maybe let's move back after, after we've drank a few of these, I guess.


Anna Rose (00:13:30):
Got it. Got it. Got it.


Guillermo Angeris (00:13:32):
So, but, but math camp is, is probably exactly as exciting as it sounds. Which is


Anna Rose (00:13:37):
I once went to yearbook camp, so, oh yeah. Equally bad.


Guillermo Angeris (00:13:41):
You'll, you're gonna have to define that one for me too. At some point.


Anna Rose (00:13:42):
It was a week long thing where people who did yearbooks got together to talk about the yearbook.


Guillermo Angeris (00:13:48):
Oh, that's exciting.


Anna Rose (00:13:49):
I mean, that's, that's a real thing. It existed for that moment in Canada. I don't know why. I don't know why I was there. I didn't, I wasn't even, I was like helping on the, I wasn't even like the main person I just happened to be there.


Guillermo Angeris (00:14:02):
That's amazing. Well, I mean, it's like, you know, your book connoisseurs, I guess everyone's gotta have a hobby, but anyway,


Anna Rose (00:14:06):
You went to math camp, so sorry. Okay. It sounds like a little bit more of a bonding experience. Math camp there's long. It was longer. You actually, it was longer. Yeah. I mean, that's actually a kind of a cool exercise to get kids to go from, I guess, first principles ish that's right. Or whatever, building blocks, really basic building blocks to show them how it works.


Guillermo Angeris (00:14:24):
Yeah.


Anna Rose (00:14:24):
So, so, or even get them to show the teachers how it works it's yes. Is that how it was?


Guillermo Angeris (00:14:29):
That's roughly it, yeah. Okay. So, so you, you really do like start from like nothing. So you start from the axioms of the integers. This is kind of, I think a lot of number theory courses in college might be taught this way. Not often, actually, not as complete as this, because this was like very focused and we're kind of doing it 24/7 as opposed to, you know, for a few hours a day. But it was weird because in a lot of ways it destroyed the, you know, my preconceptions about what math was. Right. And in many ways, like writing produces a shockingly creative endeavor. Mm. It's not very mechanical. It's, there's often a lot of tricks that are involved. You require a lot of insight. Hmm. 


Anna Rose (00:15:10):
It's not technique?


Guillermo Angeris (00:15:12):
It's actually not. Okay. So, so, so math kind of in, in this let's, let's call it this incarnation of, of math. You know, there's, there's the math that you're taught where you, you learn how to add and multiply and divide. And that's like, those are, those are what one might call algorithms. Right? You, you follow a sequence of steps, you get some result and you better hope that your result is right, because that's what the test is checking you on. Then there's kind of this, you know, maybe also naive in some ways, but more nuanced notion of math that it's like, you are building this repository of knowledge and you are doing so by, you know, you start from everything that you, you know, to be true of these axioms. Maybe you don't know them to be true, but you certainly assume them to be true. And from there you can build this, this library of results. Right. You can start developing like what it means to, you know, can you show, for example, that the zero in a integer is unique. Could there be more than one, zero that's one, or


Anna Rose (00:16:12):
Were you in this case, like making proofs that's right. To prove that that's right. That there is only one?


Guillermo Angeris (00:16:17):
There's only one zero, another one that's, that's a classic. That's actually very interesting is how do you prove that zero times a number is equal to zero. That's something you have to prove it's kind of intuitive, right? And you're kind of taking zero of something and that's equal to zero, but that's not a proof.


Anna Rose (00:16:33):
That's interesting though, that you say it's creative. I guess I learned proofs very much as following. Maybe it's because I was seeing proofs being written. I wasn't necessarily making them myself, like I would see, like, what is a proof? You kind of go through these logical patterns, right. Until you, you know, this equals this and then you kind of break it down into other things and then you come back to it. That's right. And you somehow like, come back at the end and be like, be, and so, like we said, at the beginning, this equals this that's right. In my math experience, I feel like even though I was really strong in math and I enjoyed it for me, it was just sort of puzzle games. Right. I didn't, I don't think of it as, it's not, it's not that I wasn't creative, but I feel like a lot of the math education would've been a lot of memorization. And just like being able to use techniques. And if I was listening, if you understood it, it was like super easy. Yeah. I always just found math incredibly easy.


Guillermo Angeris (00:17:29):
So that's the thing. Yeah. So there's a lot of things to unpack at the very beginning. I agree. Right. And in some ways, as you're taught math, math is this kind of sequence of things you do. It gets you some solution, often a solution you want ideally, or hopefully, but at the end of the day, it's nothing more than kind of a repository of knowledge that you just draw from. You like apply it to your problem, turn a crank and out you get the thing you want. You know, you wanna solve a system of linear equations to know weirdly enough actually has a problem. I solved not too long ago, how much milk, 2% milk versus cream you should add in order to get whole milk. Right? It turns out the system of linear equations, although you can solve it in other ways, but we just set it up and solve it. And congratulations, you know, how much milk you need to add to cream to get, you know, the percentage of fat isn't whole milk. Yeah. this is one of the possibilities of how to think about math. But it's very, very, very different than I think how a lot of mathematicians even applied mathematicians or physicists, or even a lot of engineers think about math.


Anna Rose (00:18:29):
Actually, this starts to speak to like the interviews that I've been doing with people who are very, very much math focused, right. The way they talk about it is not the way I've ever understood math. Right. And I just to maybe finish my story on math is like, I did math up until like first or second year university. Linear algebra was the last proper math class I think I did in university. And


Guillermo Angeris (00:18:52):
That's a good one to do though, to be fair.


Anna Rose (00:18:53):
It's a good one to do, but it was like the way I did it was like I just had at the time a pretty good memory and I did well, but I didn't like it wasn't creative for me. Right. It was just like, I figured out the techniques I saw the test. I did the test, the test was good. That's right. It was not in a place like, even if it was doing proofs, it would've been proofs with like a lot of help, like the template basically that I was going through. So I never felt creative and probably because I didn't have that many techniques to draw from. Or something like that. But, but yeah. So for me, that's where math stops. Like that's my experience with it. And so I do wonder, like, so you're kind of saying, going back to your story, like throughout high school, you weren't into it. Right. You were probably good at it, but it wasn't like, not even


Guillermo Angeris (00:19:40):
I was, I was not bad at it.


Anna Rose (00:19:42):
Okay.


Guillermo Angeris (00:19:43):
But math is still consistently my low or has been, I guess at every test I've ever taken at math is actually my lowest score. Oh.


Anna Rose (00:19:50):
And yet


Guillermo Angeris (00:19:51):
And I mean, and yet I do math for a living I guess.


Anna Rose (00:19:54):
Oh, wow. Okay. Well then, but at what point does math switch over? What was it for you? Was it this camp where you felt like all of a sudden math wasn't pure technique being executed in this very like easily packaged way?


Guillermo Angeris (00:20:07):
I think in part, yes. I did understand math as also having interesting puzzles, I guess maybe the best way of dividing math kind of in the formulaic approach versus how maybe mathematicians think about math or mathematicians and people who actually do math all day, think about math, but we can get to that later. But the difference is maybe, you know, it's the difference between like a linear game where you have some puzzles to solve. This is kind of the formulaic approach. You know, you have a storyline, you go through the story, the story guides, you kind of hand holds you through a bunch of puzzles. And then congratulations, you know, at the end of the story, you get your reward. Which is an A, or whatever you like. And the latter approach. It's a little bit more like these weird open sandbox games, like Minecraft or something, you know, you can build something really cool, but it is up to you to do it. Mm. Right. And it requires solving kind of weird problems that you weren't expecting to come up at the beginning.


Anna Rose (00:21:07):
Are you and math though? Always looking, is it optimization? Like, is it basically the thing is using that metaphor of like the sandbox, like you could build something and it maybe does something kind of fun for you, but it's useless.


Guillermo Angeris (00:21:21):
Mm-Hmm,


Anna Rose (00:21:21):
Like, is that also happening there? Or is it like, it's only really what you're describing. If it's like optimizing something it's like making something faster, it's making something smoother. It's, it's achieving something.


Guillermo Angeris (00:21:33):
That's the difference. I would say there's a more nuanced difference between kind of pure mathematicians. And perhaps I don't, I dare say applied mathematicians, but you know, there's kind of a spectrum of, of how you view math as a tool versus as an art. Oh, wow. Right. Like, you know, everyone has their own daily variation of this, right. Some days you wake up and you're like, ah, I am an artist. I do math all day. And I, it is my canvas that I am painting on. And then some days you wake up and you're like, God, I just want this shit to work. And you know why it would work. It'd be great to work. Because like, if I solve this problem, I get $500,000 in arbitrage. Right there, there are, you know, and that is a spectrum in


Anna Rose (00:22:11):
Between. Right. Because like, couldn't it be like, I solve it and I feel good too. That's right.


Guillermo Angeris (00:22:14):
So, absolutely.


Anna Rose (00:22:15):
Or I get fame or you get fame or it gets used


Guillermo Angeris (00:22:18):
That's right. I mean, so, so I would say a lot of pure mathematicians do math, not because it's going to be used, but maybe you don't spend your entire life doing something. If the only thing you're chasing is fame.


Anna Rose (00:22:30):
Actually, what it almost sounds like is, and I hope we don't offend anyone in the audience here, but it almost sounds like the math as art for people to really do it, there probably is a prize. Sure. That the prize is not monetary. Yeah. It would probably be like some recognition in the scientific community. Or some like in deep, like pleasure, they're getting out of that. Like some joy, right. That like,


Anna Rose (00:22:52):
I think its some maybe mystery they're like, I wanna know if I can do this and they do that. And then it's really fun for them.


Guillermo Angeris (00:22:58):
That's right. So, so it's, I would say it's a lot of those things. So, so why is math interesting. Surely it's, you know, you, in a lot of ways, math is a video game that you're solving in your head all the time. Right? It's like, you know, the rules of the game and you, all you need is sometimes a sheet of paper, but often you just walk around, you know, the streets of Amsterdam, thinking about some math problem you've been thinking about and you just get to play it all the time. In a lot of ways, mathematicians are also drawn to math, weirdly enough. You know, we think of them as kind of isolated gremlin sitting somewhere. But, but in fact, actually I think a lot of people are drawn to math. Maybe not


Anna Rose (00:23:26):
Poor mathematicians.


Guillermo Angeris (00:23:27):
Sorry.


Anna Rose (00:23:27):
Who thinks of them in that way. I don't.


Guillermo Angeris (00:23:29):
You don't really? No. I don't believe it. Okay. Well I certainly do so. Okay. You do. Okay. But, but actually, so math is actually a, a very social activity.


Anna Rose (00:23:39):
Ah, it's a lot. I have, I mean, I have seen this in math departments, right. That there's often a whiteboard. Yeah. And a few people standing around it. That's right. Trying to solve something, going through the steps. Yep. Others like jotting down things on their desk. So I have seen that.


Guillermo Angeris (00:23:54):
So, but it, it is, it is inherently kind of, you know, you, don't, it's hard to do math, like truly do math and have like math, you know, TM as a thing just by yourself. Like there are people who do sit and figure out a proof or figure out an important problem by themselves. But at the end of the day, that problem is a little useful in so far as it is assimilated into math itself. And when I say useful, I don't mean useful in a very practical sense. I mean useful in like this social sense of mathematics. Like, you know, when you write a proof, you're not writing a proof to convince a computer, you're writing a proof to convince other humans that your proof is correct. And then inherently has a lot of interesting social dynamics about it. But also generally also it's a social act, right?


Guillermo Angeris (00:24:39):
You solve problems with people and you solve problems that are interesting to you and people as well. Right. And there's things that are fashionable and drop out of fashion in math as well. And that's, that's not an accident, right. In a lot of ways, like no one, you know, we like to think of the lone genius toiling away, which is true. I mean, there's certainly are like brilliant geniuses that pushed the field. But at the end of the day, they push the field in so far as other people see it as useful and interesting. Huh?


Anna Rose (00:25:05):
What about the history of some of these mathematicians though? Like if you do go back, especially like maybe during the time of like intense religiosity where like, it was kind of a bit of a dark art to play with this kind of thing. I mean, often it was like in astrology and sorry. Right, right. Sorry. Actually it was in astronomy is where it's actually coming from


Guillermo Angeris (00:25:25):
And astrology actually weirdly. Oh


Anna Rose (00:25:26):
Really? Yeah. What were they doing?


Guillermo Angeris (00:25:30):
So...


Anna Rose (00:25:31):
Cause they were like being bad actually.


Guillermo Angeris (00:25:34):
Well, I actually don't know if they were necessarily actively being bad. Right. A lot of math in the, you know, so-called dark ages was done by priests and monasteries. Right. For example, a very famous result from, I, I believe it's the 11 hundreds or the 13 hundreds is the fact that the sum of the reciprocals of the natural numbers. So one plus one over two plus one over three plus one over four, all the way infinity actually is not finite it in fact diverges. Hmm. And it's not obvious it, I mean, it's obvious of course you now ahead of time, but if you don't have modern algebra, it's really not obvious how to show this. And there's a lot of beautiful arguments. And so this was figured out by some monk actually originally another one that's very famous a little bit later was a solution to the cubic so we can solve quadratic pretty easily. But the cubic, when you have you know, X3 plus I guess BX plus a equal zero, that's the depressed cubic, I think you can solve that and you can write down a close form solution for it. It's rather complicated unfortunately, but you can do it. And that was also done by, by monks actually.


Anna Rose (00:26:41):
But was it accepted?


Guillermo Angeris (00:26:43):
I don't think it was, I mean, math had to be taught for them to be able to do this. Right. Yeah. So I don't think it was actively rejected in any sense that I know of, but it was certainly not common as far as I know.


Anna Rose (00:26:58):
Do you imagine at that time, I mean, obviously you're not a math historian. No, no necessarily, unfortunately, but, but even like going back to that idea of the socialness and the fact that you would have it as a collaborative thing, do you think maybe it is like a bit of a more modern idea to be doing math together? Like maybe it starts with like the printing press and I mean, it, maybe it starts, it probably starts earlier like library of Alexandria or something like that. But like, you know, once you could share these ideas, maybe not in the same room, but you're able to share it at least like in books. Yeah. And then later having academic settings where people could actually get together, cuz it just in those monasteries, like those examples still seem like sort of like odd bird, right? Like characters who just got really into something. Yeah. And I've never seen paintings of the, the monks and maybe it exists, but maybe there's paintings of the monks, like all, you know, doing that, doing math. Right. Maybe, maybe I am wrong. I don't wanna make that call one day. I should have a math historian on here. Yeah. That be fine. Set me. Right. So,


Guillermo Angeris (00:27:58):
So unfortunately, yeah, my, my problem with math history is that it's very easy to look and this is just history in general. It's very easy to look back at history with modern biases. I'm about to in approximately three seconds, the, you know, doing this. But but for example, Pythagoras right. Who probably did not actually figure out Pythagorean theorem, but someone else said like how to cult around math.


Anna Rose (00:28:19):
Oh wow.


Guillermo Angeris (00:28:20):
Like it was that, that was a thing,


Anna Rose (00:28:22):
But this is Alexandria.


Guillermo Angeris (00:28:23):
That's right. That's right. So, so you're absolutely right. So there was, there was no notion of


Anna Rose (00:28:26):
It's not the religiosity, like it's not the monks, right. That's right. That's right. It is bringing science up and like wanting to understand. Right.


Guillermo Angeris (00:28:34):
Yeah. But, but I think for a lot of history, you know, the, our modern preconception of math was a very social art. If I may, right. It is presenting results to other mathematicians and things like that. But yeah, perhaps in the past it was not the case. And in a lot of ways, math was very utilitarian. Right. You know, geometry was a particularly utilitarian it was interesting. Right. For example, you know, Euclid elements, don't always prove things that are immediately useful in practice. Like the fact that there are infinitely many primes, but in some ways, right. These things got written down for a reason and they got passed down for some reason. So it's hard for me to not assume that there was some amount of social context there. I, of course I, I'm also not a historian of math. I do like to read about the history of math, but I don't know much about it. Unfortunately.


Anna Rose (00:29:21):
I'm just realizing though, as we were talking about this, like why, like it was so driven early on by the stars. Yeah. I'm like, why wasn't another, like, there's so many physical things happening. Why that,


Guillermo Angeris (00:29:34):
I, I don't know,


Anna Rose (00:29:35):
Egypt loved the stars. Right. And all the smartest math minds or math things come from, or they seem to often come from that, like mapping stars and trying to figure out like how quickly something's moving and


Guillermo Angeris (00:29:48):
Yep. So Hmm. What some of it does have to do. I think I suspect with this astrology, not, not astronomy, although astronomy obviously is they're kind of very related up until relatively modern history. But I think some of it did have to do with, you know, these astrological notions, but also generally, right. What's really useful when you're sailing. The seas is the ability for you to be able to know where you are. Right. True. And how do you do that? Well, it's, you would expect to be yeah. Given the positions of certain stars, certain astronomical objects.


Anna Rose (00:30:18):
Right. So the minute it's the move to discover.


Guillermo Angeris (00:30:21):
So I think that's in part, I mean, of course this is later than I think maybe some of the time periods you're referring to. So I think that that one might be just more out of curiosity of the cosmos, right?And the same way that the infinite suit of primes is an interesting thing. One might wonder about the cosmos out there or whatever that meant to ancestors. I don't know. This is just a very much a conjecture. And in fact, I suspect that at least 50% of the things I'm saying here are like, not exactly correct.


Anna Rose (00:30:45):
I also wanna caveat at that


Anna Rose (00:30:47):
These are theories. These are the ideas. I wanna come back to what we were saying just before history, rabbit hole, like going back to that collaborative nature, I was trying to find examples in history of like it being solo. But you're saying like, especially today, this is not a solo activity. Right. It's actually incredibly social that's right. Let's kind of come back to that point.


Guillermo Angeris (00:31:07):
Yeah. Yeah. So, so when I, when I say social, I don't mean that all papers are published with someone else, although that is incredibly common. Of course. But I do mean that like math, as it develops is a social endeavor, right? You're only doing math. If you are talking to mathematicians in a lot of ways that sounds weird and elitist, but I, I do mean it in a very specific sens e of like, if you have a paper that's sitting somewhere in the shelf that no one's ever seen before and no one's ever read except you and maybe your mom


Anna Rose (00:31:35):
It's really useless.


Guillermo Angeris (00:31:36):
Yeah. It's really useless. Even if the result you proved is very interesting. It doesn't really do anything. And in particular one might not even call it math because in some sense it's not known or read or, or even can be interacted with wider community. Similarly, if you discover some extremely complicated, fancy new thing using your own standards and your own thing, that might be interesting to study as its own topic, but one might still not necessarily want to call it. You know, what, what we call the refined polished notion of modern math, right? It's maybe, maybe just a sparkling system of equations perhaps


Anna Rose (00:32:12):
There, it really does start to sound like art, right? Like the artist who never shows the thing that's right. Lives somewhere in a basement and maybe the house burns down and never gets shown it's it doesn't exist. That's right. In a weird way. That's right. That's right. I mean, it might have been fun to do, but


Guillermo Angeris (00:32:26):
Yeah. Yeah. Which is a, I mean, it's a perfectly valid thing, right? Yeah. You know, clearly some mathematicians have gone a little crazy. Right. the millennium prize winner for proving the Poincare conjecture was saying Perelman, right. Just like quit math. Essentially. He proved two very famous things in math, some of the biggest open problems and then was just like, I am never gonna do math again. So it was now like a potato farmer, I think, somewhere in Russia or something like that.


Anna Rose (00:32:53):
Probably still doing a little bit of math.


Guillermo Angeris (00:32:55):
You, you would think maybe. I mean, but honestly


Anna Rose (00:32:57):
The crops need some like careful every,


Guillermo Angeris (00:33:00):
Every once in a while,


Guillermo Angeris (00:33:01):
Just sneak in a paper there to, wouldn't surprise me.


Anna Rose (00:33:06):
Look, I kind of wanna go back to your story of math though. So you were talking about the spectrum of like, there is the very, very, you didn't say applied what's the opposite. It's the pure math and then you're getting more into the applied math. I kind of wanna even come back to crypto, like this is applied, I'm guessing, right? Yeah.


Guillermo Angeris (00:33:26):
Yeah. It is what some, some mathematicians might scoff at how applied it is in fact


Anna Rose (00:33:29):
Why, tell me why?


Guillermo Angeris (00:33:31):
No, I mean, it's, it's, it is usually a joke that mathematicians, you know, they, I think it's from SNBC but more generally it's an open joke of the math media. It's like, you know, someone used your results, a number theory to cure cancer and their pure mathematician yells. No


Anna Rose (00:33:47):
Why?


Guillermo Angeris (00:33:48):
But, but the, the joke, especially as like, you know, math is art, it is not,


Anna Rose (00:33:51):
They went mainstream. They've got picked up.


Guillermo Angeris (00:33:53):
That's right.


Anna Rose (00:33:54):
That's right. By the major labels. That's right. That's not what you want.


Guillermo Angeris (00:33:58):
That's not what you want. That is what


Anna Rose (00:33:59):
Is not, when you're an indie rock artist.


Guillermo Angeris (00:34:01):
That's right. You, you would know about that. Right. I believe about our


Anna Rose (00:34:03):
That's fine. That's where I draw my, my understanding of the pure maths.


Guillermo Angeris (00:34:08):
It's closer than you think. And I think most of us wanna admit. That's fine.


Anna Rose (00:34:12):
Wow. That's so interesting though. Do you think that actually prevents pure mathematicians from like making some of their work accessible because of fear of it being used?


Guillermo Angeris (00:34:24):
I it's more


Anna Rose (00:34:25):
In a way they don't want maybe.


Guillermo Angeris (00:34:27):
Yeah. So, so I guess there there's a few things there, but, but it's more of a joke in a lot of ways, right? Like I'm sure most mathematicians that do stuff that can actually be used for something would be happy to see it used for something ideally socially positive things. But you know, sometimes you can't control that, but more generally, or the problem is when you're talking about pure math, you're talking about a field that is so, so specific that often it takes you many years just to get to the boundary of the field. Like analytic number theory is one example of a particularly hairy math that people spend their entire PhD to write, to understand the state of the art and then write maybe one paper that pushes it just slightly. Hmm. Right. There's kind of, not really a lot of hope for accessibility there without kind of this mountain of requirements.


Anna Rose (00:35:12):
I kind of wanna talk, like, just thinking about this topic about language in math in that case, is it learning the vocabulary of the field that is so complicated or are the concepts so impossible to get into the human brain?


Guillermo Angeris (00:35:25):
Oh, I have a lot of thoughts about this. So, so I do think in the case of analytic number theory, that's a particularly difficult edge case. The concepts really are almost alien. A mathematician in this field would obviously say, oh, they're perfectly natural, but, but in fact they're not right. You know, there's many paradoxes in math that kind of come up and people understand them in some weird way, but they're not intuitive. Banach-Tosky is a particular example of this, right. Where it's like, you can take a sphere and decompose it into five different spheres, all of equal size. It's like not a thing that you can like touch or make sense of. It doesn't make any sense. Mm. Right. The base ideas are simple, but the language that's necessary to express them in that simplicity is very non-trivial right. In a lot of ways, it's, it's kind of like computer science, you, you build on abstraction and abstraction, abstraction abstraction until you get to a point where it, like everything kind of makes sense.


Guillermo Angeris (00:36:16):
The, the nice part about computer science is that, you know, most computer sciences don't know how a transistor works and that's perfectly fine because the abstractions are not necessarily easily leaky on the other hand in math, or for example, analytic number theory, or even more generally, not that I'm an analytic number theorist, by the way, just generally speaking. But this is a particularly hairy part of math, you know? And sometimes you do depend on the fact that these things are abstracted away, very many levels, but like the details really are important. Like the details of why something works just can't you can't simply say like, oh, I'm just gonna write some C code and like, not worry about like how my transistor works, because all of the things that you do depend fundamentally on this thing that has like very hairy requirements to work and you need to know them extremely well in order for your proof at the end of the day to work.


Anna Rose (00:37:04):
But don't you think right there, you're getting more into the applied part then?


Guillermo Angeris (00:37:08):
It's applied in the sense of like you're applying previous theorems, but I would say that's less applied math, I think is more regarding like connections to the real world. In some sense, rather than like applied as an applying, you know, previous theorems or things that people have developed prior. Okay. To further that field in itself, right. Much the same way that one can make derivative works of art that have no practical importance, but there are interesting derivative works of art. One does the same thing with, you know, number theory and analysis, things like that. It's like you're studying it now for its own sake and you're building on people's work, but you're not necessarily applying it to some other field that might be useful.


Anna Rose (00:37:47):
Now let's bring it back to the original topic. Oh my. Which is like your experience with cryptocurrency. Let's really let's. I just skipped, applied into yeah. Yeah. Silly art. Not even art. What do we call it? Gambling, gambling.


Guillermo Angeris (00:38:02):
Degenerate gambling. I might say in fact.


Anna Rose (00:38:03):
Okay. But let's go a little bit back to your story. Well, I think we stopped somewhere at high school and that's right. Not loving math and then math camp.


Guillermo Angeris (00:38:13):
That's right. And then I, I really didn't love math. Okay. After that for about a few months, cuz I was like, wow, this is, it is incredible and amazing. And it truly opened my eyes to, and I was like, this is utterly inane. Ooh. Why the hell would anyone do this for a living? I think it's beautiful. And I think it's interesting, but who the hell would ever do math for a living? That's what I got out of that camp.


Anna Rose (00:38:34):
How old were you?


Guillermo Angeris (00:38:36):
Shit. I was, sounds like a very teenage thought. That's right. That's right. I was about between 15 and 16 my guess.


Anna Rose (00:38:41):
Yeah. I would imagine that though. You probably just, your interests were elsewhere.


Guillermo Angeris (00:38:44):
Yeah. I was interested actually and for me it was the applications of math to topics. So physics and at the time I think it was more like quantum mechanics and quantum computing and that kind of, you know, that's what I found cool. I was like, I wanna learn math as a tool to like solve real problems. And to me, you know, proving whether zero time something is zero is not a real problem. TM.


Anna Rose (00:39:08):
Yeah. Well the probably fun exercise. Good for your mind.


Guillermo Angeris (00:39:11):
That's right. That's right. That's right. Was the sudoku puzzles.


Anna Rose (00:39:13):
It was maybe just too. It was like training. It's like healthy.


Guillermo Angeris (00:39:17):
Exactly. It's like eating your broccoli, eating your vegetables


Anna Rose (00:39:20):
A bit like that. Like you're supposed to do that. You that's right. You need to know. I'm sure it helped you, but where did you go after that? What was your direction? So, so you said you took a few months where you're like, eh, I don't wanna do this.


Guillermo Angeris (00:39:31):
Yeah. So after that I think, you know, I did see math as a tool and it did dawn on me. That math could be very beautiful and very interesting for its own sake. Although I was not interested in doing that. Yeah. So, so it, it became interesting because I started learning a lot of math. Cause I wanted to do things I wanted to, you know, do quantum mechanics and I wanted to learn like analysis because I thought that was a good thing to do.


Anna Rose (00:39:55):
Why did you wanna do quantum mechanics?


Guillermo Angeris (00:39:57):
So I was interested in quantum computing. Yeah. I was like, this thing is the future. Yes. But I don't understand any of it. People are telling me these weird things about like what's quantum computing is how it works. And like doesn't really make sense. Right? Like, you know, there's all these popular science articles, there's all these like cool, like interesting, you know, PBS like here is like these crazy experiments. Like, but none of it really made sense. And it turns out I would say no one really ever makes sense of quantum in a lot of ways like you do, you kinda just get used to its strangeness, but it's never intuitive. And so in order to do that, you need math. Like you need to, you can't


Anna Rose (00:40:38):
Can't see it. Yeah. You can't really understand it cuz it kind of doesn't make sense. Like your eyes wouldn't be able to perceive that that's right. As the most basic crazy thing is the quantum something like Schrodinger's cat, like two things are actually happening at the same time in parallel. And only the observation will like define one. Yeah. As being, being real. I like this is very poorly articulated.


Guillermo Angeris (00:41:00):
That's that's roughly the's


Anna Rose (00:41:02):
To the listener sake glass number three. That's right. Please give me some credit.


Guillermo Angeris (00:41:08):
Cheers to that.


Anna Rose (00:41:09):
Getting drunk and talking about math. This is, this is a good life.


Guillermo Angeris (00:41:12):
It's the only way to talk about math. One might say very nice. It's this idea. Strongest guy is this idea of like, you know, you connect quantum behavior, the behavior of like some particle that's decaying in some box to like global behavior, there's sort of this like large thing, behavior, large things. Here are things that don't really experience superposition. Right. And it's like, oh, you know, if the atom decays like the cat is dead, but we don't know if the Adam has decayed. So like is the cat like half dead and half alive


Anna Rose (00:41:41):
In, in that moment before, you know.


Guillermo Angeris (00:41:43):
Before you open the box, it's like, does that doesn't of course make any sense, fucking sense, sense.


Anna Rose (00:41:47):
It might be a bit like the billiard ball example for zero knowledge.


Guillermo Angeris (00:41:51):
I actually, I'm not do


Anna Rose (00:41:52):
You, this one, like the red and blue. I mean, it's just, it's basically just trying to simplify something,


Guillermo Angeris (00:41:57):
The magical color experiment,


Anna Rose (00:41:58):
Which, but then it's like so real life. Right. And although actually maybe in the, in the case of the ZK one, it's not, so


Guillermo Angeris (00:42:06):
This you pretty good. I, I think, I don't know. Maybe not.


Anna Rose (00:42:08):
Because it is a probabilistic thing. Like you're putting it behind your back. You're switching it a bunch of times. That's right. So actually, no, maybe that's not the same thing. I've heard that in other cases where you're like, you're just trying to, you're trying to explain. Yeah. And I mean, I'm trying to explain, we're all trying to explain and communicate also to people who aren't as deep in it. I'm actually very pro that. But I think in the case of the quantum stuff, it's so magical when you make it about a cat in a box that it's like, but if you look at what it actually is, it's like, isn't it like electrons heading like a piece of paper. There's like a thing, right? There's like an actual experiment.


Guillermo Angeris (00:42:44):
It's the double slit experiment.


Anna Rose (00:42:46):
Yes. I mean, that's the most basic one. Right. But it's like, it's not a cat in a box.


Guillermo Angeris (00:42:49):
That's right. That's right. That's right.


Anna Rose (00:42:50):
Because when you say it that way, it's like, it sounds nothing is real. Unless you can see it. Right. And that sounds like magic.


Guillermo Angeris (00:42:57):
That's right. That's right. That's right. Yeah. Although some people would have thoughts about whether things are real, unless you can see them, by the way, you should be very careful on who you, who you ask.


Anna Rose (00:43:05):
What is it? Does a tree falling into the forest make any sound?


Guillermo Angeris (00:43:08):
Making sound. Yep. Yeah, yeah, exactly. So that's, that's the question


Anna Rose (00:43:12):
Perceiving. Yes, it does.


Guillermo Angeris (00:43:13):
<Laugh>


Anna Rose (00:43:14):
Because,


Guillermo Angeris (00:43:15):
So something about waves.


Anna Rose (00:43:16):
Airwaves are yeah, that's right. Sound waves are created. That's right. Period.


Guillermo Angeris (00:43:21):
But, but a sound, you know, have to be perceived in order to be anyway, but you could get down this whole philosophy, but apparently I don't know if this, the veracity of the story, but apparently the Schrödinger thing is actually at an academic shit post by Erwin Schrödinger.


Anna Rose (00:43:33):
It was a joke


Guillermo Angeris (00:43:34):
To explain how ridiculous he thought his own partial theory like seemed


Anna Rose (00:43:39):
Wow. Oh, that's cool.


Guillermo Angeris (00:43:41):
Right? Yeah. He was the one to derive Schrödinger equation and...


Anna Rose (00:43:43):
OG Twitter troll right there.


Guillermo Angeris (00:43:44):
That's right. That's right. There you go. I, I do wonder how many like classical results or things that we seem weird are just like complete shit posts. I suspect,


Anna Rose (00:43:51):
How funny. We just didn't have the same terminology. That's right. And everything was like in this very academic sense. So like the world would've seen it as like quite regal of course


Guillermo Angeris (00:44:01):
Was one does. I mean, I, I suspect that at some point someone's gonna read our tweets or some papers or something. And by, by that, I mean your isn't mine. And actually think that we are being very serious for some god forsaken, reason or another


Anna Rose (00:44:13):
Wow. Well, I'm, I'm very bad on Twitter. You're very good on Twitter. You and Tarun are very good on Twitter.


Guillermo Angeris (00:44:19):
Good is a very interesting descriptor. I'm not sure I would use that.


Anna Rose (00:44:22):
You are very, you show personality. I've become an incredibly boring tweet person. <Laugh> I got put on a list recently where someone's like people you should follow and I'm like, why, I'm incredibly boring on Twitter.


Guillermo Angeris (00:44:36):
You're you? Yeah. We'll say yeah. About talking about the other day, right in real life for sure. But that sounds like something you could fix. I don't know.


Anna Rose (00:44:42):
Should I?


Guillermo Angeris (00:44:43):
No, actually, maybe not actually. It's probably better for your health to not. Yeah. I think


Anna Rose (00:44:47):
Anyway, Back to math. Right? Okay. So quantum, right. Actually we don't have to dwell on the quantum. I think the point here is you were exploring a lot of things and all of a sudden math mattered that's right. That's right. Math. So continue on this


Guillermo Angeris (00:45:02):
Story. So yeah, because, because of this whole notion of quantum math did seem interesting. But, but again, as a tool, as an operational tool and, and this kind of continues certainly through undergrad a little bit, there's certain fields in math that you can say very powerful things with very little, you know, there's not really a lot of complexity and this idea of simplicity, like using very clear definitions, thinking very clearly about problems, appeal to me like math, not as a tool to do things, also not math as an art, but math as a way of clarifying thinking was a really, really interesting idea that I hadn't really thought of or come up with. And until I started doing some, some work in optimization theory and a little bit in physics as well, it was just shocking kind of, you know, much of the same way that people say, like, if you want to clarify your thoughts, write them down.


Guillermo Angeris (00:45:58):
Yeah. I think a lot of ways it's the same it's and this is not universally helps you. Sometimes math is used to completely obscure stuff. And certainly in, you know, these parts of Twitter perhaps, or, you know, the parts that we frequent math can be used as very much as a, as a curtain to obscure things. But, but math is a very powerful tool to clarify exactly what model you're using, how it's being used, where it breaks down is a fascinating thing. Yeah. And I think that's kind of what drew me back to studying it in more of an applied sense. If you ask physicists what I'm doing is theory. And if you ask mathematicians, what I'm doing is just utterly applied. But


Anna Rose (00:46:35):
Can you say again, I remember we did talk about this on a previous episode, the, I wanna say convex something, theory,


Guillermo Angeris (00:46:42):
Analysis,


Anna Rose (00:46:43):
Convex analysis theory, that's


Guillermo Angeris (00:46:45):
The just convex analysis or convex theory. Yeah.


Anna Rose (00:46:46):
Okay. But that's the sort of field that's right. That's right. And I do remember we, we talked about like what that meant. Right. But are you saying right now that like, that there's a judgment on this type of math?


Guillermo Angeris (00:46:56):
There is in a lot of ways. Yeah. So because my work was kind of in between math and physics, it's a funny thing. Right. Because the second year math kind of touches some real application in a very concrete way. It becomes very applied. But people who are in that field that you are applying math to often see math as being just purely theoretical of being like, oh yeah. It's just like a, the thing you're doing. And it's interesting, but it's you know, it's fine. It's just, you know, until you can show me exactly the problem I wanted to solve, it's interesting as like a thing, but it is not necessarily, you know, what one might call like an important or like immediately useful result. Hmm.


Anna Rose (00:47:39):
Do you see almost like parallel here to like an engineer and a researcher?


Guillermo Angeris (00:47:43):
That's right. I think, I think in a lot of ways, the parallel is very, very similar, right? It's like the engineer probably. I mean, depending on which year and which researcher, of course, but on average, perhaps engineers see researchers as like working with their own toy models and vice versa, you know, researchers might see engineers


Anna Rose (00:47:59):
Like, and those researchers who are actually working on the applied part, that's right by their peers would be seen as very applied.


Guillermo Angeris (00:48:05):
That's right. That's right. That's right. Exactly.


Anna Rose (00:48:07):
So, okay. So now we can, I think, bring it back. I know I tried earlier, but like now I think we can bring it back to your knowing Tarun getting pulled into these problems. Right. It sounds like your early experience of any crypto is kind of just like varying, like I wanna play with this thing for a second, and then you were kind of bored, but you stopped being bored at some point. Like it started to actually be relevant to you. Yeah. You started working on these papers. You could actually use some of the work that you were doing. That's right on these papers. I have a question right before we go into that though. What's your thoughts on like the trading world? Like cuz high frequency trading also does cool math stuff.


Guillermo Angeris (00:48:45):
That's right. They do. In fact, a lot good amount of my friends go and work for high frequency trading.


Anna Rose (00:48:49):
Would you, could you have seen yourself going that way


Guillermo Angeris (00:48:52):
For a while, I did. Cuz I was like, what's the easiest way of getting to retire and do my favorite thing. It's go work at some high frequency trading firm, you know, deal with the shittiness for whatever five years or isn't


Anna Rose (00:49:04):
That kind of sad. So it is sad in retrospect, like it's kind of that story of like, you're gonna pay your dues in some job you hate just to make a lot of money and therefore, and then you would be able to do something after, you know, what such the myth of that is always. I think people do not understand how much that changes you. That's fair. Yeah. Like that experience if you really are in it really in it changes people. Yeah. It can burn people out. It can change your values, it changes your friends. There's an impact to those choices. And I think a lot of people see it, the shiny they think I'll get through it, but they're often so young when they're making that decision, they are not like fully formed and like shit's gonna impact you.


Guillermo Angeris (00:49:48):
Yeah. Yeah. It's true to me. I saw it as like the option. Yeah. You know, as going in as like a person who knows a lot of optimization theory. Yeah. And a lot of math and I can go and I know pretty concretely actually pretty much exactly what I would be working on. And then there was a very easy path. Had I, you know, sticking with it, to like making reasonable amounts of money and then being like fucking off and retiring, you know, at the point within the next 10 years or so


Anna Rose (00:50:15):
The choice you took was like that's right. I'm well, I mean, it seems like it just kind of happened like you all of a sudden had this other path and now yeah. The math that you work on, is it, is it similar to what one would do in high frequency trading? Yes.


Guillermo Angeris (00:50:33):
In a lot of ways it's very, very similar.


Anna Rose (00:50:34):
And yet I'm a hundred percent sure that the style in which you're creating this stuff and communicating this stuff is so, so different. That's right.


Guillermo Angeris (00:50:43):
So the idea of, I mean, convex optimization, general optimization theory in general is like very, very, very common. In fact, one might say it's the bread and butter of a lot of the, you know, kind of high frequency trading portfolio rebalancing, things like that. There might not be exactly convex, but often you solve convex versions of these problems as approximations to the real thing. So in a lot of ways the, you know, the overarching field is very useful, but the, yeah, the style, the thinking, you know, writing papers, all of that is very, very different. That's not really something you would do in trading, unless, unless you were doing something like, like my advisor does Steven Boyd, who, you know, he is like the head of the AI lab and, but he's still a professor and he's still, his purpose is mostly to us as a inhouse consultant, but also to write interesting papers based on things he's discovered and things like that, which he continues to do. But as someone, you know, as a quant or something like that, it would be very, very different. Yes. Than here. It would certainly not be anywhere as open. I would not be putting, you know, papers up on archive and things like that.


Anna Rose (00:51:47):
Are you happy that you didn't end up a quant?


Guillermo Angeris (00:51:49):
Yes. I'm happy that I ended up a lot of things to be fair, but certainly that's, that's that's one I'm particularly happy about.


Anna Rose (00:51:56):
Do you think you could have been happy there in the math?


Guillermo Angeris (00:52:00):
Yeah. In some ways I think I could have been happy in some ways I,


Anna Rose (00:52:04):
I almost feel like I should have this interview also with Tarun who did do that,


Guillermo Angeris (00:52:08):
Who did do that? That's right. You should definitely ask about


Anna Rose (00:52:10):
It. I have had a few interviews with Tarun before he was starting to cohost and I know a lot of his story, but it might be fun to talk to him about that role cuz I don't think I've ever actually explored it.


Guillermo Angeris (00:52:21):
So I, well, I was say Tarun's probably might, might be cringing a little bit at, at some of the stuff that I'm saying about trading, which is might, might or might not be as close to as experience, you know, but generally speaking. Yeah. I don't know. I'm also curious about Tarun's story and in that I've heard a little bit of it of course, but


Anna Rose (00:52:35):
We'll keep that for the next one. Yeah. Probably pick a different alcohol, but maybe a different location. Right. We'll we'll get Tarun to do something like this too. Actually. I mean, even having this conversation is making me think it would be really fun to explore a little bit more of the, like the, I mean one's interest in math and what they're doing with it. Yep. Just in general, I kind of wanna bring it back just to math. I mean we've focused mostly today on like your story, but let's talk a little bit about why do math like generally, like I think we've now we've kind of mapped out a little bit of like there's pure, there's applied. We talked about the monks who maybe were really like, just keen on it, but maybe to, to listeners, like especially listeners who might be right now thinking about what to do next. Why do math?


Guillermo Angeris (00:53:26):
Well, the easiest and obvious and silly answer is it's fun. Okay. Right. That's I described it earlier as a video game. It's fun.


Anna Rose (00:53:35):
Math is fun from the person who went to math camp. That's


Guillermo Angeris (00:53:37):
Right. For the person who went to math camp, who would've, who would, who would've thought shocked.


Anna Rose (00:53:41):
Very good. Really, very good. You are a PSA right now. It's fantastic.


Guillermo Angeris (00:53:45):
That's right. That's right. Here being like, you know, to the people of the nation nation to those know something that's right. That's right.


Anna Rose (00:53:50):
Who what was actually, no, there's a star.


Guillermo Angeris (00:53:51):
What it's the more, you know,


Anna Rose (00:53:52):
The more, you know, the more, you know, sorry.


Guillermo Angeris (00:53:54):
<Laugh>


Guillermo Angeris (00:53:55):
Okay. So, so I think I have this shitty joke that I think more kids would learn math if they were told at a young age that it's really a video game, you get to play in your head all the time and nobody can stop you. Wow. Right. I mean, so here it is, right. You have a fixed set of rules. You wanna get to some objective. Yeah. You wanna solve some problem or you wanna prove something often. It's I think proving is, is to me the most interesting part, not just an objective and what do you have to do to get there? You have no idea, but you have these rules and you have to put the rules together in some way that makes sense and gives you the result. And often there's some crazy insight. There are many ways of getting such an insight, but there is some crazy insight that gets you there. You know that like you go pretty much all the way there. And you're like, crap. Like there is something that isn't quite clicking and then clicks and it's like, you solve the cool puzzle that you've been like, that has been torturing you for weeks, you know, or whatever. It's, you know, in many ways it's a video game on hard mode perhaps. Right. You often don't spend many weeks on a single level or something and if you do, I'm so sorry


Anna Rose (00:54:59):
And there's no colors and that's right.


Guillermo Angeris (00:55:01):
Yeah. Well, there can be colors if you're, if you're very creative about it, but you know, I, I'm not, so. Okay. yeah. So there's a whole thing about whether


Anna Rose (00:55:09):
Yeah. People who can like see colors in math or that's right. They think of a math thing and then there's a color that I,


Guillermo Angeris (00:55:14):
Yeah. So, you know, some people have this isn't quite happened to me, but some people definitely have like this thing where different numbers feel different. Wow. And like things look, prime will feel a certain way and things like that. I unfortunately don't have this. I actually, for me, weirdly enough, math is very like purely visual in my head. It's like a white board that I write down. Okay. And a little bit of verbal, but some people have purely visual. Some people have purely verbal. Some people have neat. Some people are like, I can't even like look at an equation. Like it's just pure geometry. Some are like, it feels weird. I'm sure there's someone who's like, oh, it tastes like ripe blueberries in, you know, like, I don't know. Weird, but I'm sure it exists. Right. Okay. It's weird. It's weird to say that you experience math in different ways, but very literally, also not very literally generally too, but, but yeah. Yeah. Getting back to that. So why do math? I think the biggest reason is because it is fucking fun. It is really fun. It is really interesting. And to me, and kind of, you know, more generally the second order reason is you get to work with like cool people to solve a problem together. And when you do solve a problem, it is extremely satisfying. Wow.


Guillermo Angeris (00:56:18):
Right. I mean that's


Anna Rose (00:56:19):
But would it be different in physics?


Guillermo Angeris (00:56:21):
No. I think people do physics for roughly the same reasons too. I mean physics,


Anna Rose (00:56:25):
But what is the nuance there of the collaborativeness?


Guillermo Angeris (00:56:27):
What do you mean by the nuance?


Anna Rose (00:56:28):
Well, think about it like in a physics problem, you are also getting together. I guess it depends also if you're pure or applied, but


Guillermo Angeris (00:56:35):
That's right.


Anna Rose (00:56:36):
Say it's somewhere in the middle. I don't know. It's always a little more applied. Yeah. Yeah. You're I agree that you're kind of dealing with something in the physical world. Yeah. So you like a group of people getting together to do physics would be a lot of fun I can imagine. But what is maybe unique about the math part? If you can think of it. I know you haven't necessarily lived in the physics part, but


Guillermo Angeris (00:56:58):
Well, I technically my PhD was in physics, so oh,


Anna Rose (00:57:02):
Excuse me. Excuse me.


Guillermo Angeris (00:57:03):
That's right. That's right. That's right. Sorry.


Anna Rose (00:57:04):
Then you can absolutely


Guillermo Angeris (00:57:06):
Take on that. I physicist would, would tell me I did math and mathematicians on me in physics, but, but you know, I understand. No, don't worry. No, no. I mean, I think it's the same reason actually. So math, it also depends, right? Like there is a lot of math to physics and sometimes the physics and the hard parts and the communal parts are figuring out the math. This is certainly true in the step. For example, in my PhD thesis. Right. I got together with people who I was like, here is a physics problem. It turns out to be a math problem at the end of the day, but it is physics. But vice versa as well, right? Like often, you know, you're trying to come up with some crazy mechanism to do X, right. And you know that you have these like things you can put together, these like devices or these like, you know, processes or whatever it is in physics.


Guillermo Angeris (00:57:46):
Talk specifically about photonics, right? There's like certain manufacturing processes you can do. And then there's the question of like, I wanna build a specific thing and I have these manufacturing, you know, these specific processes I can do. Right. Like how do I put them together to build a thing I want? Right. That's one classic question that pops up a lot is like, I wanna build these micro ring resonators. Right. But I want them on this like very, very small thing. And I want this particular material that's really hard to work with. And I know this material has like certain things that I can do. I can etch in particular ways I can. So, and the question of course then is, you know, how do I do that? And that, that is another puzzle to solve in a lot of ways.


Anna Rose (00:58:23):
Sure. But do you think, I mean, actually in physics, in that regard, is it more like, are you must, you then rely much more on computer processing cuz there's like, just there's elements of that. That one could never hold in their mind at this point, like materials and like it's just too many factors. Yeah. Or do you actually think that like maybe math is also at that level?


Guillermo Angeris (00:58:47):
This is actually a super interesting question I've been thinking about lately, but I think a lot of the way we work right now is we work on simplified models, then later test for assumptions. Right. Okay. And like often simplified models are close enough to correct that it's fine.


Anna Rose (00:59:00):
To be able to figure out yourself that's kind of that's right. That's right. Or at least comprehend yourself.


Guillermo Angeris (00:59:05):
Yeah. Even if, you know, the model is leaky, it's often good enough to get you to an answer. The question of computation and math actually is very, very interesting. So I guess for a little bit of context, one way of looking at the thesis that I did was essentially automated theorem proofing is one way to think about it is in the specific case that I was working on is you wanna maximize the efficiency of the device and you wanna say certain efficiencies are impossible. There is no device that could ever be more than for example, 90% efficient in a lot of ways. It's a, that's theorem right. There's I have a device. This device satisfies some physics equations, right? And then immediately what you have from that is you can try to put these equations together in interesting ways to tell you something that, you know, for example, maybe you cannot achieve 90% efficiency, right?


Guillermo Angeris (00:59:51):
Like maybe you can achieve 88% efficiency, but you cannot ever by kind of combining these equations that the device must satisfy. You can show that you can never achieve 90% efficiency. So actually what the thesis is is this weird idea that instead of having a human try to put these equations together in some interesting or important way, why not just feed the problem to a computer and have the computer essentially automatically prove a theorum that says, if you put these equations together in this very specific way, I can prove to you human, That in fact there exists no device that will ever do better than 90% efficiency on the task you've given me. And that is in many ways a proof, right? So this is, this is the question of when does computation intersect with math and there's a slow, but mature move and some mathematicians are very not happy about this.


Anna Rose (01:00:40):
I'm also making a face, as you say this, I'm like, that's right. It scares me a little bit. What you're going on. Yeah. Okay.


Guillermo Angeris (01:00:45):
That's right. That's right. So it, it is very weird, right? Because a lot of mathematicians and certainly the current modern notion of mathematics and by the way, this has shifted through the years. But the certain current of mathematics is that you do math to have an insight to like truly deeply understand, you know, the mechanics of a proof, but you might imagine in some future, and this is a very minority opinion in math here. So, you know, I will probably be shunned for this, but you can imagine future that, you know 


Anna Rose (01:01:15):
You feed it in.


Guillermo Angeris (01:01:15):
Yeah. You're just like at a certain, you're at a certain point in your proof, it's simple enough. You say, I know a computer, we solve this. Instead of me, I'm gonna go put it into a computer. I'm gonna press enter. And then the computer fills in the rest of the steps. Right. And the rest of the steps don't have to be simple things, but


Anna Rose (01:01:30):
Actually the way you just said that doesn't sound that if it's just filling in the steps, that's one thing that's right. But I think there's a scarier part of that. Or like, I shouldn't say scary a more


Guillermo Angeris (01:01:39):
Scary, I think is fine.


Anna Rose (01:01:41):
It's scary because I mean, basically living in the space that I've been in for a while, this sense of like open source, being able to prove yourself, being able to like verify da, da, da, da, what it starts to be almost like black box AI.


Guillermo Angeris (01:01:54):
Uhhuh,


Anna Rose (01:01:55):
You don't can the human mind or in one lifetime, would you be able to actually go through such proof? Can one person prove that that was proven correctly. So, and that is where it becomes a, a little bit scary. It sort of undermines that idea of like, if we can prove it, then it's provable that's right. And then we trust it. That's right.


Guillermo Angeris (01:02:17):
So, and


Anna Rose (01:02:17):
We in this is human mind, right? Not outsourced to a computer.


Guillermo Angeris (01:02:23):
Well, so, so here's the deal. I can guarantee you that the bridges that are being built nowadays are not proven by a human mind to, you know, stay upright.


Anna Rose (01:02:33):
When you say bridges, do you mean bridges?


Guillermo Angeris (01:02:34):
I mean literal


Anna Rose (01:02:35):
Like a bridge, not like a bridge crypto bridges. No,


Guillermo Angeris (01:02:38):
No, not crypto bridges. Sorry. Sorry. Yeah. I was like a literal suspension bridge.


Anna Rose (01:02:41):
Are you who is going under the bus?


Guillermo Angeris (01:02:43):
That's right. That's right. That's right.


Anna Rose (01:02:47):
OK. Okay. Sorry. Literal bridges. Like


Guillermo Angeris (01:02:49):
Yeah. You trust the simulation. Yes. To correctly tell you that the bridge is gonna stand. I mean, no, no one person like surely people do look at it, right? Yes. And verify that need the things make sense and stuff. But at the end of the day, we are relying on computers yeah. To simulate things, to make sure they


Anna Rose (01:03:04):
And I guess stand and guess what we could have is like, you could have human brains verify pieces. That's right. Of these models. That's right. And that the data's been inputted correctly and,


Guillermo Angeris (01:03:14):
That's right. And I'll,


Anna Rose (01:03:15):
But the outcomes are on a 99.9%, whatever, like very safe.


Guillermo Angeris (01:03:20):
That's right. That's right. That's right. Okay. And you're, you're within a, you know, safety factor of 10 or five or whatever it is. But at the end of the day, right. You're still trusting a computer, which was also programmed by people by the way. And that's the scary part. Yeah. But you can run that. I mean, you technically, like I could take a file. I could run it on my computer and verify that indeed their results were correct. And I could, even if I wanted to, I could write my own opensource for software, which confirms the, you know, there's often a lot of standards for software, but you know, could conform to some notion of a standard for simulations. Yeah. And indeed verifies this thing. It's the same thing with math and math is kind of weird because people see it as this art of like understanding truly the proofs. But


Anna Rose (01:04:01):
There is a simulation factor, I guess


Guillermo Angeris (01:04:03):
There is. And there could be right. Certainly there's no reason why not.


Anna Rose (01:04:06):
But there, I mean, in pure math, going back to that spectrum, like right now, is there the use of simulation or is it mostly actually still being held within a human brain articulated by one human? Oh


Guillermo Angeris (01:04:18):
No, no. There's the use of,


Anna Rose (01:04:19):
Or like maybe a group of humans, but still human brains.


Guillermo Angeris (01:04:22):
So there's the use of just pure computation to solve proof. So for example, a very, very famous example is the four-color theorem. So the four-color theorem says that you cannot color a 2d map, or you can color every 2d map with four colors using only four different colors, such that no two, no two regions of the map that are adjacent share a single color. This is that's the four-color theorem. I mean, essentially just as you can color a map with four colors and no, no two states or whatever regions will ever share a given color. So that actual theorem, no one knows how to prove it, except by the use of reducing the true problem to about, or a few million cases, a finite number of cases and just checking all of 'em in a computer,


Anna Rose (01:05:03):
That's the unsolvable by human brain.


Guillermo Angeris (01:05:05):
That's right. So, so it's, it's not clear and right. No one has no one has yet to come up with a proof that does not require computation. There are similarly other problems, mostly in sphere packing that. In fact there exists no like handwritten proof, the proof is an algorithm at the end of the day. Wow. The proof is literally here is an algorithm that correctly computes the quantity I want. And that is the proof. I mean, the proof is run this algorithm check verifies algorithm is correct. And run this algorithm on a computer, but technically a mathematician could run it by hand, but there's no need for that. Right.


Anna Rose (01:05:39):
Can you, I mean, you do get into this question of like, as much as I'm going, like, oh my gosh. But it's like, are humans really that correct? Anyway, that's right. That's right. Like have we always been right? No,


Guillermo Angeris (01:05:50):
That's right. And in fact like,


Anna Rose (01:05:50):
Yeah. I mean, part of me goes like, this is scary. It's getting like outside of definitely like human control


Guillermo Angeris (01:05:57):
In some sense, perhaps


Anna Rose (01:05:58):
Right. Because you're like, it becomes something that like, we can't fix this by hand if we have to


Guillermo Angeris (01:06:06):
That's right.


Anna Rose (01:06:07):
If we rely on it, if that became something that was relied on, maybe more applied than, I don't know how or why or whatever. Right. But like maybe not that case, but some other case where it's like, it's built more through simulation. Sure. Yeah. Yeah. And then it's relied upon for applied something or other, right. Then if there's a failure, you can't go back in as a human.


Guillermo Angeris (01:06:31):
Right. But, but then there was either a failure in the algorithm or a failure in the implementation. Right.


Anna Rose (01:06:35):
So you would check that


Guillermo Angeris (01:06:37):
That's right. But at the end of the day, we rely on these things. We rely on computation all the time. Right? Like pure computation that like, no human is gonna solve a 10 million by 10 million matrix equation. But that's what you do every day when you're solving, you know, like basic flow problems. How do you, one example is how do you station wind turbines? Is that like, they're, you know, the weird chaotic effects of wind don't intersect, don't interfere with other turbines behind it. That's, I mean, that's a simulation. You can't really answer that. Similarly, I mean, you do this all the time with cars, right. And really pretty much any most physical processes. Like surely you can test them, you can build them and test them. And that's certainly what happens, but we rely on computer simulations and just computational aid to do pretty much everything nowadays.


Guillermo Angeris (01:07:22):
Like, so in some ways it's weird and scary. It's like, is it weird if you can't intuitively explain why something works? Is that a bad thing? And, and a lot of would say that, that in fact that is a, that is a terrible thing. You know, of course, I, I worked in a field where this is kind of the whole point, right. So I obviously have a slight bias, but I don't know if it's a bad thing. Right. Imagine if like you could verify the algorithm that essentially verifies something else for you. Right. If that skips hundreds of pages of steps of a proof


Anna Rose (01:07:58):
And all of the people you'd have to train to be able to do that. That's right. Understand it.


Guillermo Angeris (01:08:02):
Right. Then, is it worth it? I don't know. I mean, to me, the answer is kind of yes. For most. I mean, maybe not everything, but for most things, I think if you can reduce a proof to a set of computational questions, maybe it's not beautiful in a artistic sense in some ways, but I don't know. I think it has its own like share of beauty.


Anna Rose (01:08:21):
I have sort of one last question for today's interview


Guillermo Angeris (01:08:25):
Yeah. Yeah.


Anna Rose (01:08:26):
Poor Guillermo you're so jet lagged, we're talking about math and I'm asking you hard questions, but you're a trooper.


Guillermo Angeris (01:08:33):
That's great. Again, the sake. Thank you. Great idea. With the sake, by the way,


Anna Rose (01:08:37):
I think my last thought question here is very much on the use of math in the way that we're using it. And like


Guillermo Angeris (01:08:47):
We, as in crypto or zero knowledge world?


Anna Rose (01:08:48):
I mean, It's basically like this show. And a lot of the work I do is it's so tied to like math and academia and yet it's so exciting and fun, and there's a lot of academics kind of coming out of that world going, like, I'm gonna look over here and spend some time over in this part of the space, which goes against a lot of the traditions of like living a little bit cloistered excuse the throwback to the monks in, in academia. What I'm trying to figure out is like in bringing them out of this, I feel like we're in a way like accelerating it, like it's making it incredibly cool and fun and neat. Like you're hearing from those folks in a space that's booming and all these new people are arriving, but do you think there's also a side of this that is kind of like diluting the quality or almost like undermining a lot of the crystal palaces that have been created.


Guillermo Angeris (01:09:44):
So I mentioned before that math is kind of a social endeavor and, and I, I do mean that right. Like math is written to be understood. There's kind of two answers to the question that I have the first is no, I don't think it's anything. I think doing more math is very cool. Right. And like the more math you can do the cooler it is because that's the point,


Anna Rose (01:10:03):
But can you do bad math?


Guillermo Angeris (01:10:05):
What I do think, and this is kind of generally true, and this might sound a little bit, I don't wanna say elitist, but like kind of silly is that there are people who are very like smart and they're very good, but by not having kind of a, a certain training and I don't mean a certain pedigree as in like being like, oh, like you are from this fancy institution. I do mean like a certain training of like the language and like a certain notion of how to write and how to have like a specific clarity of thought. You can end up with these weird kind of things where you, you know, you can write a paper that isn't fully intelligible or like maybe doesn't prove what you think it proves, or maybe it doesn't prove what you wanna to prove. And that's hard, right? Like, I wouldn't say dilutes math in any way.


Guillermo Angeris (01:10:53):
I think math kind of stands on its own independent. And that's the whole thing of whether math is created or discovered as a whole other story. But I do think like, you know, on average, like people who kind of come out of the edifice, right. They've been post selected to be part of the edifice and therefore have this kind of social context of like, how do you explain math? And often, you know, how do you think through math? How do you like write it? How do you present it in a way that it can be understood? And I think it's true of any language. One might say is like, as an outsider, you might think you're like, you know, going through the motions. Right. Exactly. But it is very diff sometimes it's very, very difficult. Like there are certain details that appear as details, but are actually extremely important, for example, in explaining why a certain mechanism works or how to, how to perhaps, you know, compartmentalize certain parts of math.


Guillermo Angeris (01:11:47):
Hmm. And it's not to say that that can't be learned or like anything like that. But it is just like, there are certain kind of, you know, lessons you learn from kind of being knocked around many, many, many times, right. That like do involve you, like, you know, your first presentation as here as example, as a PhD student, again, I'm not a mathematician myself. And certainly, you know, people wanna call me a mathematician, but your first presentation is always like, kind of a failure, right. At the end of the day, like your professor is always gonna be like, or, you know, whoever you're working with will always be like, look, you explain this, but like, you've totally forgot to do like X, Y, and Z. And you're like, why the hell does anyone care? Like, that's kind of detail. It's like, no, no, that's really important.


Guillermo Angeris (01:12:27):
And then you go talk to other people who saw that and they're like, yeah, you kind of missed that. Like, that's really important detail, right? It's this thing that it's not a requirement. Right. But it is like at a certain point, you, you like accumulate these very small things that turn out to make presenting, writing, even understanding in a lot of ways. Cause I would say writing and presenting, clarify your own thoughts, you know, much easier for everyone else to understand. Right. And so this is, this is kind of where the crack pot, you know, all the way to the end goes in and where it's like, you know, it's very easy to also go all the way to the opposite side and be like, you know, no understands me because like you guys are in stuck in your own castle. Yes. And you don't wanna like learn the things that I'm teaching you, you know?


Anna Rose (01:13:12):
Or it's like, I don't wanna learn the language you want me to speak that's right. But yet my ideas are very, very good


Guillermo Angeris (01:13:17):
That's right. And so it goes both ways, right? Yeah. And certainly there are people who are very much in the castle and are like, you don't, you know, unless you know exactly how to speak our language, you are like will not be allowed in there's. The opposite case of like idea is, is, should be just based on their own merit. And like, but like, look, if I have to read a 10,000 word dictionary in order to understand, like even what you're talking about, like at a certain point, I have to, you know, there, there has to be some like for sure, you know, you have to cut your losses and similarly, the other way too,


Anna Rose (01:13:45):
I think the scariest part is even bringing in that computation side of things. Like once you start to outsource this, right. And then you have folks who maybe don't fully either understand or be able to express themselves using tools that have never been documented in that case. Right. An algorithm's not gonna understand that. Right. There's not, there's not gonna be the nuance of like, I mean maybe eventually, but for now there's no nuance of the language being similar to. Right. Right. I figure,


Guillermo Angeris (01:14:12):
I mean, in a lot of ways, the parallel can draw is like that people say you should write your own cryptos and exercise, but never roll your own crypto. Yeah. I would say it's the same, you know, vibe perhaps as the, maybe the closest term I'm trying to get to, you know, there are, there are certain things that are like really not obvious, right. Even if you have a really good idea, there are a lot of things that are really not obvious in order to make that idea work or to explain that idea or to do that. And certainly, you know, even though you might have a correct idea that is useful, it does not necessarily imply that the way you're doing it or the way you're explaining it or the way you're programming it is the right way. Right. There's a lot of thought that has been given to like standard crypto libraries, for example. And so in many ways, you know, like academics in some ways are, are a little bit right. And distrusting kind of like outsiders, I guess the best way is it is infinitely easier to generate bullshit than it is to refute it.


Anna Rose (01:15:00):
I know.


Guillermo Angeris (01:15:01):
Right. And that is really hard, but vice versa at the same time, it's like, it's also really easy to put up these stupid guidelines that are like, oh, you must like, blah, blah, blah. Use the right note. And like, I run to this all the time. Like as someone who literally does it,


Anna Rose (01:15:14):
Lived through it and went through, you have a PhD, you did it.


Guillermo Angeris (01:15:17):
That's right. But even so completed that's I have there, you know, I've had many academics. Tell me like your presentations too informal. Wow. I know I'm, I'm someone who, you know, knows the measure theory, someone comes and asks me, does your series converge the right value? And in fact, can you justify it by, you know, using the weak star topology? I'm like, yeah, I could tell you, but who gives a shit? Right.


Anna Rose (01:15:39):
Also, do you want an audience of one or do you want an audience of many's actually, there is an alternative, there's the flip side of this that I think we didn't mention yet, which is the use of math and math terminology and big math terminology as a weapon. That's right. Or as a obfuscation or as a status play. I see this all the time. So I would say this is because, and I've seen it since 2017. Right. But in 2017, when I started in this space, like, I didn't actually know that much about this space. So there was a lot that I couldn't fully read as correct or incorrect. It was just very, it was over my head. Yeah. I often had to rely on friends, people who had been in this space for a long time, who actually understood engineering a lot better than I would I'd show them something.


Anna Rose (01:16:22):
They'd be like, yeah, that's impossible. And they're not doing that. Right. Right. Right. And, and it's ridiculous. There's way those words don't exist in our space. Right. Other times they'd be like, it's possible. It's gonna be hard. Not sure that group will be able to do it, but early on it, it required a lot of like around and finding out what other people who had been in the space longer thought. But now, and I still don't think I'm on the engineering front able to vet stuff, but like, I am used to language more in our space. Right. And then I do see sometimes teams use language that looks really familiar to stuff that we talk about maybe on the show, but that isn't yeah, that's right. And then I'm the one who's going like, oh, interesting. Like sometimes it's like, it isn't, but it's interesting. But sometimes it's like, it isn't, but they're trying to use terms that most people won't understand in order to sell something that I don't think is what they're trying to sell that's right. Or they're just scammers. Yeah.


Guillermo Angeris (01:17:14):
Yeah, yeah. Absolutely.


Anna Rose (01:17:14):
And that's something it's also interesting to try to explain that to people who are joining the space now, because they're where I was at in 2017 where you're like, it looks really interesting and complicated and it says stuff that I think I've heard somewhere, maybe even on your show, but I don't know how that all fits together. And you're like, yeah, but that's also bullshit. Like sometimes it's bullshit. Sometimes it's actually malicious almost that's right. It's people who maybe know better or they're just, they're just literally like copy pasting stuff with words. Yeah. Yeah. It's branding. It's insane. It's marketing. Yeah. It's not real. That's right. And yeah, that's something, I think that's when I mentioned this diluting part, it's almost like undermining. Yes. Basically by bringing it into the, oh gosh, am I gonna say this? But like bringing it into the public's fear out of the ivory tower, right. Not even that the actual math gets misused or bad math gets created, but rather will, like all that has been constructed to explain itself to itself be muddled


Guillermo Angeris (01:18:18):
That's right. Yeah. Be like obfuscated with weird definitions. And it, this is absolutely true. And this is, this is where a lot of, you know, a word is useful in so far, it is defined correctly. And you know, there's, there's also weird things about that too, but that whole debate comes in too. Right. And kind of, it's a really difficult, tricky thing, right. Because language generally terminology ideas can be co-opted to do things that are not intentionally what they were supposed to do in initially. Right. And this is, this is true certainly with math and in particular, it's very, you know, a classic filter, right. It is less of a job of understanding and more of a job of defending, right? Like you have to have a heuristic for which you judge, you know, the enormous amount of bullshit that is coming at you at every point in time. And often the heuristic is simplistic and it's silly, but it works 90% of the time. And that's good enough. Right. And the heuristic often is are you using the right terminology in the right way? Right. And to some people, again, that will seem like


Anna Rose (01:19:26):
Elitist


Guillermo Angeris (01:19:27):
Elitist, and which is it's true. And it can be used in elitist way, unfortunately. Yeah. But similarly, you know, you're bombarded with like incredible amounts of bullshit all the time and you have to be able to filter it. You know, you can't take the time to understand every crackpot email that comes to you telling you, like, I have solved like X, Y, and Z problems, which are obviously like, not even often, they're not just unsolvable. Totally. They're like, not even problems. They're just like properties of the thing.


Anna Rose (01:19:54):
And the sad thing is one of those emails might actually do something that's right. Something really cool. That's and you might ignore it. So to me, the solution here is give tools to translate that's right. But like really what I spend time thinking about and working on is, is basically like bring people in yeah. To this space as well as you can. Yeah. Without the need for the formal education that's right. But like, get them in touch with people who do at least present some of this stuff. So that if say in that group of random ideas, there's like a great one that they don't like lose interest. Right. But rather like reframe it to be able to communicate it better. Yeah. To people who might be able to help them, like really bring it into a space that a lot of people could understand it. Yeah.


Guillermo Angeris (01:20:39):
That's kind of the only solution one might say. Yeah. at the end of the day, it's only a partial one because you know, of course there's always gonna be more stuff produced, but that is, I think the best anyone can hope to do right. Is like, it's not to purely, you know, gate keep or whatever. Yeah. But it's, it's purely like, you know, there is a thing that exists. There's a knowledge base that exists. There's a notion that exists as a community that exists since you can shout separately from the community and the community can shun you or whatever the hell or there's, you know, some nice, beautiful connection it too. Right. And it's not easy. It's really fucking hard when I actually say, you know, everyone has their own stupid norms. And like, whether those are good as all their story ego, there's egos, getting people are on


Anna Rose (01:21:22):
Tracks and they think of status in a certain way. And then someone achieves status in a different way. It's really confusing to people. Right. They get really angry. They've dedicated their whole lives. Yeah. Why is it different over there?


Guillermo Angeris (01:21:33):
Why, yeah. Like why would anyone say anything else? Or like, you know, and intrinsically the whole medium is a lossy medium. Right. It's, it's a medium where mistakes get made in communication. And sometimes people getting angry for stupid things that are actually completely irrelevant or things like that. And so that's, you know, at the end of the day, right. Like, you know, bringing it back to math, math is done by humans. And for humans. Right? Like you don't do math, if not for humans, like why do you do anything? I'm not for humans, but like, very generally, even like math is a, like I've said a social thing. Right. And you know, the best thing you can do to bring people into the space, I think is not necessarily like, you know, be like, oh, go develop your own ideas or whatever. It's very much like it's a community, your with us, yeah. Come with us. Like, let hang out,


Anna Rose (01:22:17):
Share thing, find ways to connect. That's right. Your ideas to our ideas.


Guillermo Angeris (01:22:21):
And that's the fun part. I would say that's one of the most fun parts of math. And so is like finding a community that is excited to, you know, listen to your hair-brained ideas, which like somehow people still do with mine. God forsaken reason or another, but like, you know, right.


Anna Rose (01:22:34):
Cause you're good at Twitter.


Guillermo Angeris (01:22:36):
Ah that's right. That must be it. I think that's what it is at the end of the day.


Anna Rose (01:22:38):
All right. I wanna say a big thank you to Tarun's alt for coming on the show.


Anna Rose (01:22:44):
Just kidding. Thank you Guillermo for this incredible conversation into, I mean, we went to places, there's a few things we didn't get a chance to talk about, which are like new ideas that you're actually working on that's right. But given that you are a repeat guest and I have a sense you will be on again soon.


Guillermo Angeris (01:23:00):
If you'll have me, at least


Anna Rose (01:23:00):
I think so.


Guillermo Angeris (01:23:03):
Careful what you signing yourself up for.


Anna Rose (01:23:04):
True. No promises or maybe next time. Maybe we can talk about what you're actually working on right now. That's much less fun. I think still. Yeah, I really appreciated this. It was cool.


Guillermo Angeris (01:23:18):
Thank you, by the way.


Anna Rose (01:23:20):
Thank you to the team at ZK podcast and to our listeners, thanks for listening.