Pioneer Park Podcast

The limits of human-derived mathematics with Jesse Michael Han


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Pioneer Park interviews Jesse Han, co-founder of Multi AI. Jesse discusses his background, experience at OpenAI, and his philosophy towards research. He draws inspiration from Alexander Grothendieck's philosophy of listening to the universe and arranging theories accordingly. He also talks about the differences between research and startup thinking, the potential for machines to inspire new algorithms, theories, and results in mathematics, and the use of language models and compute to reduce the risk of misaligned outputs. He believes that language models will become as cheap and accessible as microprocessors, and that the value will go to those who build the software and infrastructure to make them accessible to end users. He recommends that those looking to shift their career in the direction of deep learning and generative AI should work hard, find good mentors, and aim for something that will endure.

Transcript

Jesse Han

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[00:00:00]

Bryan Davis: Welcome to Pioneer Park. My name is Bryan Davis and this is John. Today we're interviewing Jesse Han. Jesse Han is the co-founder of Multi AI, an AI startup based in San Francisco. He holds a PhD in mathematics from the University of Pittsburgh, and previously worked as a research scientist at OpenAI.

I know Jesse through working for Multi, for a few weeks last year, in which I was helping out with some of their product launches. And was thrilled to invite Jesse to talk a little bit more depth about his background, his experience at OpenAI and Multi as it goes forward. Welcome, Jesse.

Jesse Han: Thanks for having me on the podcast, guys. Thrilled to be here.

Alexander Grothendieck

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John McDonnell: Yeah. So Jesse, like I wanted to start this off by asking about on your personal webpage you have a picture of you looking up like very thoughtfully at this picture of Alexander Grothendieck. So I was curious what that picture means to you.

Jesse Han: What that picture means to me. So I just thought that picture of him was really funny, [00:01:00] Because it's like this shrine. So for context, that hangs in Tong Long University in Vietnam, which was founded by one of the students that he mentored when he visited Vietnam during his career. And this was during a time that Vietnam was being bombed and he wrote some, like very moving recollections about how he would teach at the university.

And then they would all have to dive into an air rate shelter and they would come out and one of the mathematicians had been like, hit by the bombs. And , that student became a very prominent mathematician in Vietnam, and he had such a lasting influence that they made this, the shine and honor of him. There's this nine foot tall portrait of him there. And I just thought it would be funny to kinda like Adam and God .

But the other thing is that I take a lot of inspiration from his philosophy towards research. There's a saying that he has, a saying that he was famous for, which I think is still relevant for people working in startups today or like trying to run a company, which is that so he says that the, so I'm paraphrasing, but the mark of a good researcher is someone who listens very carefully [00:02:00] to the voices of things.

They try to listen to what the universe is trying to tell them about the structure of the universe. And they they arrange their understanding and their theories and what they're doing accordingly. And I think similarly when you are trying to build something, when you're trying to do something new, you have to listen to what the world is telling you.

You have to listen to what the market is telling you and build accordingly.

I hope that was philosophical enough for you, .

John McDonnell: Yeah, I love it. There's this there's this guy David Whyte, who's who's a poet, and he has this kind of concept that he likes to incorporate into poetry that life should be a conversation between you and the world.

And

John McDonnell: like a really meaningful life or a great life is one where that conversation is really effective and goes both ways. And so that really reminds me of that.

Jesse Han: Yeah, totally , it's a reminder to be open to what the world is telling [00:03:00] you. And I think that's really important to remember as you like go heads down and you try to make something happen in a startup. You have to be on the lookout for signals that maybe you should be doing something different.

Maybe you should be pressing something harder. It's a careful balance that you have to strike.

Research vs startup thinking

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Bryan Davis: Do you find that the signals you're listening to or the incentives present are different in a research context versus startups? And if so, how so?

Jesse Han: To be honest, I don't really think they're that different. Like in research. So especially if you're in like a high pressure environment or if you're working in like a field that's moving really quickly, like AI , like what research looks like is taking a bunch of bets and choosing how to allocate your resources and figuring out Like what kinds of unfair advantages that you have that might make you unusually capable of capitalizing on the outcomes of some of those bets.

And so I think that a lot of. So a lot of the thinking [00:04:00] around what kinds of bets one should take in their career apply equally well to startups and similarly thinking around what kinds of activities are useful for startups to think about, apply equally well to research. So like an example is pursuing like very high impact research events.

Like you could spend a large majority of your career just pursuing incremental advances which carry less risk and are more likely to be published but which don't have an endearing legacy in terms of the research activity of others in the field. Or on the other hand, you can work on something that fundamentally changes the way that people think about some problem inside of the field. And that has a far more scalable... so I think a lot of the same thinking applies.

Jesse's path from research to startups

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Bryan Davis: And how did you navigate with that perspective? You were previously a researcher, you were a PhD student, you recently finished your PhD, and you've obviously worked in technology prior to launching a startup. [00:05:00] But how did you, what was your own journey from going from the research context into deciding to work in industry?

Did you ever aspire to be a professor?

Jesse Han: I did at some point. So at some point I was very deeply enmeshed in the pure mathematics world. I was trained a logician for most of my undergraduate years. And then I spent my masters just studying mathematical logic and model theory. But I think that gradually shifted towards a more ambitious vision, which formed the basis for the research program which I pursued in my PhD.

Partially due to my realization that I probably didn't have what it was gonna take to become a top mathematics researcher. I simply didn't have the let's say the intellectual horsepower. Because there are a lot of very talented people working in math, and it's a super small field.

So to like really get up there, it's like being a star athlete. It's like you have to train every day, you have to study the work of the masters.[00:06:00] You have to be in the right place at the right time with the right advisor, working on the exact right field to me making that kind of impact.

And towards the beginning of my PhD I came to the realization. The more impactful thing for me to do would be to try to just automate all of mathematics instead. And so I had this grand vision of eventually building some kind of planetary scale system for automatically searching for mathematical theorem improves.

So that one day human mathematicians would just be the operators of such a machine whose details. And intricacies would be hidden from them, like an operating system hides most of its complexities from the end user. And so that was what sort of drew me towards AI and got me into more industry adjacent things because building a system like that requires a lot of engineering skill, requires some pretty compute heavy resource.

And that kind of brought me into the orbit of people trying to apply the [00:07:00] latest techniques and deep learning to automate theorem proving.

Automating mathematics

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Bryan Davis: To anchor a little bit more in the math world, do you ever think we'll reach a point in mathematics or perhaps are we already there where we're at the limits of the capacity for human brains to comprehend and do you think that there's a zone in mathematics, in pure math where machines will begin to inspire, be the chief creators of new algorithms, new theories, new results?

Jesse Han: Yeah, I think that's a really interesting question. I think the fields where computers have a large advantage is with like really concrete kinds of combinatorics. That's one thing that stands out. Like subfields of discreet mathematics, like places where computation is really the main way to see how phenomena occur. For example, if you are like studying the dynamics of Conway's game of life, [00:08:00] then running computer simulations, or say you're just like studying say cellular automata, then running computer simulations is probably the best way to gain a good understanding of what's going on with any of the phenomena happening there.

But on the other hand, if you're working in more abstract fields that require like a large tower of definitions say algebraic geometry, then. The computer based foundations get a bit more shaky because there are many ways that you can represent various things. And there hasn't been a lot of work on shoring up, commonly accepted foundations.

Does that answer the question?

Bryan Davis: Yeah, I think it does. I remember reading, I believe it was a, or listening to an interview with Richard Fineman several years ago where he was talking about understanding the universe as peeling layers off an onion, and his hypothesis was that, there may never be an end to the layers.

We could just keep peeling and keep peeling, and eventually we might reach a boundary at which our capacity just to [00:09:00] abstract, our capacity to represent what is actually beyond the next layer, is just somehow limited or contained by the limits of, biologically based IQ or biologically based intelligence and I thought that was an interesting concept that I was, I'm curious to, to investigate whether the same thing might apply or whether you think the same thing might apply to mathematics.

Jesse Han: Oh, yeah. There are totally trivial cases, right? Like there, there are like there are prime numbers that require more bits to represent than is representable inside of the human brain?

Like that would be like a really trivial example. But you can already see this happening with the social fabric of mathematics. So what happens now is that a professional mathematician will go really deep and it's like harder and harder to become a true polymath. Like someone who's achieved mastery of like many fields of mathematics.

And so what happens is that the social fabric of like mathematics is made up of these experts who only see a [00:10:00] very narrow slice of the entire picture. Like for example, there's a vanishingly small number of people who have a complete understanding of the classification of finite groups. And that's simply one piece of mathematical lore, which has been written down in relatively, maybe not low fidelity, but written down in questionable fidelity in a constellation of like papers and preprints and surveys. But the true understanding of the proof, the the thing that is communicated from a master to a student in mathematical practice is very hard to grasp.

And it's only owned by a very small number of people today. So that's definitely happening and there are more examples in other fields of mathematics as well. This kind of phenomenon where where, you know it's becoming increasingly unclear. What parts of mathematics stand on firm foundations and what parts don't spurred a lot of research activity over the past few years in formalizing mathematics in a computer understandable way. This [00:11:00] research program was championed by Kevin Buzzard at Imperial College, where he drove a lot of people to organize a lot of mathematics in a computer understandable format, in a theorem proving language called Lean theory.

And he gave a very good talk at Microsoft Research titled The End of Mathematics where he talks about things like this where there are so many parts of math where the highest standard of proof is just social understanding between mathematicians. And when you think about it, these things are on shakier foundations than you might first believe.

John McDonnell: So where does that put us with, so you were saying that your hope was to build an, some kind of AI or automated system that could move the field forward essentially. And I think you mentioned like the foundations are firmer in a place like combinatorics. Do you feel like this is already having an impact? Or what are the kind of milestones to having impact.

Jesse Han: Do you mean the milestones to having impact in terms of in terms of [00:12:00] like fully automating a part of mathematics or just in verifying the existing knowledge?

John McDonnell: Maybe your perspective on both of those. How far is your vision from being realized even in a small way and what would it take to get there?

Jesse Han: I don't think a system like this has really been constructed for any particular field of mathematics. Of course mathematics is vast and there are many talented people working in it. Like many of whom have, are, have been schooled in the ways of formal proof. And so a system like this might have been built, but as far as I know, like nobody's built like this automated proof search thing where ... So the thing that, that I would like to be automated there is like how mathematics research is conducted by a very senior researcher, right?

Like they, they have this deep, deep understanding of the field and like what things are provable, what things should be proved, what kind of like [00:13:00] research programs should be carried out. It's kinda like building of like giant building, right? Like you say oh you can add an arch there if you like, use these tools from over here and because you have five years of experience already, it should only take you three months.

And so that's like something which requires really intense focus, incredible amounts of persistence, superhuman willpower at times. And if computers were able to do that, and we

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Pioneer Park PodcastBy Bryan