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EPISODE LINKS:
Fermat's Library Twitter: https://twitter.com/fermatslibrary
Luis's Twitter: https://twitter.com/luismbat
Joao's Twitter: https://twitter.com/joao_batalha
Fermat's Library Website: https://fermatslibrary.com

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OUTLINE:
0:00 - Introduction
2:22 - Backstories to research papers
17:13 - Fermat's Library
37:14 - Scientific publishing
1:00:54 - How to read a paper
1:06:48 - Taking good notes
1:15:27 - Favorite papers on Fermat's Library
1:56:18 - Fermat's Library on Twitter
2:05:50 - What it takes to build a successful startup
2:14:46 - Game of Thrones
2:17:34 - Realism in science fiction movies
2:23:33 - Greatest soccer player of all time
2:46:22 - Advice for young people

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The following is a conversation with Louise and João Batala, brothers and co-founders of Fermat's Library, which is an incredible platform for annotating papers.

As they write on the Fermat's Library website, just as Pierre de Fermat scribbled his famous last theorem in the margins, professional scientists, academics, and citizen scientists can annotate equations, figures, ideas, and write in the margins.

Verma's library is also a really good Twitter account to follow.

They post little visual factoids and explorations that reveal the beauty of mathematics.

Skiff, SimpliSafe, Indeed, Nutsuite, and 4 Sigmatic.

Check them out in the description to support this podcast.

As a side note, let me say a few words about the dissemination of scientific ideas.

I believe that all scientific articles should be freely accessible to the public.

In 1 analysis I saw, more than 70% of published research articles are behind a paywall.

In case you don't know, the funders of the research, whether that's government or industry, aren't the ones putting up the paywall.

The journals are the ones putting up the paywall while using unpaid labor from researchers for the peer review process.

Where is all that money from the paywall going?

In this digital age, the costs here should be minimal.

This cost can easily be covered through donation, advertisement, or public funding of science.

The benefit versus the cost of all papers being free to read is obvious.

And the fact that they're not free goes against everything science should stand for, which is the free dissemination of ideas that educate and inspire.

The more people can freely learn and collaborate on ideas, the more problems we can solve in the world together.

And the faster we can drive old ideas out and bring new, better ideas in.

Science is beautiful and powerful, and its dissemination in this digital age should be free.

This is the Lex Friedman Podcast, and here's my conversation with Luis and Joao Batalla.

Imagine if most papers had a backstory section, the same way that they have an abstract.

So knowing more about how the authors ended up working on a paper can be extremely insightful.

And then you went on to give a backstory for the Feynman QED paper.

How much of the human backstory do you think is important in understanding the idea itself that's presented in the paper or in general?

I think this gives way more context to the work of scientists.

I think a lot of people have this almost kind of romantic misconception that the way a lot of scientists work is almost as the sum of eureka moments where all of a sudden they sit down and start writing 2 papers in a row and the papers are usually isolated.

And when you actually look at it, the papers are chapters of a way more complex story.

And the Feynman QED paper is a good example.

So Feynman was actually going through a pretty dark phase before writing that paper.

He lost enthusiasm with physics and doing physics problems.

And there was 1 time when he was in the cafeteria of Cornell and he saw a guy that was throwing plates in the air and he noticed that there was, when the plate was in the air, there were 2 movements there.

The plate was wobbling, but he also noticed that the Cornell symbol was rotating, and he was able to figure out the equations of motions of those plates, and that led him to kind of think a little bit about electron orbits in relativity, which led to the paper about quantum electrodynamics.

So that kind of reignited his interest in physics and ended up publishing the paper that led to his Nobel Prize, basically.

And I think it's, there are a lot of really interesting backstories about papers that readers never get to know.

For instance, we did a couple of months ago, an AMA around a paper, a pretty famous paper, the Gans paper with Ian Goodfellow.

And so we did an AMA where everyone was, could ask questions about the paper and Ian was responding to those questions.

And he was also telling the story of how he got the idea for that paper in a bar.

So that was also an interesting backstory.

Cedric Villani is this mathematician, the Fields Medalist.

And in his book, he tries to explain how he got from like a PhD student to the Fields Medal, and he tries to be as descriptive as possible every single step how he got to the Fields Medal.

And it's interesting also to see just the amount of random interactions and discussions with other researchers, sometimes over coffee, and how it led to like fundamental breakthroughs in some of these most important papers.

So I think it's super interesting to have that context of the backstory.

Well, the Ian Goodfellow story is kind of interesting, and perhaps that's true for Feynman as well.

I don't know if it's romanticizing the thing, but it seems like just a few little insights and a little bit of work does most of the leap required.

Do you have a sense that for a lot of the stuff you've looked at, just looking back through history, it wasn't necessarily the grind of like Andrew Wiles or the Fermat's Last Theorem, for example.

It was more like a brilliant moment of insight.

In fact, Ian Goodfellow has a kind of sadness to him almost in that at that time in machine learning, like at that time, especially for GANs, you could code something up really quickly on a single machine and almost do the invention, go from idea to experimental validation in like a single night, a single person could do it.

And now there's kind of a sadness that a lot of the breakthroughs you might have in machine learning kind of require large scale experiments.

So I wonder how many low-hanging fruit there are in science and mathematics and even engineering where it's like you could do that little experiment quickly.

But you have an inside of the bar and then just implement and the world changes.

It's a good point, I think it also depends a lot on the maturity of the field.

When you look at a field like mathematics, like It's a pretty mature field.

A field like machine learning, it's growing pretty fast.

I looked up the number of new papers on archive with the keyword machine learning.

And like 50% of those papers have been published in the last 12 months.

So you can see the magnitude of growth in that field.

And so I think like as fields mature, like those types of moments, I think naturally are less frequent.

The other point that is interesting about the backstory is that it can really make it more memorable in a way.

And by making it more memorable, it kind of sediments the knowledge more in your mind.

I remember also reading the sort of the backstory to Dijkstra's shortest path algorithm, right?

Where He came up with it essentially while he was sitting down at a coffee shop in Amsterdam.

He came up with that algorithm over 20 minutes.

1 interesting aspect is that he didn't have any pen or paper at the time, and so he had to do it all in his mind.

There's only so much complexity that it can handle if you're just thinking about it in your mind.

And that, like when you think about the simplicity of Dijkstra's shortest path finding algorithm, it's, you know, knowing that backstory helps sediment that algorithm in your mind so that you don't forget about it as easily.

It might be from you that I saw a meme about Dexter.

It's like he's trying to solve it and he comes up with some kind of random path and then it's like my parents aren't home and then he does, he figures out the algorithm for the shortest path.

I don't know if it's in post that we construct stories that romanticize it.

Apparently with Newton, there was no apple.

Especially when you're working on problems that have a physical manifestation or a visual manifestation, it feels like the world could be an inspiration to you.

So it doesn't have to be completely on paper.

Like you could be sitting at a bar and all of a sudden see something and a pattern will spark another pattern and you can visualize it and rethink a problem in a particular way.

Of course, you can also load the math that you have on paper and always carry that with you.

So when you show up to the bar, some little inspiration could be the thing that changes it.

Is there any other people, almost on the human side, whether it's physics with Feynman, Dirac, Einstein, or computer science, Turing, anybody else, any backstories that you remember that jump out?

Because I'm also referring to not necessarily these stories where something magical happens, but these are personalities.

Some of them are super friendly, some of them are like self-obsessed, some of them have anger issues, some of them, how do I describe Feynman, but he appears to have appreciation of the beautiful in all its forms.

He has a wit and a cleverness and a humor about him.

So does that come into play in terms of the construction of the science?

Newton is a good example also to think about his backstory because there's a certain backstory of Newton that people always talk about, but then there's a whole another aspect of him that is also a big part of the person that he was, but he was really into alchemy, right?

And he spent a lot of time thinking about that and writing about it, and he took it very seriously.

He was really into Bible interpretation, trying to predict things based on the Bible.

And so there's also a whole backstory then, and of course you need to look at it in the context and the time that when Newton lived.

But it adds to his personality and it's important to also understand those aspects that maybe people are not as proud to teach to little kids but It's important, it was part of who he was and maybe without those, who knows what he would have done otherwise.

Well, the cool thing about alchemy, I don't know how

it was viewed at the time, but it almost to me symbolizes dreaming of the impossible.

Like most of the breakthrough ideas kind of seem impossible until they're actually done.

It's not completely obvious to me that alchemy is impossible or like putting myself in the mindset of the time.

And perhaps even still, everything that, you know, some of

the most incredible breakthroughs would seem impossible.

And I wonder the value of believing, almost like focusing and dreaming of the impossible, such that it is actually is possible

in your mind, and that in itself manifests, whether the accomplishing that goal or making progress in some unexpected direction.

So alchemy almost symbolizes that for me.

I distinctly remember having the same thought of thinking, you know, when I learned about atoms and that they have protons and electrons, I was like, okay, to make gold, you just take whatever has an atomic weight below it and then shove another proton in there and then you have a bunch of gold.

It seemed like conceptually it's like, you know, this sounds feasible, you might be able to do it.

And you can actually, it's just very, very expensive.

So in a sense we do have alchemy and maybe even back then it wasn't as crazy that he was so into it, but people just don't like to talk about that as much.

Yeah, but Newton in general was a very interesting fella.

in terms of people that you just are happy that they have once or still exist on this earth?

Yeah, Freeman Dyson was, I've had a chance to actually exchange a couple of emails with him.

It was probably 1 of the most humble scientists that I've ever met and that had a big impact on me.

We were trying, we're actually trying to convince him to annotate a paper on Fermat's library and I sent him an email asking him if he could annotate a paper and his response was something like, I have very limited knowledge, I just know a couple of things about certain fields, I'm not sure if I'm qualified to do that.

And this was someone that should have won a Nobel Prize and worked on a bunch of different fields, did some really, really great work.

And then just the interactions that I had with him, every time I asked him a couple of questions about his papers and he always responded saying, I'm not here to answer your questions, I just want to open more questions.

It was like just an example of an extremely humble yet accomplished scientist.

And Feynman was also a big, big inspiration in the sense that he was able to be, you know, again, extremely talented and scientist, but at the same time, socially, he was able to, he was also really smart from a social perspective, and he was able to interact with people.

He was also a really good teacher, and was also to, did awesome work in terms of explaining physics to the masses and motivating and getting people interested in physics.

And that for me was also a big inspiration.

Yeah, I like the childlike curiosity of some of those folks, like you mentioned, Freeman.

I have Daniel Kahneman, I got a chance to meet and interact with some of these truly special scientists.

What makes them special is that even in older age, there's still that fire of childlike curiosity that burns.

And some of that is like not taking yourself so seriously that you think you've figured it all out, but almost like thinking that you don't know much of it.

And that's like step 1 in having a great conversation or collaboration or exploring a scientific question.

It's cool how the very thing that probably earned people the Nobel Prize or work that's seminal in some way is the very thing that still burns even after they've won the prize.

And to that point, I remember like the last email that I sent to Freeman Dyson was like in his last birthday.

He was really into number theory and primes.

So what I did is I took a photo of him, picture, and then I turned that into a giant prime number.

So I converted the picture into a bunch of 1 and eights, and then I moved some numbers around until it was a prime, And then I sent him that.

Oh, so the visual, like it still looked like the picture

So the way you do it is like you convert the darker regions into eights and the lighter regions in ones.

And then just keep flipping numbers until-

But there's like some primality tests that are cheaper from a computational standpoint.

But what it tells you is it excludes numbers that are not prime.

Then you end up with a set of numbers that you don't know if they are prime or not.

And then you run the full primality test on that.

So you just have to keep iterating on that.

And it's funny because when he got the picture, he was like, how did you do that?

And again, it was already 90, I think 92 or something.

So you can really see that in some of these scientists.

It is a platform for annotating papers in its essence.

And so academic papers can be 1 of the densest forms of content out there and generally pretty hard to understand at times.

And the idea is that you can make them more accessible and easier to understand by adding these rich annotations to the side, right?

And so we can just imagine a PDF view on your browser and then you have annotations on each side.

And then when you click on them, a sidebar expands.

And then you have annotations that support LaTeX and Markdown.

And so the idea is that you can, say, explain a tougher part of a paper where there's a step that is not completely obvious, or you can add more context to it.

And then over time, papers can become easier and easier to understand and can evolve in a way.

But it really came from myself, Luis and 2 other friends.

We've had this long running habit of kind of running a journal club amongst us.

We come from different backgrounds, right?

I studied CS, we studied physics, and so we'd read papers and present them to each other.

And then we tried to bring some of that online.

And that's when we decided to build Fermat's library.

Then over time, it kind of grew into something with a broader goal.

And really what we're trying to do is trying to help move science in the right direction.

That's really the ultimate goal and where we want to take it now.

So first of all, for people who haven't seen it, the interface is exceptionally well done.

That's like execution is really important here.

The other thing is just to mention for a large number of people apparently, which is new to me, don't know what LaTeX is.

So be careful Googling it if you haven't before.

It's, sorry, I don't even know the correct terminology.

It's a typesetting language where you're basically program, writing a program that then generates something that looks from a typography perspective beautiful.

And so a lot of academics use it to write papers.

I think there's like a bunch of communities that use it to write papers.

I would say it's mathematics, physics, computer science.

Because I'm collaborating currently on a paper with 2 neuroscientists from Stanford.

So I'm using Microsoft Word and Mendeley and like all of those kinds of things.

And I'm being very Zen like about the whole process, but it's fascinating.

It's a little heartbreaking actually, because it actually, it's funny to say, but we'll talk about open science, actually the bigger mission behind it for Mars libraries, like really opening up the world of science to everybody is These silly 2 facts of like 1 community uses LaTeX and another uses Word is actually a barrier between them.

That's like, it's like boring and practical in a sense, but this makes it very difficult to collaborate.

Just on that, like, I think that if there are some people that should have received a Nobel Prize, but will never get it.

And I think 1 of those is Donald Knuth, because of tech, and latech, and then.

Because it had a huge impact in terms of just making it easier for researchers to put their content out there, like making it uniform as much as possible.

Maybe a Nobel Peace Prize, yeah, I think so.

I mean, he at a very young age got the Turing Award for his work in algorithms and so on.

So like an incredibly, I think it's in, it might be even the 60s, but I think it's the 70s.

So when he was really young, and then he went on to do like incredible work with his book and yeah, with tech that people don't know.

And going back just 1 on the reason why we ended up, because I think this is interesting.

The reason why we ended up using the name Fermat's library, this was because of Fermat's Last Theorem.

And Fermat's Last Theorem is actually a funny story.

So Pierre de Fermat, he was like a lawyer and he wrote like on a book that he had a solution to Fermat's Last Theorem, but that didn't fit the margin of that book.

And so Fermat's Last Theorem basically states that there is no solution, if you have integers a, b, and c, there's no solution to a to the power of n plus b to the power of n equals to c to the power of n if n is bigger than 2.

And he said that, and that problem remained open for almost 300 years, I believe.

And a lot of the most famous mathematicians tried to tackle that problem.

No 1 was able to figure that out until Andrew Wiles, I think was in the 90s, was able to publish the solution, which was, I believe, almost 300 pages long.

And so it's kind of an anecdote that, you know, there's a lot of knowledge and insights that can be trapped in the margins.

And there's a lot of potential energy that you can release if you actually spend some time trying to digest that.

You actually can share the contents of the margins with the world.

That could inspire a solution or a communication that then leads to a solution.

But, and if you Think about papers, like papers are, as João was saying, probably 1 of the densest pieces of text that any human can read.

And you have these researchers, like some of the brightest minds in these fields, working on like new discoveries and publishing these work on journals that are imposing them restrictions in terms of the number of pages that they can have to explain a new scientific breakthrough.

So at the end of the day, papers are not optimized for clarity and for a proper explanation of that content because there are so many restrictions.

So there's, as I mentioned, there's a lot of potential energy that can be freed if you actually try to digest a lot of the contents of papers.

Can you explain some of the other things?

So Journal Club is what a lot of people know us for, where every week we release an annotated paper in all sorts of different fields, physics, CS, math.

Margins is kind of the same software that we use to run the journal club and to host the annotations, but we've made that available for free to anybody that wants to use it.

And so folks use it at universities and for running journal clubs.

And so we've just made that freely available.

And then Librarian is a browser extension that we developed that is sort of an overlay on top of Archive.

So it's about bringing some of the same functionality around comments, plus adding some extra niceties to archive, like being able to very easily extract the references of a paper that you're looking at or being able to extract the bib deck in order to cite that paper yourself.

The idea is that you can have that commenting interface without having to leave Archive.

And once I learned of it, it's like, holy shit.

Why isn't it more popular given how popular Archive is?

Archive is a pretty incredible project, right?

And it is, in a way, it's, you know, the growth has been completely linear over time.

If you look at like number of papers published on archive, like, you know, it's just been, it's pretty much a straight line for the past 20 years.

Especially for, you know, like, if you're coming from a startup background and then you were trying to do archive, you'd probably tried like all sorts of growth acts and try to then maybe have paid features and things like that and that would kind of maybe ruin it.

And so there's a subtle balance there and I don't know what aspects you can change about it.

For some tools in science it just takes time for them to grow.

And for people that don't know, Archive is this kind of online repository where people put preprints, which are versions of the papers, before they actually make it to journals.

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Luís and João Batalha: Fermat's Library and the Art of Studying Papers | Lex Fridman Podcast #209