Lex Fridman: preference

Transcript context

…That’s a good question. When I came to graduate school in Princeton, so John Conway was there at the time, he passed away a few years ago, but I remember one of the very first research talks I went to was a talk by Conway on what he called extreme proof. So Conway just had this amazing way of thinking about all kinds of things in a way that you wouldn’t normally think of. So he thought proofs themselves as occupying some sort of space. So if you want to prove something, let’s say that there’s infinitely many primes, you have all different proofs, but you could rank them in different axes. Some proofs are elegant, some proofs are long, some proofs are elementary and so forth, and so there’s this cloud, so the space of all proofs itself has some sort of shape, and so he was interested in extreme points of this shape. Out of all these proofs, what is one of those, the shortest, at the expense of everything else, or the most elementary or whatever? So he gave some examples of well-known theorems, and then he would give what he thought was the extreme proof in these different aspects. I just found that really eye-opening, that it’s not just getting a proof for a result that was interesting, but once you have that proof, trying to optimize it in various ways, that proofing itself had some craftsmanship to it. It’s certainly informed my writing style, like when you do your math assignments and as you’re an undergraduate, your homework and so forth, you’re sort of encouraged to just write down any proof that works and hand it in, and as long as it gets a tick mark, you move on, but if you want your results to actually be influential and be read by people, it can’t just be correct. It should also be a pleasure to read, motivated, be adaptable to generalize to other things. It’s the same in many other disciplines, like coding. There’s a lot of analogies between math and coding. I like analogies, if you haven’t noticed. You can code something, spaghetti code, that works for a certain task, and it’s quick and dirty and it works, but there’s lots of good principles for writing code well so that other people can use it, build upon it so it has fewer bugs and whatever, and there’s similar things with mathematics. Yeah, first of all, there’s so many beautiful things there, and [inaudible 00:59:42] is one of the great minds in mathematics ever, and computer science, just even considering the space of proofs and saying, “Okay, what does this space look like, and what are the extremes? ” Like you mentioned, coding as an analogy is interesting, because there’s also this activity called the code golf, which I also find beautiful and fun, where people use different programming languages to try to write the shortest possible program that accomplishes a particular task, and I believe there’s even competitions on this, and it’s also a nice way to stress test not just the programs, or in this case, the proofs, but also the different languages. Maybe that’s a different notation or whatever to use to accomplish a different task. Yeah, you learn a lot. I mean, it may seem like a frivolous exercise, but it can generate all these insights, which, if you didn’t have this artificial objective to pursue, you might not see……

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