Lex Fridman

Is it fair to say that in general it means if I give you a statement, you can't know if your axiomatic system would be able to prove it?

Can you describe the halting problem?

Because it's a thing that shows up in a very useful and again, traumatic way through a lot of computer science, through a lot of mathematics.

Maybe to take a little bit of a tangent, can you speak, you've written a wonderful book about proofs and the art of mathematics.

So what can you say about proving stuff in mathematics?

What is the process of proof?

What are the tools?

What is the art?

What is the science of proving things in mathematics?

We should say, you dedicate the book to my students.

May all their theorems be true, proved by elegant arguments that flow effortlessly from hypothesis to conclusion while revealing fantastical mathematical beauty.

Is there some interesting proofs that maybe illustrate for people outside of mathematics or for people who just take math classes in high school and so on?

And we should say that sometimes the power of proof is such that the non-obvious can be shown, and then over time that becomes obvious.

So in the context of money or social systems, there's a bunch of things that are non-obvious.

And the whole point is that proof can guide us to the truth, to the accurate description of reality.

We just proved a property of money.

To what degree, sticking on the topic of infinity, should we think of infinity as something...

It is very true that we don't know anything about the soda bottle or the steam locomotive just because we can poke at it.

Again, we anthropomorphize, and that actually gets us into trouble sometimes because I'm not feeling the quantum mechanics when I'm touching this.

That's right.