Lex Fridman

We should say you've worked quite a bit on infinite chess, which we should definitely talk about.

It's awesome.

You've worked on so many fascinating things.

Has philosophy ever clarified mathematics?

Why do we have two theorems when one implies the other?

And of course, just as an example, you've given a really great, almost historical answer on the topic of the continuum hypothesis.

Maybe that's a good place to go.

We've touched it a little bit, but it'd be nice to lay out what is the continuum hypothesis that Cantor struggled with, and I would love to also speak to the psychology of his own life story, his own struggle with it.

The human side of mathematics is also fascinating.

So what is the continuum hypothesis?

Everything I've seen, it seems to be the question of Brokham.

I mean, just struggling with different opinions on the hypothesis within himself and desperately chasing, trying to prove it.

Can you define the open and the closed set in this context?

The Cantor set is constructed by iteratively removing open intervals, middle thirds, like you mentioned, from the interval, and trying to see, can we do a thing that goes in between?

Yeah, well, spoiler alert, can you go to the independence result?

Sure.

So what does that mean?

So continuum hypothesis was shown to be independent from the ZFC axioms of mathematics.

Right.

We should mention, I apologize, that it was the number one problem in the Hilbert's 23 set of problems formulated at the beginning of the century.