Alexander Grothendieck

And then you have who's writing the new definitions.

And so here you have, it's like Galois or Grothendieck or in modern times, Peter Schulze, where if you say, what is it that these like truly monumental figures in the field were creating? It's not so much any one problem that they were solving.

It was like a completely new way of thinking about a body of work as represented by a new set of definitions, essentially.

And so one of the shifts in math over the last century is one towards thinking in terms of something called categories.

Information such as the number of holes in an object.

A primitive version of the hypothesis comes from Poincaré in 1895, though the canonical formulation came from Grothendieck in 1983, nearly 100 years later.

Ever since, the hypothesis has been analysed, proven, or disproven with variants of the choice of algebraic object or the dimension of space.

For some mathematicians, this problem took up much of their research lives over 30 or more years.

Information such as the number of holes in an object.

A primitive version of the hypothesis comes from Poincaré in 1895, though the canonical formulation came from Grothendieck in 1983, nearly 100 years later.

Ever since, the hypothesis has been analysed, proven, or disproven with variants of the choice of algebraic object or the dimension of space.

For some mathematicians, this problem took up much of their research lives over 30 or more years.

But I mean, there is a-

It's, it was a, it was a joke by Grothendieck, I think.

Yeah, yeah, exactly.

I know, I know.

Hmm.

I don't necessarily think that's true, because when I think of the great mathematicians, I think of Newton, I think of Cantor, I think of, um, Grothend-- um, is it, it's Grothendieck, I think.

I'm pronouncing his name correctly.

Yeah, yeah.

We know which guy.

But the mathematicians who fundamentally changed the way we think about the world, and who opened things up for me, and stuff like that.

And I, I think at least in the case of, of, of Grothendieck, like, he kind of didn't do that.

Right, right.

Insofar as any given industry utilizes code these days, artificial intelligence looms in all workplaces, albeit unevenly.

There are some people to whom correctness matters even more than it matters to coders, however—mathematicians— When a mathematician brushes up against correctness, they have good reason to believe they are doing so in a truly fundamental way.

And today's mathematicians seem to feel like they have recently come under existential threat.

Here's a question you might not have considered before, but is probably a bit richer than it would seem at first glance.

Why is math hard? Mathematicians and theoretical computer scientists concern themselves with proofs, starting with a small, fixed set of basic axioms and armed with a smattering of Latin phrases.

If you're an aspiring mathematician who encounters these thoughts, you have a few options.

Obviously, the first and easiest choice is simply to leave math.

If you stay, you're allowed to ignore these foundational issues, as most working mathematicians do.