Much (most?) of math consists in transmission of it (according to Thurston [1]), a 1000-page proof with no possibility of transmission is mostly useless. The proof of Fermat's last Theorem is important in itself, and adds much more than the mere result.

I am not talking about the supposed "beauty" of a proof (I do not believe in that concept, rather in "elegance", which is not the same), I am talking about the proof itself, and the insights it provides.

[1] https://www.ams.org/journals/bull/1994-30-02/S0273-0979-1994...

Outside of some niche specializations like cryptography, math isn't practiced because of "consequences". Most mathematicians take pride in their work not having any obvious practical applications. They're also overwhelmingly working in university settings where they're not expected to generate revenue or deliver practical results.

We basically subsidize the practice of mathematics as an art form, and if you try to take the artistry away, you might find that the artists don't want to play along. And I guess you can imagine future robo-math production lines without any human involvement, and then LLMs finding applications for the resulting theorems, but it's not possible today.

You want to understand why it’s true, and that often correlates with beauty.

Why prove the Pythagorean theorem rather than just prove 3^2 + 4^2 = 5^2?

For any practical application, you are only interested in finite set of concrete identities, so anything beyond that is surplus to requirements, surely?

> Why does it need to be beautiful?

“Beauty will save the world”