[mostly_a_lurker]

> Also not a number theorist...but I'd bet those so-called experts had invested far, far too many of their man-years in that unproven conjecture. All of which effort and edifice would collapse into the dumpster if some snot-nosed little upstart like you, using crude computation, achieved overnight fame by finding a counter-example.

Are you maybe confusing math academia for psychology or social sciences? There is no replication crisis in math, no house of cards of self-proclaimed experts riding on bullshit. Mathematicians are _actually experts_ at a deep and extremely rigorous technical field -- many of them are even experts at computational approaches to problems! -- and when outsiders and upstarts resolve old conjectures, mathematicians generally react by celebrating them and showering them with fame, job offers and gushing articles in Quanta.

[CJefferson]

Maths may not have a replication crisis like some other areas, but when I go to maths events, it seems widely agreed there are far too many papers with incorrect theorems, it's just no-one cares about those papers, so it doesn't matter.

It turns out to be very, very common (as discussed in the linked article) that when someone really carefully reads old papers, the proofs turn out to be wrong. They are often fixable, but the point of the paper was to prove the result, not just state it. What tends to save these papers is that enough extra results have been built on top of them, and (usually), if there had been an issue, it would have showed up as an inconsistency in one of the later results.

The trunk is (probably) solid, but there are a lot of rotten leaves, and even the odd branch.

[baruz]

> no house of cards

As I understand TFA, from a formalist’s perspective, this is not necessarily the case. People were building on swathes of mathematics that seem proven and make intuitive sense, but needed formal buttressing.

> _actually experts_ at a deep and rigorous technical field

Seeing as the person you’re addressing was a mathematics graduate student, I’m sure they know this.

[bell-cot]

Yep. Here's an easy-looking one, that lasted just under 2 centuries (quoting Wikipedia) -

> In number theory, Euler's conjecture is a disproved conjecture related to Fermat's Last Theorem. It was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n many kth powers of positive integers is itself a kth power, then n is greater than or equal to k...

> ...

> Euler's conjecture was disproven by L. J. Lander and T. R. Parkin in 1966 when, through a direct computer search on a CDC 6600, they found a counterexample for k = 5.[3] This was published in a paper comprising just two sentences.[3]

> [3] - Lander, L. J.; Parkin, T. R. (1966). "Counterexample to Euler's conjecture on sums of like powers". Bull. Amer. Math. Soc. ...

[mostly_a_lurker]

> Seeing as the person you’re addressing was a mathematics graduate student, I’m sure they know this.

The OP (u/boothby) was not the person I was addressing (u/bell-cot).