[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. ...

[gjm11]

What exactly are you saying this is an example of?

It's certainly not something that people believed and built stuff on the basis of; it was never regarded as anything more than a conjecture and I would be a little surprised if even one paper was published that took the conjecture as a hypothesis, even explicitly (i.e., "We show that if Euler's conjecture is true then ...").

It's also not, so far as I know, a case where anyone reacted with defensiveness, horror, insecurity, etc., when a counterexample was found. They published a paper in a reputable journal. They don't seem to have had much trouble getting it published, if they discovered the counterexample in 1966 and the paper was published in a 1966 issue of said journal.

So if you're suggesting that this is a case where "people were building on swathes of mathematics that seem proven and make intuitive sense, but needed formal buttressing", I'd like to see some evidence. Same if you're suggesting that this is a case where "so-called experts had invested far, far too many of their man-years in that unproven conjecture" and there'd be a hostile reaction to a counterexample.

On the other hand, if you're not suggesting either of those things, I'm not sure what the connection to the rest of the discussion is.

[bell-cot]

> What exactly are you saying this is an example of?

A prominent conjecture in number theory, taken quite seriously for centuries, but which was quickly and rather easily disproven once computers became powerful enough.

No, it is not a exact analogy for Fermat, nor BSD, nor Riemann, nor ...

My initial point of interest was u/bootby's comment - why the heck would a room full of experts (presumably noteworthy math professors) become so angry at some grad student's comment? Then /usr/baruz's comment, about things which "seem proven and make intuitive sense, but needed formal buttressing". On occasion, "seemed" and "intuition" prove to be wrong, and Euler was a pretty-good example that.

[subsistence234]

they didn't become angry, they became excited.

and a famous conjecture is by definition something for which all the experts know that its truth is UNKNOWN (even in cases where most experts believe it's true).

[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).

[baruz]

Does this not imply that /u/bell-cot had been a graduate student in mathematics?

> If I could give my many-decades-ago younger self some advice for math grad school

[XorNot]

It's HN bread-and-butter to insist that all experts are wrong, and it must be because BIG <random field> is just protecting the sweet sweet lower middle-class living of being a tenured professor or something.

[lmm]

The worst part of middle-class life in the US is its precariousness. A guaranteed lower middle-class living for life is a pearl indeed.