Same is true for any area/topic though. Countries at war stop playing friendly football games against each other, as a very basic example.

Where else are you going to keep your large primes?

Wait what ? Does nobody use RSA anymore ?

It is easier to trust what you can understand.

> He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...

That's how maths works yes...

What you’re talking about is his proof of (a specialised version) of the Taniyama-Shimura-Weil conjecture[1] which had been proven to imply Fermat’s Last Theorem. The technique he used to prove this was adopted by his students to prove the conjecture in full generality so it now known as the modularity theorem. Given its importance to the Langlands programme it may be that when history looks back on this it will consider this a more important contribution than the fact that it proved FLT even though that is obviously the thing that grabs the headlines, but there’s nothing at all wrong with proving something that implies your goal rather than proving the goal directly. There’s a reason the words “it suffices to show” often turn up in proofs.

[1] https://mathworld.wolfram.com/Taniyama-ShimuraConjecture.htm...

Obviously, he was trying to avoid being labeled as a crank for working on a famous problem like that for so long.

While I can sympathize with this perspective, I don’t think it’s right to call it driven by “ego.” Sometimes one just wants to go at a problem without being second guessed on approaches or led astray with suggestions by others.

> He didn't even proof the last theorem of Fermat directly, he proved some conjeture that someone else before him, proved that it implied Fermat last theorem...

I think that was Ken Ribet?

Grigori Perelman and the Poincaré Conjecture is more interesting. IIRC he turned down Millennium and was decidedly not all about the Fields Medal - mostly because Richard Hamilton didn't get credit? Anyway, I am grateful I had the opportunity to learn about Poincaré in college taking a few classes from a professor who was a key contributor to the conjecture and got a Fulbright for it when I was there

Eh, it seems like it's pretty necessary for success on such a problem (but obviously not sufficient). These problems gain a reputation, and you either get judged for it or get too much attention for it.

Of course you can. Stockfish plays very different compared to a human, and it never ever blunders or makes mistakes.

because we value competence

It is a strong argument in this case though, because Terence Taos expertise is directly linked to his ability to not misstate the history of mathematics.

Also note how the quote by Tao is in all likelyhood not meant as an absolute; rather than a statement of a trend - a handfull of counterexamples do I no way change anything about the truth value of Tao's quote.

On the other heand; consider how absurd it would be if "... in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science ..." would indeed be a misstatement; which would imply that far more promising research directions were not shared with the broader community (i.e.: published). I wonder what different reading of that counterfactual there could be other than secret societies that kept their discoveries and research directions to themselves - which we just learned about (since we would otherwise not be refering to the secret societies and their supposed promising research directions).

All pretty straightforward, I would say - both that "misstatement" is hopefully based an overly strict reading of Tao's quote, and that mentioning Tao's background as one of the fields leading practitioners is relevant as well. Again; to make sure: A few counterexamples achieves nothing here. It would need to reach a certain threshold of such counterexamples before we will have to write the history of mathematics; and before Tao actually made a misstatement here.

And the other an appeal to tradition. There was only one Gauss to scoop and focusing on him misses the larger math culture which Terry might be aware of, where most trust others to not scoop.

And if any mathematician's AI usage on a problem leads to scooping, the volume of agents involved gives them a huge advantage which could prompt mathematicians to not use LLMs.

Though you can say Terry's claim is a slippery slope.

So let me get this straight: you're saying that Terrence Tao, one of the most prominent mathematicians alive today, doesn't know math history? And me pointing this out is merely an appeal to authority?

Get outta here.

> Nothing in their comment reads to me as "arguing against"

If competition is somehow the opposite of "centuries of traditions of open science", and "mathematics has always been highly competitive", then open science is neither sufficient or necessary for the future of mathematics. Their clear implication is that we don't need to worry about it, though, because it's always been that way.

> Reads like nothing but historical context

They literally accuse Tao of "a misstatement of mathematical history".

> They aren't arguing against open science, they are trying to educate you on the history of science. It's always been this way.

Always been what way? And how does that contrast to what Tao said (since it was apparently "a misstatement of mathematical history")?

> Also, your third paragraph is highly ironic.

You'll have to be more specific, since I engaged with my parent's argument, while they waved away Tao's quote by suggesting he was wrong because of exactly the kind of events that helped lead to the norms and mores working mathematicians have today.