Pure mathematics, almost by definition, doesn't typically argue the field is always or even often "useful" (for some other purpose or application).

But, as mathematicians learn and push forward, occasionally something like elliptic curves will emerge as having useful applications, making all that previously "pointless" specialized knowledge newly valuable.

Or advances in physics, that suddenly have a need for a specific mathematical underpinning to develop a theoretical framework. Like how Einstein benefited from Minkowski's work on hyperboloids to create a coherent mathematical description of spacetime.

It was the AI labs themselves not mathematicians who were happy to conflate proofs for open math problems with some kind of tangible technological advancement in the real world. They would surely prefer to be able to claim a cure for cancer vs. a math problem but that loop requires a lot more time/money/test tubes/etc and they need headlines now not in a decade.

And so, thanks to OpenAI/Anthropic, we're now in a world where thousands of crypto bots on X breathlessly hype up each new problem being solved that previously wouldn't have any got any attention beyond academia and passionate fans of math.

Hopefully this won't lead to a trough of disillusionment as more people start to feel like you, with mathematicians getting the blame for inflating the value of their work even though the hype was coming entirely from the labs not them.

His issue is more nuanced than that. Most of the value was in humans reaching new insights or new math during failed attempts to solve these problems, whereas AI is basically "too efficient" in beelining to the goal and discards potential new insights reached along the way. I assume this is solvable.

Where was Tao unhappy? I thought he was sort of anticipating this.

He's not unhappy with it being solved, but the solution is less important than the learning you have to do to arrive at the solution. If they're just chucking compute at it and publishing the answer and hiding the path to get there, it sort of negates the whole point of posing such problems to begin with.

I suppose this is how Lee Sedol felt when AlphaGo beat him. But in the same vein, didn't it ultimately advance human understanding of the game?

Here's the point: when people solve problems, they come together and create a community to eventually use the new knowledge in positive ways, including inspiring younger mathematicians by sharing insights. The human element is key and it's not just about solving problems. People only think that because we've been conditioned by computers to value answers more than how we got to them.

But if AI can solve any problem and existing mathematicians just use AI to solve problems for the sake of solving them, the community itself with wither and so will the interest in mathematics and over a longer period of time, it will just become soul-less and uninteresting and the entire community powered by the fire of fascination will simply die.

Where did you even read that Tao is unhappy with “open problems being solved”? There was no indication of that in his Bluesky thread.

Why would you go out of your way to make a case of something being not useful when, ironically, so much advancement in human history has come from the discipline?

Your motive is more worrying than your straw man argument.

I think the point is that one of the biggest problems in the field has been solved and yet the excitement from this is nearly nil. Can you imagine if say breast cancer were cured under similar circumstances, or even worse (say OpenAI openly admitting it basically stole a bunch of other researcher's chatGPT conversations)? No one would care about these petty bickerings- or at least the headline "CURE FOR BREAST CANCER FOUND" would completely swamp anything else. This is embarrassing: it tells you almost no one- not even mathematicians themselves really care about their own problems- if they're not careful people will get the impression it's all a form of bean counting in a carefully constructed "safe space" where making sure people get the credit is more important than the work itself. That only happens in fields/problems where no one actually really cares about the output.