All your jobs are belong to them.

OpenAI was started because Elon and Sam thought Demis was going to make himself dictator and they wanted a piece of that action (reading between the lines). All the labs, even Anthropic have the same idea dressed in different marketing gloss. The major exception (I imagine) are Chinese labs, since the Communist Party of China will demand control over these labs and their models. Good! Democratic human control is a good thing. Certainly, there is more democracy in China than in America. That's the idea of socialism, democracy for the workers, not for the capitalists (we do the inverse).

reminds an old sci-fi story where top engineers were shown a video of a genius inventor who invented anti-gravity and unfortunately died while testing his apparatus which was clearly anti-gravitating in the video. Thus believing that it is a solved problem, just need to rediscover the lost solution, the engineers quickly developed anti-gravity. The original video happened to be a fake specially created for that purpose.

>thus themselves holding a monopoly on certain aspects of mathematics

Monopoly prevents others. In science me knowing something doesn't prevent others from obtaining the same knowledge, especially in math where any knowledge is just a result of thinking.

The math establishment is trying to bring into the math the rules and notions similar to those of the patent and trademark laws. Those attempts should be outright rejected.

Difficult math problems are useful benchmarks and milestones. It's well worth throwing money at solving a problem if it drives competition and improves models significantly. The benefits become available to everyone, including the thousands of professional mathematicians who can use them to become more productive.

- releasing papers using the normal process to allow peer review

- giving talks etc to disseminate knowledge so humans understand the result

- writing papers in a way (standard terminology etc) that allows mathematicians to digest the result (some AI math papers comprise a huge verbose load of non-standard terminology and waffle and then a massive lean proof. This is very hard for humans to actually understand, and means it's hard for others to take the work forward.)

- giving appropriate credit to results that are used to derive the work

It includes some specific recommendations for situations where the person prompting the model is not in a position to understand the output, and frankly these are really welcome given situations like the recent case at Anthropic where a non-mathematician at Anthropic prompted claude to make a significant improvement to the bounds of a problem related to the Riemann Zeta function[1] which led to widespread misreporting and claims (not by Anthropic themselves notably) that the Riemann hypothesis itself had been proved, which is emphatically not the case.

Research mathematics is fundamentally a collaborative activity and the way in which some of these results are released is done to maximise PR but means a ton of the mathematical value is left on the table.

[1] https://www.anthropic.com/research/riemann-zeta. As I understand it, the Riemann Hypothesis says that all non-trivial zeroes of the zeta function lie on a line called the critical line. Two centuries of previous work had established that at least something like 40.9% of the zeroes lie on the line and noone has ever found a non-trivial zero that does not lie on that line. Claude (with prompting from a non-mathematician to "try harder" etc) improved this bound massively to 67%. Now a lot of people said things like "OK so all we've got to do is to improve that to 100% and we've proved the RH", which is definitely not true unfortunately, because you can say that in the limit the proportion of the zeroes on the line is 100% and still have infinitely many which are not.

Pretty sure AI will do better for that.. mathematicians need to be centaurs like the rest of us and stop rhetoric that is going to make existing math centaurs feel like they might get math-cancelled

LLMs have been around for years, and they're explicitly trained on the entire history of human mathematics (without which they'd be unable to do anything).

In a sense, how do you know whether the problem your AI has just solved is important? A simple proxy is to just check whether humans have thought it's important.

That's also why famous open problems are a good benchmark or proxy: you don't need to convince the rest of the world that the problem your lab's new AI just solved is actually useful or hard.