Comment by seanhunter | Hacker News Reader

Comment by seanhunter | Hacker News Reader

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TFA isn't asking for mathematicians to be protected from AI. It's asking AI labs to hold themselves to the standards of the mathematical community:

- 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.

From the opening paragraph:

we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models

From point 2 under section "1. Background":

AI labs should provide significant support, including funding, to help develop this understanding

Point 3 under the same section:

The development of human understanding must remain organic and community led. It should not be directed by AI labs, even when the labs have produced the results.

If, as you say, they are "asking AI labs to hold themselves to the standards of the mathematical community", I must conclude that the mathematical community

1. Ideally wants a monopoly on mathematics research.

2. Demands money from those who dare violate their ideal monopoly.

3. Insists that the ideal monopoly remain in charge.

Math is a tool. It's what people do with the tools after they are invented that matters - and with mathematical tools sometimes that wait is hundreds of years.

The mathematics community has found that the tools have value long after being invented if the inventor leaves his tools in a specific format. The community is doing its best to preserve that - not because they want less toolmakers, but rather because they want the tools to be useful when they become needed.

Your monopoly theory lacks a credible motive and also ignores the fact that your quote specifically targets the frontier labs, not LLMs or computational tools in general. The group (https://agmai.org/) comprises of world-renowned mathematicians, including several Fields medalists, who have nothing left to prove. If they felt like it they could quit mathematics today and take private sector jobs paying far more than their professor salaries.

The basic purpose of mathematics has always been human understanding (see for example https://mathoverflow.net/a/44213), and the working group's various recommendations simply aim to ensure that computer-generated mathematical activity aligns with that purpose.

Yes. It’s remarkably flagrant, and it’s an example of an academic mindset that’s likely been holding progress back across multiple fields. It’s about to be broken rather badly, and it will show where progress has been stifled.

Maintaining the existing standards is in fact a form of protection from AI disruption. They are asking the AI companies to follow their norms, instead of them having to conform to new norms created by AI. They don’t want to have to change the way they do things, understandably!, and are asking the companies to accommodate their way of life.

New norms are only worth adopting if they are clearly better, and that is far from obvious for whatever norms the proprietary AI companies are trying to push. Also their letter specifically targets proprietary AI companies, not computational tools in general which mathematicians do use when they advance mathematical understanding.

Better for who? If I don’t care about the welfare of mathematicians and just the advancement of mathematics, would AI doing the math not be better for me?

As well, if the open models were as good as the proprietary ones, do you think they wouldn’t still have complaints?

Those seem reasonable apart from this one:

> - releasing papers using the normal process to allow peer review

I'm not an academic but I've heard enough stories about how this can very much act as gatekeeping that I don't think it is a good request.

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