A Misalignment of AI in Mathematics

Comments moved to https://news.ycombinator.com/item?id=49662371.

Tao's calls for respect for provenance in mathematics publication are laudable but most likely naive given the closed nature of frontier model training data curation. Anthropic and OpenAI may react with a symbolic and short-lived olive branch, yet provenance is a larger issue that has impacted other fields beyond mathematics. While traditional respect for lineage in mathematics is of value in the academy, industry and science at large will likely be much more Machiavellian about concern for attribution. Mike McCoy's recent article is also timely (https://mbmccoy.dev/posts/mathematical-conservatory/). The parallels to the music conservatory are quite telling -- academic music describes a musical culture in preservation that has completely lost touch with musical developments beyond the early 20th century. Mathematics may very well evolve separately and with very different values than the academy upholds. The crisis of music at the academy is a cultural disconnect and a serious loss of critical analysis add acknowledgement of widespread music practice; however, for mathematics, the impact would have much more severe ramifications for education and human development if the academy forces a schism with AI. As models improve they very well may be inventing mathematics -- science and engineering may grasp for them -- they may exist with or without attribution. Would be a shame for the academy not to take on the responsibility of stewardship of coming mathematics, including provenance, because of this misalignment.

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0].

Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a painting could.

He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts.

Do you see some parallels as well?

[0] https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiq...

It's a turning point for science and beyond. AI has shown itself to be transformative. Even today, it is already changing how research in math (and other sciences) is conducted. In the near future, whether it is LLMs or some other superior method, its capabilities are only expected to grow. The time to ask the question is now: Will AI be arguably the best tool at scientist's disposal, or will it instead be paraded around as a super brain collective that no human or group of humans can compete with, discouraging entire new generations of future scientists from ever entering the field? The jury is out on this one.

In the Economist article Tao links, Hugo Duminil-Copin, draws a comparison: airdropping someone on the summit of Mount Everest is very different from climbing it.

The fundamental issue with AI solving any perceived difficult problem is that we have lost the journey. The sight atop Mount Everest looks much different when you have climbed compared to being dropped from above.

All clear and understandable. I completely agree.

As developers, we’re seeing this a little earlier.

At this rate AI will be doing all of the mathematics within 5 years, I don’t see why a mathematician would be worried about anything other than that at this point?