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A misalignment of AI in mathematics

mathandai.org

311–320 of 642 posts

Re: A misalignment of AI in mathematics

#311

Earlier quoted context omitted.

Yeah. My other favorite example are books. Why do nonfiction books exist? There are some pathologies and corner cases, but fundamentally: to develop and share new ideas. Downstream from that, if it reads well and if you're lucky, you make some money. But now, LLMs can generate hundreds of books per hour. They make up 80-90% of new arrivals in many nonfiction categories on Amazon. They short-circuit the system, allowi…

Now you piqued my interest. Any good AI-written books out there? I thought it's all slop.

Given the witch hunts around AI creative output, nobody who has put in work to avoid the stigma is going to out themselves.

Re: A misalignment of AI in mathematics

#314
post #266

Earlier quoted context omitted.

So it wasted everyone's time, thousands of hours of research trying to disprove something said very loudly. What OpenAI is doing is a DoS of the scientific community: wasting your time trying to check if they're not wrong, and claiming glory in the mean time.

Agreed! Although, if done by a mathematician, it's not a ~complete waste. I think the community learns something along the way. Is there an established term for the idea of "DoS"? I've taken to calling it slop fatigue.

Denial of service is the established term. Hammering their API (reviewer committees) would be an informal one

Re: A misalignment of AI in mathematics

#315
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 to the academy, industry and science at large will likely be much more Machiavellian about such concerns. 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 and acknowledgement of widespread and dramatically evolving 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'll exist with or without attribution. Would be a shame for the academy to land on the wrong side of history and refuse stewardship of upcoming AI-assisted mathematics, including provenance, because of this misalignment. If attribution is important, then the academy will set aside the institutional resources to do it. If you succeed at having model developers participate, I commend it. To let mathematics be born in isolated context windows and only serve narrow, localized engineering purpose without rightful addition to the canon, would be a tragic, yet preventable, loss.

Re: A misalignment of AI in mathematics

#316
post #290

Earlier quoted context omitted.

It's not a simple matter of "becoming good at", and yes, I could very well have similar concerns, depending on how it impacts the field. The statement itself mentions that such concerns exist in many other fields. I doubt OpenAI will take such a combative stance and accuse these mathematicians of "demanding" things, as you do. As I said, the purpose of this is marketing and the statement simultaneously undermines the…

So let’s say OpenAI cure cancer and put every cancer researcher out of work depriving them of intellectual satisfaction, this would also be a problem? It would certainly impact the field. The fact is these fields are supported by society because of the benefits to everyone else. Once the same results can be achieved in a cheaper and faster way that is what will be done. We should mourn this in the same way we do bugg…

Why don't we first assume OpenAI can create a cold fusion reactor and then give them a trillion dollars to get it done?

Re: A misalignment of AI in mathematics

#317

To be honest I didn’t get that much outrage here: https://news.ycombinator.com/item?id=49662116 It seems like a lot of the issue here is that these problems aren’t interesting in and of themselves, but they lead down interesting roads. It defeats the purpose if you solve them without getting any real understanding. It’s akin to saying you’ve solved “pancake flipping” problems with a waffle maker, or “travelling sales…

Nothing is stopping these folks from continuing to study the problems and arriving at their own solutions so they can continue having whatever insights along the way. Well, one thing is stopping them. There will be no more adoration for their genius. If you truly do it for understanding and not the attention, carry on. AI should change nothing about your motivations.

Your comment perfectly illustrates why most are missing the point. Many people, including you, deeply believe that most mathematicians are chasing adoration of their genius, otherwise why would anyone care about such abstract work?

People like Grigori Perelman would baffle you, a mathematician who solved the Poincaré Conjecture, refused the monetary prize, field medal and continues to live a life of total recluse.

For most mathematicians their primary drive is chasing the unknown, not for anyone’s adoration, but to pursue their desire to see what lies in the beyond.

Re: A misalignment of AI in mathematics

#318
post #184

Earlier quoted context omitted.

It has been best at chess for quite a while. Yet everyone knows who is Magnus Carlsen, even though at no point of his career he was stronger than the machine

Magnus Carlsen plays fellow humans at the game because people still care about human competitions. What motivation would a mathematician have for solving already solved problems by hand? Can you imagine someone spending years working on a proof for an already-proved theorem just in case it leads to new insight?

If insights and human understanding are more important than specific results, I don't see why people should stop producing insights and human understanding. "Working on a proof" in today's sense of trying to come up with a proof before others probably stops being useful, other ways of working will be needed

Re: A misalignment of AI in mathematics

#319
post #254

Earlier quoted context omitted.

> Dr. Tao said the same thing. Apparently he has since changed his mind.

Did he say so somewhere? I don't think these ideas are contradictory. It's just an pro AI tooling but anti-slop stance.

Where is the difference?

Re: A misalignment of AI in mathematics

#320

They can get with the program or be the equivalent of a genius SWE writing assembly on punchcards in 2026. The only thing I read from this is their ego being bruised by a machine. If these people cared more about discovery and advancement of human knowledge the only thing they should be doing is celebrating. There's no proof of plagarism but that's an independent issue. How are they not realizing that in the future c…

for the same reason why you do not get full credit for only writing down an answer without showing work in an exam.
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