I wonder if top labs will soon abandon math progress like they did go and chess.

In example of go where I'm more familiar Google deep mind poured large resources to get a super human performance first, establish superiority and abandon it. The community then built their own tools starting from reproducing their papers.

I think similar thing might happen to math. Nobody outside of math cares too much about Hamiltonian cycles in some bizarre graphs or proving lower bounds on complexity of some problem.

Once those results stop being worthy of mainstream media attention, they will abandon math and the progress will be done by mathemicians guiding the models and the community will likely establish some new rules about what makes a valuable contribution. Merely solving not yet solved problem might not be it anymore.

The biggest problem is LLM tends to produce over engineered, very complicated proofs that are an eyesore even for relatively simple problems. Give it a beautiful Olympiad geometry problem and LLM will tear it apart into ugly algebraic calculations, turns all lines and circles into equations and calculate their intersection points that spans multiple pages because it is a guaranteed way to solve it. Correct, but hardly any use to the user.

This argument implicitly makes a few assumptions which will probably not hold in the very near future.

One is that AI will continue hallucinating in a manner that is not easy to verify, second is that AI will not be enhanced to produced more simplified amd robust outputs, and third that a human will be required to do that. What humans in the loop are doing now is verify the process, propose shortcuts and add legitimacy, through the verification process, if that ends up being succesful its highly likely a lot less mathematicians will be required in the future.

The conclusion that this is not productive focuses on the mathematicians, but it is very productive in terms of hundreds of proofs being produced that had previously consumed uncountable hours of the brightest minds. Unless it ends up being the greatest hallucination ever ofcourse

> simply dumping proofs on the math community and expecting others to do the grunt work of verifying, refining, and expanding on them is hardly a productive way to advance the field.

I tend to agree with this, but what is the alternative? Should OpenAI and Anthropic employ hundreds of mathematicians to do this work? Should they just not solve math problems within their reach?

As with any field, convincing people to care about your ideas and your approach is half the battle

Many of the best startup ideas by the best product and engineering minds failed to gain attention and funding. Same with much of the best music - relegated to hard drives with derivative ideas only resurfaced decades later

I would expect much of the recent math dump will be leveraged by other LLM-driven research teams rather than read in depth by a human

> the grunt work of verifying, refining, and expanding on them

What work do you think mathematicians do normally?

Like they sit whole day and have ideas? And where are the ideas?

The way I see it, _some_ mathematicians enjoy solving puzzles, and now AI is better at solving puzzles.

This does not affect people building new theories.

Also, it's quite prestigious to write a _book_ on some topic. And guess what writing a book entails? Refining and expanding. What you call grunt work.

Right, easy comparison to make the the open source community for software.

And it's not like this is something where we're loaned some top math genius for a limited amount of time and we have to make the most of it. Rather, this is a new high water mark. The accessibility of the results is no longer scarce. The scarcity has shifted, and that's where the focus of the math ecosystem should shift as well. And it doesn't help for a frontier community to saturate and take over messaging pipelines that were typically managed by the math ecosystem. It's not about "stay in your lane" but rather "we need coherence and be careful not to break the system."

Just two cents from someone who could screw up basic cashier math on any given day.

Less Liszt/Paganini, more chamber music and teaching. I like it!

> simply dumping proofs on the math community and expecting others to > do the grunt work of verifying, refining, and expanding

Hm, kinda reminds me of my college days. "Proof trivial, left as home work." was a sentence my Profs loved to say.

> Too much effort is being invested in proving that the exponential curve is still holding.

Given sustained exponential growth is mathematically impossible to maintain with finite resources, it's funny to me they're using advanced mathematics to try and achieve this.

I'm sorry I disagree entirely.

The more information the better.

The entire purpose of published work is to remove noise (and perhaps incentivize work through attributing credit).

This information is now out there. You can choose to ignore it if you wish. You may just find yourself a century behind in research.

And on that point most of this research has been looked at by their mathematics panel and comes with lean certificates, it's not exactly noise.

This to me is more the old guard not willing to let go or change their ways.

Once LLMs pass the threshold to being to invent new general-purpose methods and frameworks, the frontier is irreversibly lost to AI and it becomes simply a hobby that mathematicians pursue. They work through, digest, and maybe write up the proofs for understanding. But the real meat will be growing the LLMs. Who knew software eats the world was so true?

> but simply dumping proofs on the math community and expecting others to do the grunt work of verifying, refining, and expanding on them is hardly a productive way to advance the field

This is a transitive period. In a few years, verification and exchange between model instances will happen faster than humans can follow. Human input will be an ethical question, and not a productivity one, because it will be the bottleneck in any science.

Its kinda like the arms race in the cold war. There came out some truly marvelous technologies but the actualy goals were frankly terrifying.

Generate and dump on others to verify is how the generative-AI people operate. Be it in maths or just your regular job.

The amount of Confluence pages of "research" that is just a dump of LLM output someone passed to me to review is staggering

I hate this approach, it's unbelievably selfish

That seems short sighted though. A few years ago models couldn't do this at all, I'm not sure there's any evidence to suggest exploring and refining results is outside their capabilities or will remain so.

OAI obviously have a fiscal incentive here, but to presume a year from now we won't see improvements and more succinct work on the results coming from models?

> There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems) than in genuinely contributing to mathematics

I feel the same way about academia, the papers, the citations, the ego, the narcissism and the taxpayer codependency that got cut off and turns out wasn’t necessary at all thanks to a private sector entity running laps around them

I don’t feel that academics need to pursue the discipline and distributed brain-wracking that has sometimes resulted in the solved math problems, just because more times they find other nooks and crannies to explore along the way. I think the blueprint is enough. Standing on the shoulders of giants is good enough.

and if the concern is that they can’t figure out what to do with a proof, next year’s AI will

Why not asking another chatbot to verify, like what we are doing with coding ?

> There seems to be more interest in hitting some arbitrary benchmark (we proved X unsolved problems)

> genuinely contributing to mathematics

What's the difference between the two? Proofs are no longer the goalpost?

Yes, it is indeed a balanced view.

Those few thousand mathematicians are now getting a taste of their own medicine. After all, it was people with extraordinary mathematical talent who developed machine learning and large language models, leaving hundreds of millions of people who earn their living through speaking, writing, or teaching worried about their future job prospects.

Still, I believe almost everyone will be fine. Perhaps AI will also prove good at coming up with new conjectures, and some mathematicians may shift towards applied mathematics or other sciences.

This Math 1.0 followed by Math 2.0 framing is wrong. Mathematics did not start a few decades ago when problem solving became the norm. And it will not end now when problem solving turns out to be "easy".

Mathematics will revert to it's main practice, which is to study.

There are lots of weird panic reactions by some prominent problem solvers. See for example the ridiculous cease and desist like statement of AHM shared at Tao blog.

Put this Math 1-2.0 with that AHM statement together and you'll realize that this is a power struggle and that you see only one side of it.

Mathematicians have very diverse opinions about this. I, for example, am for as much as possible automatic harvesting of all these "low hanging" fruits. Should be disclosed as soon as possible, free of any bottleneck, and citable. The mathematics community may do whatever its various members desire to do with these results. Let them decide individually what to do with them. This AI tool is here to stay.