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Caltech Mathathon – first hackathon ever devoted to research level mathematics

mathathonchallenge.com

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Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#91

Post by wltyn »

brian-bfz wrote: post #56
maypop wrote: post #54

Earlier quoted context omitted.

Is this hackathon only for those with formal math backgrounds? I've seen a few instances of AI assisted advances math and cs this year that were _not_ published by authors with formal backgrounds in those fields (or even institutional affiliation). Which makes me wonder if they would have a place at the event.

Yes. To us, solving a problem with AI doesn't matter as much as selecting the right problem and understanding the proof. A participant must have a good mathematical intuition.

Does Mech Eng masters count?

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#92

Post by reasonableklout »

brian-bfz wrote: post #79
reasonableklout wrote: post #74

Earlier quoted context omitted.

It’s a noble goal to change the incentives, but how will you prevent the headlines from this event being “students prove Collatz conjecture with Claude” and instead be “students give great explanation of Collatz conjecture proof”?

You're right that we can't. We'll be responsible in our press releases and award prizes based on explanation, but we don't control the headlines. However, this is already an improvement over the current state, where results are announced by headlines alone.

Perhaps monetary prizes would help? "Doe & Smith explanation of Erdos #423 solution wins $10,000 prize" would certainly attract attention.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#95

Post by nill0 »

If anybody is competing in the contest, this may be helpful as a starting point!

Open Problems in Computational Geometry Listed by Erik Demaine, Joseph Mitchell, Joseph O'Rourke in 2024

https://topp.openproblem.net/

And also the popular list below, which contains some of the frontier problems and undefeated beasts that have remained unsolved for decades, some even for centuries.

https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_m...

Caution: Solvability is not guaranteed!

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#96

Post by youoy »

brian-bfz wrote: post #59
youoy wrote: post #57

Earlier quoted context omitted.

Hey! Thanks for answering, i appreciate it. Dont get me wrong, this is what you should be doing, understanding what these models are good (and most importantly bad) for. My observation is that this is very very valuable for the labs, and in an ideal world they should be paying you to do this, not just the tokens and "prize" for the winners. I am also a bit frustrated seeing maths go in the direction of prompt enginne…

Agreed. I think we share the same concerns about LLM use. We just drew different conclusions. Mathathon's goal is to reshape rather than stop LLM use. Can we set high standards for LLM use? Can we highlight the roles of a mathematician beyond proof generation? Can we redesign our incentives to promote these standards and roles? I'd love to hear your thoughts on how to improve this event. We're very open to criticisms…

Thanks again for answering! As I told you I think the event is a good idea from your side. I would try to go beyond proof prompting and verification, and discussing the questions that you wrote above is the way to go.

I am mathematitian that is working as a software engineer. I have see first hand what these models are doing to SE. Its not that writting well thought, and compact code is not a good idea anymore, or that it doesnt beat LLM code, but that the people that see the value are a minority. If you write a piece of old school code in an LLM repo, it doesnt really make a difference, because old school code requires a team effort.

In maths the situation is not exactly the same. Probably reading a good piece of well thought math inside a book of LLM assisted proofs will stand out so much for the carefull reader that there will be no question about the value.

However, if the only way to get a position at a university is to print as much papers as possible, then who would risk printing 1 paper instead of 5 for doing old school maths?

So the solution to this is building a culture and community effort around these topics. And for that the topics need to be openly discussed.

Good luck with the organisation! And thanks again for the conversation!

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#97

Post by ktallett »

a2ff6eeb0 wrote: post #64
ktallett wrote: post #62

Earlier quoted context omitted.

I get your point and agree to some extent, but you can't understand the proof without significant background in Maths so it will just allow mathematicians to solve issues faster than not have the opportunity at all.

Why do people need to understand proofs? If Amazon improves package routing with new advances in graph theory, my cat doesn't need to understand it to benefit from better shipments of cat food. Similarly, humans don't need to be involved in scientific advances to benefit. We just need an aligned AI to take over the scientific thought for us. AI is already better than all but the top tier of humans at doing mathematic…

It is the top tier of humans in these fields that are making the significant breakthroughs. The top tier of breakthroughs are not being post on here (which are nowadays usually short form articles of not incredible quality). The code at start ups is not commonly in the top tier of a breakthrough. AI can do averaged work and derivations off what has gone before which Maths works very well for as there is a clear set of rules. The same in physics if you ask AI for help adapting a simulation, yet it couldn't pluck the idea if no one has done it before.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#98

Post by Ey7NFZ3P0nzAe »

falcor84 wrote: post #22
Semkas wrote: post #5

Won't deny that this is an interesting idea, but I feel like waiting on the output of an LLM for 40 hours feels like it is completely antithetical to what makes classic Hackathons appealing / educative. More generally, I don't think the shape of a hackathon (intensely working for a short timespan) maps at all onto the way LLM Math progress has seemingly been made so far; AFAIK it mostly involves picking out something…

But it's not "waiting on the output of an LLM for 40 hours" any more than a regular hackathon is "waiting for my damn teammates to finish their part for 40 hours". From my experience using agentic coding for hackathons, the best teams are those that coordinate with the AI agents in relatively quick cadence, generally giving it small tasks and steering it often. Teams may want to run some long-running sessions too, es…

I can't wait to see if the team that fares best is the one that steers often or the one that interferes the least.

So far humans failed at those problems. Also IIRC there was a guy that proved a substantial problem 2-3 months ago by basically pasting over and over "keep looking for a solution" or something like that for 2 days with little formal math background.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#99

Post by a2ff6eeb0 »

tacomonstrous wrote: post #84
a2ff6eeb0 wrote: post #76

Earlier quoted context omitted.

They don't actually say anything about why anyone should fund this, though. I don't get why a society should worry about progress in mathematics if there's no practical benefit expected. Maybe there's two kinds of math that we need? Useful math and navel gazing, and we can hand the first to the machines, and let hobbyists do the second in their free to entertain themselves?

It's hard to know what math is 'useful' a priori. That's always been the argument for supporting basic research. This is not why I am a mathematician however. I think there's intrinsic value into understanding something of depth and meaning, but the societal setup we have now that mostly agrees this is valuable is probably a very contingent phenomenon that is unlikely to last much longer.

Yes, so if there's useful math, you throw the LLM at it and use the results, no humans needed.

Humans can try to extract some ideas from the million line lean proofs, if they want to, I guess. But I can't imagine anyone really funding the human part of it.

Re: Caltech Mathathon – first hackathon ever devoted to research level mathematics

#100

Post by a2ff6eeb0 »

ktallett wrote: post #97
a2ff6eeb0 wrote: post #64

Earlier quoted context omitted.

Why do people need to understand proofs? If Amazon improves package routing with new advances in graph theory, my cat doesn't need to understand it to benefit from better shipments of cat food. Similarly, humans don't need to be involved in scientific advances to benefit. We just need an aligned AI to take over the scientific thought for us. AI is already better than all but the top tier of humans at doing mathematic…

It is the top tier of humans in these fields that are making the significant breakthroughs. The top tier of breakthroughs are not being post on here (which are nowadays usually short form articles of not incredible quality). The code at start ups is not commonly in the top tier of a breakthrough. AI can do averaged work and derivations off what has gone before which Maths works very well for as there is a clear set o…

Pure cope.
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