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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

#71

Post by danielmarkbruce »

brian-bfz wrote: post #42

Hey guys, I'm one of the organizers. AMA. - We are a team of undergrads at Caltech. We don't represent Caltech, any Caltech departments, or any of our sponsors. - We don't receive monetary compensation. All the funding raised goes toward paying our judges and participants. - Our goal is to promote responsible AI use. You can read more about our commitments here: https://mathathonchallenge.com/faq.html

Why not specify 2-3 problems? Won't you have people show up having already spent a bunch of time on their self chosen problem? Which sort of defeats the point of seeing what you can do in a short period of time?

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

#72

Post by danielmarkbruce »

queuebert wrote: post #61
brian-bfz wrote: post #42

Hey guys, I'm one of the organizers. AMA. - We are a team of undergrads at Caltech. We don't represent Caltech, any Caltech departments, or any of our sponsors. - We don't receive monetary compensation. All the funding raised goes toward paying our judges and participants. - Our goal is to promote responsible AI use. You can read more about our commitments here: https://mathathonchallenge.com/faq.html

Serious question: Are you sure solving abstract mathematical problems with AI is responsible use? You will likely put mathematicians out of jobs, and I doubt solving the Collatz conjecture is urgent or will save lives. It also robs a future Fields medalist of the pride of doing all by themselves. All things AI seems to assume that more and faster is better, but there is no justification of that assumption. As a biolo…

It's more responsible than the use of electricity for a messaging board for people to argue minutiae.

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

#73

Post by [deleted] »

rookienumbers30 wrote: post #24
Donald wrote: post #21

Earlier quoted context omitted.

Have you done any math hacking with sol/astra or fable? It’s more fun than using them for coding. The models are great at the monotony, like constructing a Gröbner-basis, etc. But they’re all still absolutely awful at coming up with new ideas, new proof methods, or new constructive forms. So you spend all your time on coming up with novel hypotheses yourself and handing off the rote work to an agent. It’s also quite…

"A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies." I wonder how models perform on finding analogies between analogies

[deleted]

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

#74

Post by reasonableklout »

brian-bfz wrote: post #67
queuebert wrote: post #61

Earlier quoted context omitted.

Serious question: Are you sure solving abstract mathematical problems with AI is responsible use? You will likely put mathematicians out of jobs, and I doubt solving the Collatz conjecture is urgent or will save lives. It also robs a future Fields medalist of the pride of doing all by themselves. All things AI seems to assume that more and faster is better, but there is no justification of that assumption. As a biolo…

I don't think AI will solve more math problems in a world with Mathathon than the counterfactual by EOY. People will use AI in math anyways. What matters is: can we encourage them to do so transparently and with full understanding of their results? Can we change the incentives in academia to reward problem selection and verification over proof generation?

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”?

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

#75

Post by mattmcal »

a2ff6eeb0 wrote: post #70
mattmcal wrote: post #66

Earlier quoted context omitted.

Well, for one, most math proofs don't have any practical applications, so a proof that no one reads is basically a digital paperweight. You might as well suggest AI write novels for other AI to read.

The hope is that some of them end up being useful; otherwise, nobody would be funding math departments. Mathematics typically anticipates and enables new physics and chemistry. If people are just doing math to kill time, I don't get why anyone would bother with AI. Do people really enjoy picking through a million lines of generated Lean code, if it's not for any practical use?

If you're interested in the topic enough to comment on it, you'll probably find it worthwhile reading a mathematician's perspective. Here's the prolific Terry Tao: https://mathstodon.xyz/@tao/117219548485446992

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

#76

Post by a2ff6eeb0 »

mattmcal wrote: post #75
a2ff6eeb0 wrote: post #70

Earlier quoted context omitted.

The hope is that some of them end up being useful; otherwise, nobody would be funding math departments. Mathematics typically anticipates and enables new physics and chemistry. If people are just doing math to kill time, I don't get why anyone would bother with AI. Do people really enjoy picking through a million lines of generated Lean code, if it's not for any practical use?

If you're interested in the topic enough to comment on it, you'll probably find it worthwhile reading a mathematician's perspective. Here's the prolific Terry Tao: https://mathstodon.xyz/@tao/117219548485446992

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?

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

#77

Post by hatsix »

lovasoa wrote: post #65
suriyaG wrote: post #63

Earlier quoted context omitted.

> you will likely put mathematicians out of jobs. why is that a concern in this context? would you have asked the same about steam engines and horses? this is a really cool concept, organized very well. and that is very commendable.

steam engines solved a problem people had

Don't respond to a strawman argument with another strawman. The post you are responding to ignored the reasons given in the second paragraph. They're just trying to score points by preaching to the choir, not engage with the concern.

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

#78

Post by brian-bfz »

danielmarkbruce wrote: post #71
brian-bfz wrote: post #42

Hey guys, I'm one of the organizers. AMA. - We are a team of undergrads at Caltech. We don't represent Caltech, any Caltech departments, or any of our sponsors. - We don't receive monetary compensation. All the funding raised goes toward paying our judges and participants. - Our goal is to promote responsible AI use. You can read more about our commitments here: https://mathathonchallenge.com/faq.html

Why not specify 2-3 problems? Won't you have people show up having already spent a bunch of time on their self chosen problem? Which sort of defeats the point of seeing what you can do in a short period of time?

Solving a problem is the easy part with AI. Selecting a problem worth solving is half of the challenge.

We allow prior work as long as it's labelled. We record chat logs, so it's easy to verify what's prior work. When we evaluate the significance of a result, we focus on the part produced at the event.

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

#79

Post by brian-bfz »

reasonableklout wrote: post #74
brian-bfz wrote: post #67

Earlier quoted context omitted.

I don't think AI will solve more math problems in a world with Mathathon than the counterfactual by EOY. People will use AI in math anyways. What matters is: can we encourage them to do so transparently and with full understanding of their results? Can we change the incentives in academia to reward problem selection and verification over proof generation?

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.

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

#80

Post by ajkjk »

brian-bfz wrote: post #78
danielmarkbruce wrote: post #71

Earlier quoted context omitted.

Why not specify 2-3 problems? Won't you have people show up having already spent a bunch of time on their self chosen problem? Which sort of defeats the point of seeing what you can do in a short period of time?

Solving a problem is the easy part with AI. Selecting a problem worth solving is half of the challenge. We allow prior work as long as it's labelled. We record chat logs, so it's easy to verify what's prior work. When we evaluate the significance of a result, we focus on the part produced at the event.

it seems like a person could cheat by finding an open problem that's AI-solvable ahead of time (by trying many problems), and then pretend to do it for the first time in the competition. You can't verify past chat logs so make sure they didn't already realize it would work.

just something to think about

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