I'm a mathematician relying heavily on AI as an association engine of massive scope, to organize and expand my thoughts. One doesn't get best results by "testing" AI.
A surfboard is also an amazing tool, but there's more to operating one than telling it which way to go.
Many people want self-driving cars so they can drink in the back seat watching movies. They'll find their jobs replaced by AI, with a poor quality of life because we're a selfish species. In contrast Niki Lauda trusted fellow Formula 1 race car driver James Hunt to race centimeters apart. Some people want AI to help them drive that well. They'll have great jobs as AI evolves.
Gary Kasparov pioneered "freestyle" chess tournaments after his defeat by Big Blue, where the best human players were paired with computers, coining the "centaur" model of human-machine cooperation. This is frequently cited in the finance literature, where it is recognized that AI-guided human judgement can out-perform either humans or machines.
Any math professor knows how to help graduate students confidently complete a PhD thesis, or how to humiliate students in an oral exam. It’s a choice. To accomplish more work than one can complete alone, choose the former. This is the arc of human evolution: we develop tools to enhance our abilities. We meld with an abacus or a slide rule, and it makes us smarter. We learn to anticipate computations, like we’re playing a musical instrument in our heads. Or we pull out a calculator that makes us dumber. The role we see for our tools matters.
Programmers who actually write better code using AI know this. These HN threads are filled with despair over the poor quality of vibe coding. At the same time, Anthropic is successfully coding Claude using Claude.
That centaurs can outperform humans or AI systems alone is a weaker claim than "these particular AI systems have the required properties to be useful for that". Chess engines consistently produce strong lines: using one does not feel like gambling, even if occasionally you can spot a line it can't. Using LLMs does feel like gambling. I think you're overgeneralising.
These are very serious research level math questions. They are not “Erdős style” questions; they look more like problems or lemmas that I encountered while doing my PhD. Things that don’t make it into the papers but were part of an interesting diversion along the way.
It seems likely that PhD students in the subfields of the authors are capable of solving these problems. What makes them interesting is that they seem to require fairly high research level context to really make progress.
It’s a test of whether the LLMs can really synthesize results from knowledge that require a human several years of postgraduate preparation in a specific research area.
Not necessarily. Even the statements may not appear in the final paper. The questions arose during research, and understanding them was needed for the authors to progress, but maybe not needed for the goal in mind.
> the answers are known to the authors of the questions but will remain encrypted for a short time.
Ok. But humans may be able to solve the problems too. What prevents Anthropic or OpenAI from hiring mathematicians, have them write the proof and pass it off as LLM written? I'm not saying that's what they'll do. But shouldn't the paper say something about how they're going to validate that this doesn't happen?
Honest question here. Not trying to start a flame here. Honestly confused how this is going to test what it wants to test. Or maybe I'm just plain confused. Someone help me understand this?
This is not a benchmark. They just want to give people the opportunity to try their hand at solving novel questions with AI and see what happens. If an AI company pulls a solution out of their hat that cannot be replicated with the products they make available to ordinary people, that's hardly worth bragging about and in any case it's not the point of the exercise.
The authors mention that before publications they tested these questions on Gemini and GPT, so they have been available to the two biggest players already; they have a head start.
It's possible but unlikely given the short timeline, diverse questions that require multiple matheamticians, and low stakes. Also they've already run preliminary tests.
> It's possible but unlikely given the short timeline
Yep. "possible but unlikely" was my take too. As another person commented, this isn't really a benchmark, and as long as that's clear, it seems fair. My only fear is that some submissions may be AI-assisted rather than fully AI-generated, with crucial insights coming from experienced mathematicians. That's still a real achievement even if it's human + AI collaboration. But I fear that the nuance would be lost on news media and they'll publish news about the dawn of fully autonomous math reasoning.
The abstract of the article is very short, and seems pretty clear to both of your questions.
This is what is special about them:
> a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now;
I.e. these are problems of some practical interest, not just performative/competitive maths.
And this is what is know about the solutions:
> the answers are known to the authors of the questions but will remain encrypted for a short time.
I.e. a solution is known, but is guaranteed to not be in the training set for any AI.
> I.e. a solution is known, but is guaranteed to not be in the training set for any AI.
Not a mathematician and obviously you guys understand this better than I do. One thing I can't understand is how they're going to judge if a solution was AI written or human written. I mean, a human could also potentially solve the problem and pass it off as AI? You might say why would a human want to do that? Normal mathematicians might not want to do that. But mathematicians hired by Anthropic or OpenAI might want to do that to pass it off as AI achievements?
Well, I think the paper answers that too. These problems are intended as a tool for honest researchers to use for exploring the capabilities of current AI models, in a reasonably fair way. They're specifically not intended as a rigorous benchmark to be treated adversarially.
Of course a math expert could solve the problems themselves and lie by saying that an AI model did it. In the same way, somebody with enough money could secretly film a movie and then claim that it was made by AI. That's outside the scope of what this paper is trying to address.
The point is not to score models based on how many of the problems they can solve. The point is to look at the models' responses and see how good they are at tackling the problem. And that's why the authors say that ideally, people solving these problems with AI would post complete chat transcripts (or the equivalent) so that readers can assess how much of the intellectual contribution actually came from AI.
February 13 seems right to me. I mean it's not like LLMs need to manually write out a 10 page proof. But a longer deadline can give human mathematicians time to solve the problem and write out a proof. A close deadline advantages the LLM and disadvantages humans which should be the goal if we want to see if LLMs are able to solve these.
The goalposts have been on wheels basically since the field was born. Look up "AI effect". I've stopped caring what HN comments have to say about whether something is or isn't AI. If its useful to me, I'm gonna use it.
For policy feedback (Gas^∆ ÷ 2) · diag(u) · (Gas^∆ ÷ 2)^t A dampened shock propagates forward,is treated as independent, then feeds back into the system,that's quadratic form.
I'm a mathematician relying heavily on AI as an association engine of massive scope, to organize and expand my thoughts. One doesn't get best results by "testing" AI.
A surfboard is also an amazing tool, but there's more to operating one than telling it which way to go.
Many people want self-driving cars so they can drink in the back seat watching movies. They'll find their jobs replaced by AI, with a poor quality of life because we're a selfish species. In contrast Niki Lauda trusted fellow Formula 1 race car driver James Hunt to race centimeters apart. Some people want AI to help them drive that well. They'll have great jobs as AI evolves.
Gary Kasparov pioneered "freestyle" chess tournaments after his defeat by Big Blue, where the best human players were paired with computers, coining the "centaur" model of human-machine cooperation. This is frequently cited in the finance literature, where it is recognized that AI-guided human judgement can out-perform either humans or machines.
Any math professor knows how to help graduate students confidently complete a PhD thesis, or how to humiliate students in an oral exam. It’s a choice. To accomplish more work than one can complete alone, choose the former. This is the arc of human evolution: we develop tools to enhance our abilities. We meld with an abacus or a slide rule, and it makes us smarter. We learn to anticipate computations, like we’re playing a musical instrument in our heads. Or we pull out a calculator that makes us dumber. The role we see for our tools matters.
Programmers who actually write better code using AI know this. These HN threads are filled with despair over the poor quality of vibe coding. At the same time, Anthropic is successfully coding Claude using Claude.
That centaurs can outperform humans or AI systems alone is a weaker claim than "these particular AI systems have the required properties to be useful for that". Chess engines consistently produce strong lines: using one does not feel like gambling, even if occasionally you can spot a line it can't. Using LLMs does feel like gambling. I think you're overgeneralising.
These are very serious research level math questions. They are not “Erdős style” questions; they look more like problems or lemmas that I encountered while doing my PhD. Things that don’t make it into the papers but were part of an interesting diversion along the way.
It seems likely that PhD students in the subfields of the authors are capable of solving these problems. What makes them interesting is that they seem to require fairly high research level context to really make progress.
It’s a test of whether the LLMs can really synthesize results from knowledge that require a human several years of postgraduate preparation in a specific research area.
So these are like those problems that are “left for the reader”?
Not necessarily. Even the statements may not appear in the final paper. The questions arose during research, and understanding them was needed for the authors to progress, but maybe not needed for the goal in mind.
Can someone explain how this would work?
> the answers are known to the authors of the questions but will remain encrypted for a short time.
Ok. But humans may be able to solve the problems too. What prevents Anthropic or OpenAI from hiring mathematicians, have them write the proof and pass it off as LLM written? I'm not saying that's what they'll do. But shouldn't the paper say something about how they're going to validate that this doesn't happen?
Honest question here. Not trying to start a flame here. Honestly confused how this is going to test what it wants to test. Or maybe I'm just plain confused. Someone help me understand this?
This is not a benchmark. They just want to give people the opportunity to try their hand at solving novel questions with AI and see what happens. If an AI company pulls a solution out of their hat that cannot be replicated with the products they make available to ordinary people, that's hardly worth bragging about and in any case it's not the point of the exercise.
The authors mention that before publications they tested these questions on Gemini and GPT, so they have been available to the two biggest players already; they have a head start.
They could solve the problems and train the next models with the answers, as such the future models could “solve” theses.
It's possible but unlikely given the short timeline, diverse questions that require multiple matheamticians, and low stakes. Also they've already run preliminary tests.
> It's possible but unlikely given the short timeline
Yep. "possible but unlikely" was my take too. As another person commented, this isn't really a benchmark, and as long as that's clear, it seems fair. My only fear is that some submissions may be AI-assisted rather than fully AI-generated, with crucial insights coming from experienced mathematicians. That's still a real achievement even if it's human + AI collaboration. But I fear that the nuance would be lost on news media and they'll publish news about the dawn of fully autonomous math reasoning.
Anything special about these questions? Are they unsolved by humans. I am not working in mathematics research so its hard to tell the importance.
The abstract of the article is very short, and seems pretty clear to both of your questions.
This is what is special about them:
> a set of ten math questions which have arisen naturally in the research process of the authors. The questions had not been shared publicly until now;
I.e. these are problems of some practical interest, not just performative/competitive maths.
And this is what is know about the solutions:
> the answers are known to the authors of the questions but will remain encrypted for a short time.
I.e. a solution is known, but is guaranteed to not be in the training set for any AI.
> I.e. a solution is known, but is guaranteed to not be in the training set for any AI.
Not a mathematician and obviously you guys understand this better than I do. One thing I can't understand is how they're going to judge if a solution was AI written or human written. I mean, a human could also potentially solve the problem and pass it off as AI? You might say why would a human want to do that? Normal mathematicians might not want to do that. But mathematicians hired by Anthropic or OpenAI might want to do that to pass it off as AI achievements?
Well, I think the paper answers that too. These problems are intended as a tool for honest researchers to use for exploring the capabilities of current AI models, in a reasonably fair way. They're specifically not intended as a rigorous benchmark to be treated adversarially.
Of course a math expert could solve the problems themselves and lie by saying that an AI model did it. In the same way, somebody with enough money could secretly film a movie and then claim that it was made by AI. That's outside the scope of what this paper is trying to address.
The point is not to score models based on how many of the problems they can solve. The point is to look at the models' responses and see how good they are at tackling the problem. And that's why the authors say that ideally, people solving these problems with AI would post complete chat transcripts (or the equivalent) so that readers can assess how much of the intellectual contribution actually came from AI.
https://1stproof.org/#about
Interesting questions. I think I'll attempt #7.
February 13th is a pretty close deadline. They should at least have given a month.
February 13 seems right to me. I mean it's not like LLMs need to manually write out a 10 page proof. But a longer deadline can give human mathematicians time to solve the problem and write out a proof. A close deadline advantages the LLM and disadvantages humans which should be the goal if we want to see if LLMs are able to solve these.
I'll patiently wait for the "goalpost moving olympics" after this is published.
The goalposts have been on wheels basically since the field was born. Look up "AI effect". I've stopped caring what HN comments have to say about whether something is or isn't AI. If its useful to me, I'm gonna use it.
For policy feedback (Gas^∆ ÷ 2) · diag(u) · (Gas^∆ ÷ 2)^t A dampened shock propagates forward,is treated as independent, then feeds back into the system,that's quadratic form.