4 ms·

Benchmarks in Leipzig

138 points by root-parent 4mo ago

root-parent 4mo ago
"...Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers... We present the resulting collection of 100 questions....We evaluated these questions in three stages: a single attempt by five state-of-the-art LLMs....we concluded Stage 3 with only 2 unsolved questions. This demonstrates that the mathematical reasoning capabilities of LLMs are becoming impressive..."
- rabidvermin 4mo ago
  mathematics questions with known answers... ... that are therefore liable to be in the training data?
  - fc417fc802 4mo ago
    I had the same thought, because even if the exact solution doesn't appear there's a notable difference between performing a literature search versus solving something de novo. But I think perhaps this benchmark wasn't meant to exclude the former and that the point may have been to test the ability of the model to accurately interpret and synthesize relevant output for research level mathematical problems at all.
    - tossandthrow 4mo ago
      I can recommend reading section 2 of the paper. The goal was not to define unsolved problems. But as such, the problems are also not previously published problems. This seems quite reasonable IMHO.
    - christianstump 4mo ago
      I think you are underestimating the complexity of such problems. A PhD in the exact field of research would need days to weeks to understand what the problem means and how to solve it. This is far beyond "throwing standard techniques" at a problem. (But, I keep emphasizing this, it is also far away from solving research mathematics.)
      - fc417fc802 4mo ago
        What did I say that led you to believe I was underestimating the complexity? I don't believe I commented on it at all.
        christianstump 4mo ago
        When you write "there's a notable difference between performing a literature search versus solving something de novo", you suggest that the questions we provided can be solved doing a literature search. This is incorrect. What is correct is the following: When understanding the existing literature on a question in the dataset, one can derive the answer without creating new mathematics research. So the difference is "searching the literature" vs "understanding the literature" that made me believe it. But if you didn't that's even better!
        fc417fc802 4mo ago
        I did not suggest that, no. I stress that claiming a possibility is not the same as claiming a fact. I observed that the two things are quite different in terms of model capabilities. That's relevant when considering how to interpret the results of the benchmark. We need to differentiate between (at minimum) reproducing an (approximately) verbatim answer from the training set, assembling disparate items from the training set into an answer piecewise, and performing novel logical inference using items from the training set. I further speculated about the intent of the authors but you seem to be saying that my guess was wrong. In response I will observe that for any problem that's known to be solved it's likely to be quite difficult if not impossible to confidently determine that the model performed a de novo derivation as opposed to finding pieces of the answer in various places. Of course there's absolutely nothing wrong with the latter! It's just important to be aware of the possibility when drawing conclusions about model capabilities.
  - andy99 4mo ago
    “In the training data” isn’t really relevant for a modern LLM. The better question would be are they solvable using known techniques that have been fine-tuned in. A simple example, as a non-mathematician: I’d expect a well trained LLM to be able to solve any integral that can be solved with integration by parts. I would be much more interested to see it solve one with no know solution using some novel technique. Obviously this doesn’t really lend itself to making a benchmark, but if something is solveable by a known technique, and the LLM has has some kind of RL training re using that technique, seeing a solution isn’t too surprising.
  - criemen 4mo ago
    Partially, 2.2 Submission workflow W2 deals with this: > Stage W2 The five project-active models, see Table 2, attempted the question. Their answers were compared to the original answer by an LLM judge. If at most three models answered correctly, the contributor could proceed. So "trivially contained in the training data" is excluded, as then all models could/should easily come up with the solution.
zerobees 4mo ago
I know that people with strong feelings one way or the other will comment here, but note that this is specifically about problems with known answers that can be inferred from existing literature (e.g., training data). This is an interesting result, but as I understand it, it's not about solving frontier challenges (which LLMs can evidently do too, but that's not what's tested here). It's closer to "can a mathematician (blindly) write exercises you can't cheat on using an LLM". "Blindly" in the sense that they can't adjust the problem ahead of the time until they get a model to fail. The conclusion in the paper is: "The concept of writing exercise-style benchmark questions based on publicly accessible research has reached its limits when it comes to the best-performing available models."
- lightningspirit 4mo ago
  I think most of the value LLMs provide comes from connecting the dots between unsolved questions and patterns or structures that have already been demonstrated, which accelerates research. Now, reasoning in the sense of making truly original discoveries, as Einstein did with the field equations, is a different story for current LLMs.
- christianstump 4mo ago
  Let me also add: there is zero chance of the problems being included in the training data. The results are quite impressive: leading experts struggled to write questions with well-defined unique answers on existing research that the models were not able to solve. This should not be interpreted as AI can solve mathematics: the ability to solve exercise-style questions based on existing research is vastly different from the creation of new mathematics. But it is still impressive and not what we expected -- I rather expected that we end with 20-40 questions no current publicly available model can solve.
Towaway69 4mo ago
As long as it's not conscious, we're safe.
- esafak 4mo ago
  No, you're not. It can take jobs and be plenty menacing in embodied form in its present state.
openclawclub 4mo ago
[flagged]
qsort 4mo ago
These are the results from the website they link in the paper: https://math.sciencebench.ai/benchmarks https://math.sciencebench.ai/benchmarks I take the "2 unsolved" claim to mean "not solved by any model in any configuration in any stage with any number of attempts", the "benchmark results" are much lower. To be clear: it's extremely impressive, I still remember I was in utter disbelief when models started solving AIME problems, and this is obviously several levels above that. It's also interesting that OpenAI models perform that much better on math and math-adjacent stuff. I assume this comes down to differences in post-training?
- tux3 4mo ago
  If you're trying to compare what the models are good at, important to note that the different models did not run with the same settings. In one case they also retried with GPT until it answered all the problems but did not retry with the other models. GPT has 5 effort settings and they picked the highest (xhigh). Claude has 5 and they picked the middle one to avoid having to retry when it timed out. Gemini has medium or high effort and they picked medium.
  - christianstump 4mo ago
    the difference between gpt and gemini concerning the "retry until..." can almost be ignored. I did rerun gpt a few times, but still way below what gemini was not able to answer at all.
christianstump 4mo ago
I am the leader of the study and the author of the benchmark paper: let me add: the problems are much harder than any exam question in any exam. Think of it as: a PhD student studying exactly this area of mathematics would need days to weeks to understand and solve the question. But nonetheless, these are questions about existing research, but much closer to a question given a second-year PhD student than to an exam question.
- christianstump 4mo ago
  But it still remains far away from mathematics research. Solving any of the problems would not result in a new research paper.
  - jona-f 4mo ago
    Was this event sponsored by Surge AI? Why didn't you run the prompts yourself?
    - christianstump 4mo ago
      No, they only provided large-scale model runs for us (this is explained in the ackonowledgements). These runs would have been too expensive to perform myself, so I am happy they offered to provide them.
      - jona-f 4mo ago
        Thanks for answering this random internet guy's question. It's a bit sad that a german math prof doesn't have sufficient funds to run a few prompts. I would have paid for them for this amount of advertising. I don't like that you gave them to a silicon valley company. On that note, the tests are very US-centric. Only one chinese model and you unfairly nerfed it by limiting it's context window, when the compressed context is deepseek v4's main innovation and even with full context it is much cheaper to run than all the others.
        4mo ago
puttycat 4mo ago
Hopefully they password-protect the datasets: https://arxiv.org/abs/2305.10160 https://arxiv.org/abs/2305.10160
spuz 4mo ago
As well as measuring how many questions each model was able to answer correctly, I think it's equally important to measure how many questions each model answered incorrectly. After all, if you consider using them as a tool, you will need to have confidence that any answer they give is correct. If you look at Table 3 you can see the difference in performance between for example GPT 5.5 and Opus 4.7 for each of the 20x 100 runs: - GPT 5.5: 1389/2000 questions answered, of which 1043 were correct (75%) - Opus: 1306/2000 questions answered, of which 294 were correct (22%) So while you can claim that Opus solved 40% of the problems it still had a failure rate of 78%. That means if you chose this model to answer your homework question, there is a good chance you would fail. Perhaps a more useful benchmark for future models is measuring how many of these types of questions they can answer in one shot. I.e. how confident can you be when using them for real world tasks.
- christianstump 4mo ago
  You are 100% correct with your assessment of the situation. But I do not agree with either of your conclusions: 1. These questions cannot and must not be compared as being similar to homework questions. These are different leagues and possibly even different sports. 2. The "more useful benchmark" that you suggest is already present in the data as we ran every model exactly once in Stage 1.
  - spuz 4mo ago
    Ah you are right. I think I started reading the results of Stage 2 thinking it was Stage 1.
tomtomatoide 4mo ago
For some reason, perhaps some sort of Freudian self-defense mechanism, we tend to downplay how impressive solving never seen problems that require deep understanding of the concepts at play requires. Look for final exams of advanced courses in CS or math. It will be clarifying how close (or plainly, harder) the questions from the study are. And so how impressive the capabilities these models are achieving...
danielovichdk 4mo ago
Hypezig The new Berlin
davidmpaz 4mo ago
With all due respect to the interesting research results this paper offers.... This is the most "Hitchhiker's Guide to the Galaxy" thing I have read so far :) I am even expecting some of the question to be answered with 42!!
danielgall500 4mo ago
I almost did a double take when I saw Leipzig mentioned here. Cool work and greetings from InfAI. :)
sinuhe69 4mo ago
Did any AI lab sponsor the study? If yes, I believe a note should be included in the paper, just like commercial sponsorship in any other field.
- christianstump 4mo ago
  I am very happy to provide any information I missed to include -- but exactly what you ask for is written in the paper's acknowledgements (no sponsorship, but some model runs).

138 points by root-parent 4mo ago

"...Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers... We present the resulting collection of 100 questions....We evaluated these questions in three stages: a single attempt by five state-of-the-art LLMs....we concluded Stage 3 with only 2 unsolved questions. This demonstrates that the mathematical reasoning capabilities of LLMs are becoming impressive..."

rabidvermin 4mo ago
mathematics questions with known answers... ... that are therefore liable to be in the training data?
- fc417fc802 4mo ago
  I had the same thought, because even if the exact solution doesn't appear there's a notable difference between performing a literature search versus solving something de novo. But I think perhaps this benchmark wasn't meant to exclude the former and that the point may have been to test the ability of the model to accurately interpret and synthesize relevant output for research level mathematical problems at all.
  - tossandthrow 4mo ago
    I can recommend reading section 2 of the paper. The goal was not to define unsolved problems. But as such, the problems are also not previously published problems. This seems quite reasonable IMHO.
  - christianstump 4mo ago
    I think you are underestimating the complexity of such problems. A PhD in the exact field of research would need days to weeks to understand what the problem means and how to solve it. This is far beyond "throwing standard techniques" at a problem. (But, I keep emphasizing this, it is also far away from solving research mathematics.)
    - fc417fc802 4mo ago
      What did I say that led you to believe I was underestimating the complexity? I don't believe I commented on it at all.
      - christianstump 4mo ago
        When you write "there's a notable difference between performing a literature search versus solving something de novo", you suggest that the questions we provided can be solved doing a literature search. This is incorrect. What is correct is the following: When understanding the existing literature on a question in the dataset, one can derive the answer without creating new mathematics research. So the difference is "searching the literature" vs "understanding the literature" that made me believe it. But if you didn't that's even better!
        fc417fc802 4mo ago
        I did not suggest that, no. I stress that claiming a possibility is not the same as claiming a fact. I observed that the two things are quite different in terms of model capabilities. That's relevant when considering how to interpret the results of the benchmark. We need to differentiate between (at minimum) reproducing an (approximately) verbatim answer from the training set, assembling disparate items from the training set into an answer piecewise, and performing novel logical inference using items from the training set. I further speculated about the intent of the authors but you seem to be saying that my guess was wrong. In response I will observe that for any problem that's known to be solved it's likely to be quite difficult if not impossible to confidently determine that the model performed a de novo derivation as opposed to finding pieces of the answer in various places. Of course there's absolutely nothing wrong with the latter! It's just important to be aware of the possibility when drawing conclusions about model capabilities.
- andy99 4mo ago
  “In the training data” isn’t really relevant for a modern LLM. The better question would be are they solvable using known techniques that have been fine-tuned in. A simple example, as a non-mathematician: I’d expect a well trained LLM to be able to solve any integral that can be solved with integration by parts. I would be much more interested to see it solve one with no know solution using some novel technique. Obviously this doesn’t really lend itself to making a benchmark, but if something is solveable by a known technique, and the LLM has has some kind of RL training re using that technique, seeing a solution isn’t too surprising.
- criemen 4mo ago
  Partially, 2.2 Submission workflow W2 deals with this: > Stage W2 The five project-active models, see Table 2, attempted the question. Their answers were compared to the original answer by an LLM judge. If at most three models answered correctly, the contributor could proceed. So "trivially contained in the training data" is excluded, as then all models could/should easily come up with the solution.

zerobees 4mo ago

I know that people with strong feelings one way or the other will comment here, but note that this is specifically about problems with known answers that can be inferred from existing literature (e.g., training data). This is an interesting result, but as I understand it, it's not about solving frontier challenges (which LLMs can evidently do too, but that's not what's tested here). It's closer to "can a mathematician (blindly) write exercises you can't cheat on using an LLM". "Blindly" in the sense that they can't adjust the problem ahead of the time until they get a model to fail. The conclusion in the paper is: "The concept of writing exercise-style benchmark questions based on publicly accessible research has reached its limits when it comes to the best-performing available models."

lightningspirit 4mo ago
I think most of the value LLMs provide comes from connecting the dots between unsolved questions and patterns or structures that have already been demonstrated, which accelerates research. Now, reasoning in the sense of making truly original discoveries, as Einstein did with the field equations, is a different story for current LLMs.
christianstump 4mo ago
Let me also add: there is zero chance of the problems being included in the training data. The results are quite impressive: leading experts struggled to write questions with well-defined unique answers on existing research that the models were not able to solve. This should not be interpreted as AI can solve mathematics: the ability to solve exercise-style questions based on existing research is vastly different from the creation of new mathematics. But it is still impressive and not what we expected -- I rather expected that we end with 20-40 questions no current publicly available model can solve.

Towaway69 4mo ago

As long as it's not conscious, we're safe.

esafak 4mo ago
No, you're not. It can take jobs and be plenty menacing in embodied form in its present state.

openclawclub 4mo ago

[flagged]

qsort 4mo ago

These are the results from the website they link in the paper: https://math.sciencebench.ai/benchmarks https://math.sciencebench.ai/benchmarks I take the "2 unsolved" claim to mean "not solved by any model in any configuration in any stage with any number of attempts", the "benchmark results" are much lower. To be clear: it's extremely impressive, I still remember I was in utter disbelief when models started solving AIME problems, and this is obviously several levels above that. It's also interesting that OpenAI models perform that much better on math and math-adjacent stuff. I assume this comes down to differences in post-training?

tux3 4mo ago
If you're trying to compare what the models are good at, important to note that the different models did not run with the same settings. In one case they also retried with GPT until it answered all the problems but did not retry with the other models. GPT has 5 effort settings and they picked the highest (xhigh). Claude has 5 and they picked the middle one to avoid having to retry when it timed out. Gemini has medium or high effort and they picked medium.
- christianstump 4mo ago
  the difference between gpt and gemini concerning the "retry until..." can almost be ignored. I did rerun gpt a few times, but still way below what gemini was not able to answer at all.

christianstump 4mo ago

I am the leader of the study and the author of the benchmark paper: let me add: the problems are much harder than any exam question in any exam. Think of it as: a PhD student studying exactly this area of mathematics would need days to weeks to understand and solve the question. But nonetheless, these are questions about existing research, but much closer to a question given a second-year PhD student than to an exam question.

christianstump 4mo ago
But it still remains far away from mathematics research. Solving any of the problems would not result in a new research paper.
- jona-f 4mo ago
  Was this event sponsored by Surge AI? Why didn't you run the prompts yourself?
  - christianstump 4mo ago
    No, they only provided large-scale model runs for us (this is explained in the ackonowledgements). These runs would have been too expensive to perform myself, so I am happy they offered to provide them.
    - jona-f 4mo ago
      Thanks for answering this random internet guy's question. It's a bit sad that a german math prof doesn't have sufficient funds to run a few prompts. I would have paid for them for this amount of advertising. I don't like that you gave them to a silicon valley company. On that note, the tests are very US-centric. Only one chinese model and you unfairly nerfed it by limiting it's context window, when the compressed context is deepseek v4's main innovation and even with full context it is much cheaper to run than all the others.
      - 4mo ago

puttycat 4mo ago

Hopefully they password-protect the datasets: https://arxiv.org/abs/2305.10160 https://arxiv.org/abs/2305.10160

spuz 4mo ago

As well as measuring how many questions each model was able to answer correctly, I think it's equally important to measure how many questions each model answered incorrectly. After all, if you consider using them as a tool, you will need to have confidence that any answer they give is correct. If you look at Table 3 you can see the difference in performance between for example GPT 5.5 and Opus 4.7 for each of the 20x 100 runs: - GPT 5.5: 1389/2000 questions answered, of which 1043 were correct (75%) - Opus: 1306/2000 questions answered, of which 294 were correct (22%) So while you can claim that Opus solved 40% of the problems it still had a failure rate of 78%. That means if you chose this model to answer your homework question, there is a good chance you would fail. Perhaps a more useful benchmark for future models is measuring how many of these types of questions they can answer in one shot. I.e. how confident can you be when using them for real world tasks.

christianstump 4mo ago
You are 100% correct with your assessment of the situation. But I do not agree with either of your conclusions: 1. These questions cannot and must not be compared as being similar to homework questions. These are different leagues and possibly even different sports. 2. The "more useful benchmark" that you suggest is already present in the data as we ran every model exactly once in Stage 1.
- spuz 4mo ago
  Ah you are right. I think I started reading the results of Stage 2 thinking it was Stage 1.

tomtomatoide 4mo ago

For some reason, perhaps some sort of Freudian self-defense mechanism, we tend to downplay how impressive solving never seen problems that require deep understanding of the concepts at play requires. Look for final exams of advanced courses in CS or math. It will be clarifying how close (or plainly, harder) the questions from the study are. And so how impressive the capabilities these models are achieving...

danielovichdk 4mo ago

Hypezig The new Berlin

davidmpaz 4mo ago

With all due respect to the interesting research results this paper offers.... This is the most "Hitchhiker's Guide to the Galaxy" thing I have read so far :) I am even expecting some of the question to be answered with 42!!

danielgall500 4mo ago

I almost did a double take when I saw Leipzig mentioned here. Cool work and greetings from InfAI. :)

sinuhe69 4mo ago

Did any AI lab sponsor the study? If yes, I believe a note should be included in the paper, just like commercial sponsorship in any other field.

christianstump 4mo ago
I am very happy to provide any information I missed to include -- but exactly what you ask for is written in the paper's acknowledgements (no sponsorship, but some model runs).