this post was submitted on 24 Jun 2026
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Using computers to search for a counter example to a conjecture isn't exactly new ground and I suspect they did so with the aide of some harness tweaks like some numerical LSP. Like cool, it pushed the envelope but like what the parent said, they grafted on the ability to do a specific task.
That doesn't change the fact that llm's are capable of acing math olympiads. So what if it uses tools? You probably would too. I doubt anybody there did it without a calculator.
https://www.nature.com/articles/d41586-025-02343-x
Aren't you the least bit curious what tools they gave the LLM and how the LLM used those tools? It's like back in math class you are asked to solve a quadratic formula but you forgot how. So you use the calculator to try different numbers and the calculator is telling you if you are getting closer. Sure I got the right answer, but it's hardly a testament to my math skills.
The calculator does not tell them if they're getting closer? This isn't how anything works. No I can't say I'm very interested in whether or not the llm has access to python/a calculator as long as it completes the task, that doesn't matter.
If you are not interested in how it completes the task then you are not an authority on how it works.
I'm academically interested, what I mean when I say I'm not interested is that I just don't see the significance when we're talking about if it's capable of the task.
How are you able to understand it's capability without understanding what tools it is capable of manipulating to effect?
You aren't, and that's exactly what I'm saying, it's capable of doing these things with tools, therefore it's capable of doing these things.
So why are you allergic to people talking about the quality of the tools in regards to capability?
I don't know what you mean, I wasn't the one who claimed they couldn't do something they clearly can.
You are the one collapsing tool use into a binary when there are varying degrees of competency and hand holding.
I am not, you inaccurately said that the math olympiad was not bested by llm's because they had a tool that told them if they were close but incorrect and can just try an infinite number of times. This is incorrect, they had a number of tries with python. This just isn't a true statement. I think them besting it with use of python is equally significant and still counts as them besting it, and saying they can't do math work is absurd.
It's not "bested" by the LLM though, a mathematician used the LLM as a tool to disprove a conjecture. Subtract the mathematicians from the process and the LLM would not have successfully completed the task. It would be more accurate to say a mathematician with an LLM was able to best a mathematician who did not have an LLM. Which is cool, but we don't need to pretend the LLM is not a tool but something that "understands" math like a mathematician
You're confusing the olympiad with the erdos conjecture. This is just really not true, they just asked it and it found a solution, the mathmatician then used its solution as inspiration to create a better one. It still essentially did it on its own, and they certainly do the olympiad on their own.
The description that the LLM did it on its own is subjective at best. I'll just leave it at that. Have a good one