What sort of maths are LLMs good at?
gowers.wordpress.com
August 12, 2026
28 min read
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Summary
OpenAI has solved ten significant problems in mathematics and theoretical computer science, including the construction of a non-sofic group and a proof regarding the superexponential growth of the multicolour Ramsey number. These achievements demonstrate the capabilities of large language models (LLMs) in tackling complex mathematical challenges.
Key Takeaways
- OpenAI announced the solution to ten major problems in mathematics and theoretical computer science, including the construction of a non-sofic group and a proof regarding the growth of the multicolour Ramsey number.
- LLMs have demonstrated the ability to find proofs of difficult statements, but most notable problems they have solved involve finding counterexamples.
- There is ongoing exploration into the specific types of mathematical problems that LLMs excel at, with a focus on their strengths in identifying counterexamples.
- The definition of what constitutes a counterexample in mathematical terms is complex and not always straightforward, as demonstrated by the nuances in famous mathematical results.
Coverage & discussions
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Community discussions
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Analysis ready
Community Sentiment
Positives
- LLMs are showing signs of reaching human-level capabilities in solving complex mathematical problems, which could redefine our understanding of machine intelligence.
- The ability of models like AlphaCode to generate and filter candidate programs demonstrates that AI can outperform humans in certain programming tasks, highlighting its potential.
- There's a fascinating parallel between how humans and LLMs approach complex mathematics, suggesting that AI might one day grasp concepts we deem difficult.
Concerns
- Skeptics argue that any new mathematical theorems produced by LLMs are likely to be overly complex and not as elegant as human discoveries.
- Some commenters doubt that LLMs can truly innovate in mathematics, suggesting they mainly 'brute force' solutions rather than create beautiful or surprising proofs.
- There's a sense of skepticism about the limitations of LLMs in grasping deeper mathematical concepts without substantial training, indicating they still have a long way to go.
