Introduction to AI in Mathematics
Artificial intelligence (AI) has been making significant progress in the field of mathematics. Recently, a number of Large Reasoning Models (LRMs) have achieved high scores on the American Invitational Mathematics Examination (AIME), a test given to the top 5% of US high school math students. These models try to solve problems step by step, rather than just providing the first result that comes to them.
Breakthroughs in Hybrid Models
At the same time, new hybrid models that combine Large Language Models (LLMs) with fact-checking systems have also made breakthroughs. One key milestone is Google DeepMind’s AlphaProof, which combines an LLM with DeepMind’s game-playing model AlphaZero. Last year, AlphaProof became the first computer program to match the performance of a silver medallist at the International Math Olympiad, one of the most prestigious mathematics competitions in the world.
Recent Achievements
In May, a Google DeepMind model called AlphaEvolve discovered better results than anything humans had yet come up with for more than 50 unsolved mathematics puzzles and several real-world computer science problems. This uptick in progress is clear, with models like OpenAI’s o1, an LRM released in January, being able to solve problems that previous models like GPT-4 couldn’t.
Limitations of Current Models
However, this doesn’t mean that such models are ready to become coauthors in mathematical research. Math Olympiad problems often involve clever tricks, whereas research problems are more explorative and have many moving pieces. Success at one type of problem-solving may not carry over to another. Mathematicians like Martin Bridson and Sergei Gukov point out that while the results are impressive, they are not unexpected, and that the style of questions in Math Olympiad competitions doesn’t change much from year to year.
Expert Opinions
Experts in the field have mixed opinions about the achievements of these models. Emily de Oliveira Santos, a mathematician at the University of São Paulo, Brazil, says that while the progress is impressive, it’s not clear if these models can be used for more complex research problems. Martin Bridson, a mathematician at the University of Oxford, thinks that the Math Olympiad result is a great achievement, but not a change of paradigm. Sergei Gukov, a mathematician at the California Institute of Technology, points out that the style of question in Math Olympiad competitions is similar from year to year, and that new problems can often be solved with the same old tricks.
Conclusion
In conclusion, while AI models have made significant progress in mathematics, there is still a long way to go before they can be used as coauthors in mathematical research. The current models are good at solving problems that involve clever tricks, but may not be as effective at solving more complex, explorative problems. As the field continues to evolve, it will be exciting to see what new breakthroughs are achieved.
FAQs
- What is AIME?
AIME stands for American Invitational Mathematics Examination, a test given to the top 5% of US high school math students. - What is AlphaProof?
AlphaProof is a system developed by Google DeepMind that combines a Large Language Model (LLM) with DeepMind’s game-playing model AlphaZero. - Can AI models solve all math problems?
No, current AI models are not able to solve all math problems. While they have made significant progress, they are still limited to solving problems that involve clever tricks, and may not be as effective at solving more complex, explorative problems. - What is the difference between LLMs and LRMs?
LLMs (Large Language Models) are AI models that are trained on large amounts of text data and can generate human-like language. LRMs (Large Reasoning Models) are AI models that are trained to reason and solve problems step by step, rather than just providing the first result that comes to them.
