Is AI changing the future of mathematics?
AI systems are beginning to solve mathematical problems that have remained unsolved for decades. Associate Professor Gergely Bérczi has worked with Google DeepMind to develop and test one of the most advanced systems in the field.
This is how Associate Professor Gergely Bérczi from the Department of Mathematics describes the developments currently taking place in his field because of the AI-boom.
“Mathematics is becoming one of the humanities. Proofs will increasingly be found by AI systems, and soon theory-building will be as well. For humans, doing mathematics will mean less proving and more understanding of what AI systems produce, and the next generation of models should be built to help us with that,”
he explains.
As one of the first mathematicians, this spring he has worked closely with Google DeepMind on the development and testing of its recent AI system, AlphaProof Nexus.
Reasoning AI models learn through feedback. This works particularly well in mathematics because mathematical proofs can be written in the formal language Lean, which makes it possible to verify whether solutions are correct.
AlphaProof Nexus is such a formal system: it can work on mathematical problems independently and develop proofs that are subsequently checked by a computer using the Lean formal language. This sets it apart from informal LLM systems such as the well-known ChatGPT and Claude models, which can generate mathematical answers but cannot necessarily guarantee that those answers are correct.
As a child, Gergely was drawn to mathematics competitions in his native Hungary. He went on to specialise in algebraic geometry and pure mathematics as a PhD student. Over the last few years, he became interested in the intersection between AI and mathematics, and his research has adapted classical machine learning and developing AI models over the past 5 years.
As part of his work with Google DeepMind, his role has included identifying mathematical problems for the system to attempt to solve and assessing its results. The findings were published in the journal Science in October this year.
“AlphaProof Nexus and the results we were able to publish represented some of the most advanced work in AI for mathematical research at the time, but the field is changing at an incredible pace. Not least because the companies behind the LLMs many people use in their everyday lives are now also trying to develop their AI systems to solve mathematical problems,”
says Gergely Bérczi.
“I am optimistic. Critical thinking and mathematical understanding are still needed not least to understand the results presented by AI. There will always be a need for young people who are fascinated by mathematics, just as I once was.”