AI solves complex math problems

Artificial intelligence has recently solved several long-standing mathematical problems, including an 80-year-old puzzle and a problem over a century old. These achievements have sparked both excitement and concern among mathematicians about the future of their field.

Marketing and interest in mathematics

According to François Willot, a mathematician at Mines Paris-PSL, AI companies are interested in mathematics partly for publicity. Solving complex problems provides them with significant exposure, as such challenges are traditionally seen as the domain of human expertise.

Refuting a famous conjecture

In May 2023, an OpenAI model refuted a conjecture related to the unit distance problem, a classic question posed by mathematician Paul Erdős. The AI provided a proof that was later verified by external mathematicians, showing its ability to handle complex mathematical reasoning.

AI's proof capabilities

François Willot explained that AI models can test mathematical proofs and iterate through different ideas quickly. This is made possible by the vast amount of data they are trained on, including millions of scientific articles, allowing them to work faster than human mathematicians.

AI as a transformative tool

The impact of AI on mathematics is likened to the effect of Galileo's telescope on astronomy. AI models make few errors and their discoveries could benefit fields like engineering, economics, and climate research, according to François Charles, a mathematician and AGMAI member.

OpenAI's advisory efforts

OpenAI has formed an advisory group with renowned mathematicians to ensure responsible AI use. However, concerns remain about the lack of transparency in AI methods and the time it takes for AI to solve problems, with mathematicians calling for more detailed information on AI training processes.

Publishing and collaboration challenges

OpenAI has shared some of its mathematical findings on GitHub, but concerns persist about the speed of AI development and its ability to prove theorems without human understanding. François Charles emphasized the need for researchers to integrate AI-driven knowledge and the difficulty of accessing advanced AI models controlled by a few companies.

Controversy over communication

OpenAI's announcements of discoveries in computer science and physics have stirred debate about how these results are communicated. While some mathematicians remain confident in academia's role, the future of research may depend on collaboration between human experts and AI systems.