Marta Macho-Stadler
Full Professor of the Department of Mathematics at the University of the Basque Country (UPV/EHU)
The article presents an AI system (AlphaProof) that, unlike other systems, adds a verification method to check the correctness of its results. According to the authors, AlphaProof (like other AI systems) ‘learns’ by finding proofs of mathematical problems (and variations thereof) to adapt them and find the solution to each problem posed. Furthermore (and this is the main improvement), it is capable of refining its results through a trial-and-error system that helps optimize the solutions.
They tested the effectiveness of this system in an elite mathematics competition (International Mathematical Olympiad 2024). Of the six problems posed in this competition, AlphaProof correctly solved three problems in algebra and number theory, but failed to solve the two in combinatorics. The AlphaGeometry 2 system solved the geometry problem. All of this was accomplished in a much longer time (two or three days) than a human participant could have taken.
It's likely that the capabilities of these AI systems (in terms of speed and the types of problems they solve correctly) will improve soon. However, I understand that there are complex mathematical problems that require not only 'training' (through study and practice) to solve, but also a great deal of creativity. And creativity is a human capacity.