Reacción a "AlphaProof Nexus: A new AI tool designed to tackle mathematical proofs"

This study demonstrates that an open architecture based on artificial intelligence (AI) agents has successfully and autonomously solved nine open Erdős problems and 44 conjectures from the On-Line Encyclopedia of Integer Sequences. Beyond the specific results, the value of the authors' work lies in a methodology that enables the systematic generation of powerful mathematical discoveries—a capability previously almost exclusively held by cutting-edge research labs.

Since the beginning of the year, we have witnessed a succession of increasingly impressive AI-driven results in mathematics. A watershed moment arrived in September with the—albeit controversial—announcement that one of the "Millennium Prize Problems" (the Navier-Stokes equations) had been solved using specialized mathematical models and thousands of collaborative agents. There is little doubt left that we are witnessing the birth of a new way of exploring and doing mathematics.

The mathematical capabilities of LLMs (Large Language Models) have improved dramatically. However, as Terence Tao has noted on several occasions, the goals of AI labs and the scientific community do not always align. Labs aim to solve as many problems as possible to showcase the value of their technology, whereas the scientific community seeks to deepen its understanding of mathematics. Tao points out that automating problem-solving can come at the expense of professional practice. The value lies not merely in proving a theorem, but in the entire process leading to that proof. According to Tao, AI eliminates some of the knowledge a mathematician typically gains while attempting to solve a problem—knowledge that is just as valuable to the practice of mathematics as the proof itself.