AI Claims Erdős's $100 Bounty, Solves in One Page What a 44-Page Top Journal Paper Couldn't
An AI, in collaboration with a mathematician, has produced a one-page proof for a long-standing Erdős problem (#119), claiming the $100 bounty originally offered by Paul Erdős. The problem concerns the maximum modulus of polynomials with zeros on the unit circle. The new result, generated with the help of GPT-5.6 Sol and posted on the erdosproblems.com forum, is notably simpler than a famous 44-page proof by József Beck published in the Annals of Mathematics in 1991, which addressed a related but distinct part of the problem.
Thomas Bloom, a mathematician and the maintainer of the Erdős problems website, stated that the AI's proof uses straightforward harmonic analysis techniques and contains "interesting ideas," suggesting the problem was less inherently difficult than previously believed. This follows other recent AI-assisted proofs, such as for the Cycle Double Cover conjecture.
The development has sparked debate within the mathematical community. While some argue AI has hit a wall in pure mathematics, others point to incremental but genuine progress on tough problems, indicating that AI's relentless, non-intuitive exploration can uncover overlooked paths that human mathematicians might dismiss after initial failures. This event highlights a potential shift: some "open" problems may persist not due to sheer difficulty, but due to the limits of human patience in exploring all possible avenues.
marsbit07/20 12:34
