OpenAI claims new reasoning model solved 80-year-old Erdős problem
openai's new general-purpose reasoning model produced an original mathematical proof disproving paul erdős's 1946 conjecture on optimal geometric packings, verified by mathematicians noga alon and thomas bloom.
openai revealed that its latest general-purpose reasoning model has disproved a long-standing geometric conjecture by paul erdős regarding optimal lattice structures, which has stood for nearly 80 years. the company corrected a previous error from seven months ago by publishing verification from leading mathematicians, including thomas bloom who previously criticized openai for overstating gpt-5's capabilities. this proof demonstrates that the best possible solutions are not square grids as previously believed, but rather a new family of constructions. openai highlights this as evidence that ai systems can now sustain long, difficult chains of reasoning necessary for discoveries in fields like biology and physics.