AI in mathematics opens a new golden age of scientific discovery
Generative AI models have helped solve a famous geometry graph hypothesis by Paul Erdős that had puzzled mathematicians for 80 years. Machine learning is now used to generate and verify millions of logical chains, paired with interactive theorem provers like Lean to avoid hallucinations. This marks a shift where AI amplifies human ingenuity in mathematics rather than replacing it.
Hungarian mathematician Paul Erdős left hundreds of unsolved problems with cash prizes, one of which was the unit distances hypothesis in geometric graph theory. This hypothesis essentially asks for the maximum number of equal-length connections among a set of points, a puzzle that resisted human intuition for almost 80 years. A generative algorithm discovered non-trivial spatial structures that humans had overlooked, partially solving the problem. Today, AI handles the tedious work of enumerating millions of combinations and spotting hidden patterns, while interactive theorem provers like Lean or Coq verify every step, eliminating hallucinations. Despite these successes, fundamental problems like the Riemann hypothesis or Navier-Stokes equations remain unsolved, as they require new conceptual language. For the Russian-speaking scientific community, this computational shift leverages a strong mathematical tradition, with applications ranging from neural network optimization to quantum-resistant cryptography. AI acts as a digital exoskeleton for the human brain, freeing researchers from routine tasks and letting them focus on strategic goals and conceptual vision.
Source: Habr — хаб ИИ —
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