OpenAI решила 10 открытых задач в математике: геометрия, криптография, теория сложности

OpenAI published results on ten long-standing open problems in mathematics and theoretical computer science — the company announced this in its official blog. The new achievements cover three key areas: geometry, cryptography, and computational complexity theory.

What OpenAI Solved

These are "long-standing open problems" — challenges that mathematicians and theoretical computer scientists had been unable to solve for years. In an academic context, this term has a strict meaning: not an incremental improvement of a known algorithm, but a problem officially considered open — that is, without a verified solution.

According to the OpenAI blog post, ten new results span three directions:

• Geometry — one of the oldest branches of mathematics, studying shapes, sizes, and spatial relationships. Open problems in modern geometry often involve packing objects, optimization, or algebraic invariants
• Cryptography — applied mathematics on which the security of digital infrastructure directly depends: data encryption, electronic signatures, key exchange protocols used by billions of users
• Computational complexity theory — a fundamental branch of theoretical computer science that determines which problems computers can solve and with what computational resources

The "ten achievements" format is atypical for AI companies: they usually announce a single product or technology. Publishing a series of ten mathematical results signals systematic scientific work, not a one-off success.

Why Mathematics Has Become a Testing Ground for AI Labs

Mathematical problems are one of the most rigorous ways to evaluate the real capabilities of neural networks. A proof is either correct or it is not: unlike text-based tasks, where a model can generate convincingly-sounding but erroneous statements, mathematics can be verified independently. That is precisely why progress in this area is considered one of the most reliable indicators of a model's true intellectual potential.

Progress in cryptography and complexity theory is not merely academic points. Results in these areas affect the architecture of encryption algorithms and the theoretical limits of computation. That is why even a single new result here attracts attention from both the AI industry and the academic community.

As stated in

OpenAI's official blog, the company shares "new results on long-standing open problems in mathematics and theoretical computer science," including advances in geometry, cryptography, and computational complexity theory.

It is telling that OpenAI publishes these results at a time when competition between AI labs is increasingly shifting from consumer products to fundamental model capabilities — and mathematics is becoming one of the key arenas in this race.

What This Means

OpenAI is demonstrating that AI systems are reaching the level of fundamental science, where results are verifiable and do not admit hallucinations. If this publication is followed by details on the specific problems and methods used to solve them, it could become one of the most important academic contributions of an AI lab. At the same time, this is a new challenge for competitors: mathematics is becoming an arena where one cannot "appear smarter than one actually is."