New research has found ChatGPT-5.2 can generate original mathematical proofs, introducing “vibe-proving” as a new AI ...

Debates over how geometry is understood and learned date back at least to the days of Plato, with more recent scholars ...

Noncommutative geometry offers a radical reformulation of traditional geometrical concepts by replacing the classical notion of a manifold with a noncommutative algebra of coordinates. This approach ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

OpenAI Model Wins Gold at International Mathematical Olympiad – or Did It? Your email has been sent A Google DeepMind researcher and OpenAI’s former CTO are posing questions about the validity of ...

Google DeepMind, Alphabet Inc.’s artificial intelligence research division, said it has made strides in solving complex math problems, an area that remains challenging for today’s AI programs. On ...