OpenAI has solved ten significant problems in mathematics and theoretical computer science, including the construction of a non-sofic group and a proof regarding the superexponential growth of the multicolour Ramsey number. These achievements demonstrate the capabilities of large language models (LLMs) in tackling complex mathematical challenges.

Terence Tao explores the intersection of mathematics and artificial intelligence, emphasizing how AI can enhance mathematical research and problem-solving. He discusses the implications of AI for the future of mathematical discovery and education.

Recent developments in large language models (LLMs) have generated counterexamples to several long-standing mathematical conjectures. This has sparked varied reactions among mathematicians and enthusiasts, leading to discussions about the implications for the field of mathematics.

The Fields Medal is awarded for exceptional mathematical achievement, recognizing both past work and future potential. For 2026, the prize funds are provided by the University of Toronto and supported by the Fields Institute, with a recipient recognized for contributions to partial differential equations and the Boltzmann equation.

The Jacobian conjecture posits that a polynomial map in complex variables with a non-zero constant Jacobian is invertible with a polynomial inverse. Local invertibility is equivalent to the Jacobian being non-zero, following from the inverse function theorem.

The Jacobian conjecture is stated to be false, with a specific mapping from \(\mathbb{C}^3\) to \(\mathbb{C}^3\) shown to have a Jacobian determinant of -2. The mapping sends the points (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0).

Sixteen mathematicians have issued the Leiden Declaration on Artificial Intelligence and Mathematics, expressing concerns about the rapid advancement of AI in their field. The document serves as both a warning and a call to action regarding the implications of AI for mathematical research and practice.

Liam Price, a 23-year-old without advanced mathematics training, solved a 60-year-old problem previously unsolved by mathematicians using ChatGPT Pro. Recent advancements in artificial intelligence have led to solutions for several conjectures known as Erdős problems.

Aletheia, powered by Gemini 3 Deep Think, autonomously solved 6 out of 10 problems in the FirstProof challenge. Expert assessments confirmed the accuracy of Aletheia's solutions for the problems completed.

Top mathematicians have issued a challenge to AI systems to solve a set of unsolved mathematical problems within a week, as part of an initiative called “First Proof.” These problems are newly formulated and are not present in any large language model's training data.