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.