AI model solves ten decades-old mathematics problems

An artificial intelligence model has solved ten open research problems in mathematics that had remained unsolved for over a decade. The results span high-dimensional geometry, coding theory, arithmetic circuit complexity, group theory, operator algebras, quantum complexity, lattice cryptography, and extremal combinatorics. These advances were achieved using an early version of Astra, a forthcoming major model, requiring computational resources equivalent to approximately two thousand dollars. The technology company has launched a program granting one hundred thousand scientists and mathematicians free access to its most capable models, aiming to accelerate discovery in the field. This initiative followed the generation of an AI-discovered proof that refutes the Erdős unit-distance conjecture, a development that has already catalyzed further mathematical research. Each solution was formalized in Lean notation and accompanied by a transcript of the model's reasoning. The company emphasizes the importance of proper attribution, noting that falsely crediting human authorship to AI-generated proofs misrepresents both the system's capabilities and the essence of genuine human intellectual work. The mathematical community is invited to evaluate these results critically and build upon them in future research endeavors.