Institute of Mathematical Sciences (ICMAT)
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Research scientist at the Institute of Mathematical Sciences (ICMAT, CSIC-UAM-UCM-UC3M), specialising in arithmetic geometry
Scientific researcher at ICMAT and Vice-President for Scientific and Technical Research at CSIC
A Google DeepMind team has developed a new artificial intelligence (AI) system based on large language models capable of autonomously tackling select mathematical problems. The tool, called AlphaProof Nexus, searches for proofs and employs verification processes to ensure the resulting solutions are logically sound. According to the study published in Science, AlphaProof Nexus has successfully solved several previously unsolved problems, including nine of the 353 Erdős problems.
OpenAI has stated in a press release that the internal version of its Astra AI model has found solutions to ten research problems in mathematics and computing, in areas such as geometry, group theory, operator algebras, quantum complexity, cryptography and combinatorics, amongst others. According to the company, the total number of tokens — basic units of information — required to solve these problems would cost around $2,000. OpenAI expresses “deep respect and understanding” for those concerned about the impact of AI on these disciplines, including the signatories of the Leiden Declaration on AI and Mathematics; and states that the attribution of results must honestly reflect how each one was obtained, whilst encouraging the mathematical community to review them. The company is publishing these results openly in a paper, accompanied by the model’s account of its reasoning process.
The German mathematician Gerd Faltings has won the Abel Prize, awarded by the Norwegian Academy of Science and Letters. Faltings, director emeritus of the Max Planck Institute for Mathematics, became a celebrity at the age of 29 for proving a conjecture that earned him the Fields Medal in 1986. His contributions have revolutionised arithmetic geometry, a branch of mathematics at the intersection of the two oldest: number theory and geometry.
The Norwegian Academy of Science and Letters has awarded the Abel Prize to Luis A. Caffarelli, a native of Argentina with US-Argentine nationality, for his "fundamental contributions to the theory of the regularity of nonlinear partial differential equations". Considered the Nobel Prize of mathematics, the award recognises work over an entire career - unlike the Fields Medal, which is awarded for a result under the age of 40. Caffarelli has become the first Latin American to receive this award.