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Fields Medalist to Join OpenAI as Roughly 40 Mathematicians Gather for Closed-Door Summit on AI and Mathematics

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Fields Medalist Jacob Tsimerman announced at the award ceremony that he will soon join OpenAI to conduct AI safety research. Author and source: The Washington Post Jacob Tsimerman, who just won the Fields Medal last month, announced at the award ceremony that he will soon join OpenAI to work on AI safety research. In early August, he convened around 40 mathematicians at OpenAI’s headquarters in San Francisco with research scientist Sébastien Bubeck for a closed-door summit, one of whose talks was titled “The End of Mathematics.” Sébastien Bubeck, research scientist at OpenAI Speaker and University of Toronto professor Daniel Litt said: It is possible that we eventually end up in a world without high-quality mathematical research and the complete disappearance of human mathematical expertise. He believes extreme outcomes are unlikely, but mathematicians must take action. MIT mathematician Drew Sutherland put it more directly and coldly: Perhaps we are just the canaries in the coal mine, and mathematicians are the first to suffer. Mathematics has been chosen as a testing ground for AI because it serves as a proxy indicator for high-level cognitive ability—what can be achieved in mathematics will eventually be replicated in other domains. AI is currently performing calculations in bulk. The dense release of results served as the immediate backdrop for this summit. In May, an unreleased OpenAI model disproved the unit distance conjecture. This long-standing open problem regarding the arrangement of points on an infinite plane has been solved by AI using a known but difficult-to-operate technique from algebraic number theory—essentially applying tools across subfields. At the time, Tsimerman said he would "unhesitatingly accept" this result in any journal. This is regarded by many mathematicians as AI's first major mathematical breakthrough. Subsequent achievements emerged in quick succession. In August, OpenAI announced 10 new discoveries in mathematics and computer science generated by AI, spanning multiple subfields that typically take years to master. Anthropic hasn't been sitting idle either. Anthropic employee Levent Alpöge used Claude to construct pairs of orthogonal vectors on a 668-dimensional hypercube. Mathematicians have long believed that such a construction exists, but no one has ever actually built it. Alpöge announced the results by posting a 24,…

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外部发现 · OpenAI · Original source ↗ · Site entry ·

How Claude is accelerating protein design and analytical chemistry

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In this post, we share two results that show how Claude can help life scientists increase the pace of their research. In the first, we tested Claude’s ability to design protein binders from scratch, a key step in creating protein-based drugs that has historically taken a specialist weeks or months per target. In the second example, we evaluated whether Claude can accelerate chemical analysis. Claude Opus 5, a generally available model, was given NMR and LC-MS data (the data that allows chemists to assess the identity and purity of the compounds they work with).

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Anthropic · Science Blog · Original source ↗ · Site entry ·

Palomar – a registry of Lean verified mathematics

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In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking that a given Lean repository actually proves the claimed statement is somewhat non-trivial, especially for an audience which is not expert in the use of Lean: one has to first check that the claimed formal Lean statements have proofs that typecheck, that the proofs do not contain any “cheats” such as adding additional axioms, and that the formal statements also match (in a semantic sense) the informal description of the claimed results. To help bring some clarity to this situation, I am happy to announce that Palomar registry of Lean verified mathematics , which is an initiative incubated by the Lean FRO and by ICARM , is now open for submissions. I am serving in several roles on this registry, including on the scientific advisory board, together with Jeremy Avigad , Matthew Ballard , Jaume de Dios , Nestor Guillen , Bryna Kra , Kim Morrison , Ravi Vakil , and Akshay Venkatesh . A detailed motivation for Palomar can be found here , and further information about Palomar can be found here . A zeroth approximation of what Palomar intends to be is the analogue of a preprint server for Lean proofs. More precisely, Palomar (which is named after the astronomical observatory ) is a registry of external Github repositories (or more precisely, “snapshots” of such repositories, as represented by a specific Github commit) containing Lean code adhering to the current best practices for such formalizations, in particular containing A “challenge file” containing a short, human readable description in Lean of the results claimed. A “solution module” containing an (arbitrarily long) proof of the results claimed in the challenge file. A “ formalization.yaml ” file describing the results in informal language, and also containing a number of other relevant metadata and disclosures. (There are also some additional technical requirements for the repository which I will omit here.) If a snapshot of a repository is submitted to Palomar, it will check both (a) that the solution module typechecks and proves exactly the results claimed in the challenge file, and that (b) the informal description of the result in the formalization.yaml file appears to match the result claimed in the challenge f…

Sources and evidence

陶哲轩 · What's new 博客 · Original source ↗ · Site entry ·

Microsoft Research's Skala Model Joins CP2K to Rework DFT's Exchange-Correlation Functional

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A new artificial intelligence model designed to improve one of quantum chemistry’s most difficult calculations is now available through the CP2K software ecosystem, potentially allowing researchers to simulate larger molecular systems without sacrificing as much accuracy. Developed by Microsoft Research AI for Science, the model, known as Skala, replaces part of the conventional mathematical machinery used in density functional theory with a neural-network-based exchange-correlation functional. Its integration into CP2K gives scientists an open-source environment in which to test the approach across problems in chemistry, physics, materials science and engineering. Density functional theory, or DFT, has become one of the central tools of modern computational science. The method makes it possible to investigate the electronic structure of molecules and materials by calculating how electrons are distributed through space. Rather than tracking every electron individually, DFT works primarily with the electron density, a quantity that describes the probability of finding electrons in different regions. This reduction makes quantum mechanical simulations feasible for systems containing many atoms, but it also introduces a major approximation: the exchange-correlation functional, which describes complex interactions among electrons that are difficult to calculate directly. “The Achilles’ heel of DFT is the so-called exchange-correlation functional,” says Prof. Thomas D. Kühne, director of the Center for Advanced Systems Understanding, or CASUS. These functionals determine how the electron density is translated into energy and forces, meaning that their quality strongly influences the reliability of a simulation. More advanced functionals can deliver more accurate results, but they often require substantially greater computational resources. As the number of particles increases, the computational cost can become prohibitive, restricting the most precise calculations to relatively small molecular systems. Skala takes a different route from traditional approaches, which generally improve DFT by adding increasingly elaborate analytical expressions. Its neural network has been trained to recognize how electron densities in separate regions influence one another and to use those relationships when estimating exchange-correlation energy. In practical terms, the model at…

Sources and evidence

外部发现 · Microsoft Research AI for Science · Original source ↗ · Site entry ·