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Pushmeet Kohli on AlphaEvolve and AI's Scientific Revolution

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DeepMind’s Pushmeet Kohli on AI’s Scientific Revolution Pushmeet Kohli leads AI for Science at DeepMind, where his team has created AlphaEvolve, an AI system that discovers entirely new algorithms and proves mathematical results that have eluded researchers for decades. From improving 50-year-old matrix multiplication algorithms to generating interpretable code for complex problems like data center scheduling, AlphaEvolve represents a new paradigm where LLMs coupled with evolutionary search can outperform human experts. Pushmeet explains the technical architecture behind these breakthroughs and shares insights from collaborations with mathematicians like Terence Tao, while discussing how AI is accelerating scientific discovery across domains from chip design to materials science. Listen Now Summary Pushmeet Kohli, VP of Research at Google DeepMind, has been at the forefront of using AI to make groundbreaking scientific and mathematical discoveries, notably with AlphaFold, FunSearch and now AlphaEvolve. The episode emphasizes how combining large language models with structured search and evaluation protocols is already transforming both the pace and nature of scientific progress across domains from mathematics to materials science. The “harness” architecture is everything: True AI breakthroughs come from pairing powerful generative models with robust, domain-specific evaluators—what Pushmeet calls “the harness.” This architecture distinguishes between hallucinations and brilliant insights. For AI founders, investing in strong, trustworthy evaluators is as important as advancing core models. Remove constraints to unlock true discovery: AlphaEvolve’s breakthrough came from removing human-provided templates and searching entire algorithms rather than code snippets. This broader, less restrictive search space leads to more significant breakthroughs. Consider loosening system constraints without sacrificing safety or evaluation rigor. Multi-agent systems extract hidden value: Different models critiquing, refining and ranking each other’s outputs yield results beyond single models. DeepMind’s AI co-scientist system improved dramatically over days of computation. Models are often better at evaluating ideas than generating them, so separate generator, critic and editor roles. Interpretability remains essential for adoption: Engineers prefer interpretable code over b…

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外部发现 · Pushmeet Kohli · Original source ↗ · Site entry ·

A Digestion of the Proof of Sendov’s Conjecture

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This post concerns the following conjecture of Sendov , as well as its strengthening by Phelps–Rodriguez : Conjecture 1 (Sendov’s conjecture) Let , and let be a degree polynomial with all zeroes in the unit disk. Then for every zero of , there exists a critical point of with . Conjecture 2 (Phelps–Rodriguez conjecture) Let , and let be a degree polynomial with all zeroes in the unit disk. Then for every zero of , there exists a critical point of with , unless is on the unit circle and is a scalar multiple of . By applying a rotation around the origin, we can normalize to be a real number with . From the work of Rubinstein , both conjectures were already established in the case, so one can restrict to the case. Both of these conjectures then follow from Conjecture 3 (Sendov’s conjecture in interior) Let . Let be a degree polynomial with all zeroes in the unit disk. Then if is a zero of , there exists a critical point of with . All three of these conjectures were established for (in a sequence of papers culminating in this paper of Brown and Xiang ) and for sufficiently large (in a paper of myself , which in turn built upon several partial results in this setting). This left the case of intermediate to be settled. My arguments used some qualitative ingredients (most notably analytic continuation) and as such did not easily lend themselves to quantifying the threshold of above which the argument was valid. Recently, Lech Mazur was able to use an AI tool to resolve Sendov’s conjecture for all , with the proof verified in Lean . However, the AI-generated proof was not human-digested to be in the form of a publication-ready preprint; and it has taken me several days (with heavy AI assistance ) to perform such a digestion, to place the proof in proper context with previous literature and to simplify and streamline the argument to highlight the main ideas. (Note: the above chat log only represents a portion of the digestion work: the rest was performed with pen and paper, or using some further AI agents.) The same arguments also give a new proof of Rubinstein’s theorem, which I also give below the fold. One consequence of this digestion is that the argument in fact demonstrates Conjecture 3 , and thus resolves both the Sendov conjecture and the Phelps–Rodriguez conjecture in full generality. The proof ends up being remarkably elementary. No complex analysis is used…

Sources and evidence

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