Really worth going to the actual paper[1] instead of this rather shameful press release - the second sentence in particular deflates the optimistic mood: "The

Really worth going to the actual paper[1] instead of this rather shameful press release - the second sentence in particular deflates the optimistic mood: "The effectiveness of FunSearch in discovering new knowledge for hard problems might seem intriguing. We believe that the LLM used within FunSearch does not use much context about the problem; the LLM should instead be seen as a source of diverse (syntactically correct) programs with occasionally interesting ideas. When further constrained to operate on the crucial part of the algorithm with a program skeleton, the LLM provides suggestions that marginally improve over existing ones in the population, which ultimately results in discovering new knowledge on open problems when combined with the evolutionary algorithm. Another crucial component of the effectiveness of FunSearch is that it operates in the space of programs: rather than directly searching for constructions (which is typically an enormous list of numbers), FunSearch searches for programs generating those constructions. Because most problems we care about are structured (highly non-random), we hypothesize that solutions are described more concisely with a computer program, compared to other representations." It is perhaps unfair to say that DeepMind has brute-forced generating programs rather than brute-forcing a single program that generates an answer - but effectively that's what they did, and it's a very cool idea! They did the same with "DeepTensor" or whatever their program for finding matrix multiplication algorithms was called. I am not denying that this is a useful direction for computational mathematics research - I have personally spent a lot of time blindly fiddling with SAGE hoping the computer will spit out a nicer answer. Having this process automated seems useful. But saying that this tech "outdoes human mathematicians" is pure dishonesty, very much like saying MATLAB "outdoes human physicists" at understanding fluid mechanics. FunSearch doesn't understand what a set is (or even what a number is), any more than MATLAB understands what viscosity is. LLMs are still much worse at actual quantitative reasoning than pigeons or mice, let alone humans. [1] https://www.nature.com/articles/s41586-023-06924-6 https://www.nature.com/articles/s41586-023-06924-6