Equation 10 · FunSearch Found New Mathematics Without Ever Understanding the Problem
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Symbol n
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What the article says around this equation
The specific number this article opened with, 496 rising to 512 in dimension eight, sits at the fixed-dimension end of the problem, where a mathematician doesn’t ask about the asymptotic growth rate but about one exact number for one specific n . FunSearch’s paper reports this as its headline cap-set result and its own supplementary material adds a detail the blog post omits entirely: across 140 independent runs of the search, only four ever found a set of size 512 [ 2 ] . Fewer than one run in thirty. That is not the signature of a system that understood the structure of the problem and derived the answer. It is the signature of a system exploring a landscape with a narrow, hard-to-find…
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The specific number this article opened with, 496 rising to 512 in dimension eight, sits at the fixed-dimension end of the problem, where a mathematician doesn’t ask about the asymptotic growth rate but about one exact number for one specific n . FunSearch’s paper reports this as its headline cap-set result and its own supplementary material adds a detail the blog post omits entirely: across 140 independent runs of the search, only four ever found a set of size 512 [ 2 ] . Fewer than one run in thirty. That is not the signature of a system that understood the structure of the problem and derived the answer. It is the signature of a system exploring a landscape with a narrow, hard-to-find peak, succeeding often enough across repeated attempts to be worth reporting, and failing the overwhelming majority of the time.
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