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Equation 1 · Part 2 · FunSearch Found New Mathematics Without Ever Understanding the Problem

superscript

{0,1,2}n\{0,1,2\}^n
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

A cap set is a subset of the grid \{0,1,2\}^n with one rule: no three distinct points in it are allowed to sum to zero coordinate-wise modulo three. The largest such set in eight dimensions had been 496 points since 1994. In December 2023, a Google DeepMind system called FunSearch reported one with 512 [ 1 ] . DeepMind’s own announcement called it the largest jump in cap set sizes in twenty years [ 3 ] . Both of those claims check out — this article verified the 512-point construction and the ablation data behind it directly against the paper’s own supplementary material, not against the press release alone [ 2 ] . The question this article asks is not whether FunSearch found something real.…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.