A mathematician critiques a viral paper claiming that the 'Exp-Minus-Log' (EML) function is sufficient to express all elementary functions. While acknowledging the paper's result is clever within its own narrow definition of 'elementary', the author argues that the standard mathematical definition of elementary functions — which includes arbitrary polynomial roots — is broader than what EML terms can express. Using Khovanskii's topological Galois theory, the author proves that every EML term has a solvable monodromy group, and since certain algebraic functions (like roots of degree-5+ polynomials) have non-solvable monodromy groups, they cannot be expressed as EML terms. The conclusion is that EML is not the continuous analog of a universal gate like NAND.
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