A recent paper by Andrzej Odrzywołek claims that the single operator exp x − log y plus variables and 1 can express every elementary function. The author proves this under a narrow definition of “elementary” that excludes polynomial roots.

Odrzywołek’s construction fixes 36 symbols as elementary and shows many constants and functions, like π, can be built. However, the proof relies on a modified logarithm and does not handle general algebraic adjunctions.

Mathematician Robert Smith argues that the broader, standard notion of elementary functions includes arbitrary polynomial roots. Using Khovanskii’s topological Galois theory, he demonstrates that EML terms possess solvable monodromy groups, whereas functions like a generic quintic root have non‑solvable monodromy, proving the claim false.

The debate highlights the limits of a single‑operator approach and underscores the need for algebraic closure when defining elementary functions. Current computational tools must retain full algebraic operations to remain expressive.