The reduction: 36 → 2

The paper starts with the "button set" of a standard scientific calculator and collapses it, one stage at a time, until only eml and 1 remain.

Calc 3, 6 primitives

Drop everything a polynomial ring can imply from exp/ln and closure under arithmetic. Keep: {exp, ln, negation, reciprocal, +} plus rational constants.

Calc 2, 4 primitives

Fuse negation and + into subtraction. Reciprocal becomes derivable from exp(−ln(x)). Keep: {exp, ln, −} plus rational constants.

Calc 1, 3 primitives

Swap the pair of transcendental functions for a single pair {exponentiation, logarithm} that can take base arguments, plus one transcendental constant (e or π).

Calc 0, 3 primitives

Promote to the two univariate functions exp(x) and ln(x), plus arithmetic via their interplay. Constants emerge automatically.

EML, 2 primitives

Notice the identity:

exp(x) − ln(y) = eml(x, y)

and that you never need exp and ln separately, you only ever need to compute the combination exp(something) − ln(something). So glue them into one operator. The constant 1 is preserved because ln(1) = 0 is what lets eml(x, 1) = exp(x).

Why it lands at 2

The paper conjectures that no non-constant binary operator alone (with zero distinguished constants) is enough. At least one constant is structurally required. Whether a ternary operator could eliminate the constant entirely is an open question at the end of the paper.