Math Gets Its NAND Gate: One Operator Builds Every Elementary Function

Andrzej Odrzywolek, a researcher at Jagiellonian University in Kraków, has found something unexpected. A single binary operator, called EML, can generate every elementary function in mathematics. The operator is just exp(x) - ln(y). Paired with the constant 1, it produces addition, subtraction, multiplication, division, exponentiation, trig functions, and the constants e, pi, and i. Odrzywolek describes it as a universal primitive for continuous math, comparable to the NAND gate in Boolean logic. He found it through exhaustive search.

The practical payoff is symbolic regression. Every EML expression forms a uniform binary tree following a simple grammar: S → 1 | eml(S,S). That uniformity means you can treat these trees as trainable circuits. Run Adam optimizer on numerical data and the system recovers exact closed-form formulas at tree depths up to 4. When your data comes from an elementary law, EML trees find the exact formula rather than just fitting a curve.

Community response has focused on trade-offs. People have questioned whether composing EML gates actually reduces complexity compared to existing approaches. Hardware implementation remains speculative. Optimization gets harder as trees deepen. But the core finding stands. We've never had a single universal primitive for continuous math. Now we do.