Researchers found one 'master' math trick that can recreate every single function on your old scientific calculator.
March 24, 2026
Original Paper
All elementary functions from a single binary operator
arXiv · 2603.21852
The Takeaway
Instead of needing different formulas for sines, square roots, and logarithms, this discovery proves that a single 'universal' rule can build the entire repertoire of standard math. It suggests that the complex language of science and engineering may be built from a much simpler foundation than we ever realized.
From the abstract
A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as $e$, $\pi$, and $i$; arithmetic operations includin