Physicist Reckons Two-Button Calculator Can Do All Elementary Math
18th April 2026
Every now and then, a researcher comes up with something that sounds either wrong or unoriginal to outsiders – yet carries just enough of a chance of being correct, novel, and consequential to demand a closer look.
On this occasion, the honor goes to Andrzej Odrzywo?ek, a postdoctoral researcher at the Institute of Theoretical Physics, Jagiellonian University, Kraków.
In a recently updated, yet-to-be-peer-reviewed paper, Odrzywo?ek says he has, in essence, developed a two-button calculator that can compute the standard repertoire of a scientific calculator familiar to a high school math and science student. You might have to push the buttons a number of times, but the point is the underlying simplicity.
A single two-input gate already suffices for all Boolean logic in digital hardware; Odrzywo?ek’s claim is that continuous mathematics may have an analogous primitive. It can generate elementary functions from a single operator that would otherwise require multiple distinct operations. These include trigonometric functions such as sine, cosine, and tangent; algebraic functions; and arithmetic operations such as addition, subtraction, multiplication, and division. The two-input gate also produces constants including ?, e (Euler’s number, 2.71828…), and i (the square root of minus one).
The proposed operator is eml(x, y) = exp(x) – ln(y). Eml is the exponential-minus-log function, exp is the exponential function, and ln is the natural logarithm (or the logarithm to the base e).
“A calculator with just two buttons, EML and the digit 1, can compute everything a full scientific calculator does. This is not a mere mathematical trick. Because one repeatable element suffices, mathematical expressions become uniform circuits, much like electronics built from identical transistors, opening new ways to encoding, evaluating, and discovering formulas across scientific computing,” the paper says.
It even has a diagram showing how the functions cascade from the proposed operator.