Physicist reckons two-button calculator can do all elementary math

The claim

It has been reported that Andrzej Odrzywołek, a postdoc at Jagiellonian University's Institute of Theoretical Physics, has authored a yet-to-be-peer-reviewed paper arguing a startling simplicity: a single two-input operator plus the constant 1 can generate the usual roster of elementary functions. The operator is eml(x,y) = exp(x) - ln(y) — exponential minus log — and, the paper alleges, finite compositions of eml and the terminal symbol 1 can reproduce trigonometric, algebraic and arithmetic functions, and even constants like π, e and i. Elegant? Absolutely. Plausible? That’s the question everyone’s asking.

The catch

Odrzywołek frames the idea as an analogue to universal binary gates in digital logic — NAND and NOR let you build every Boolean function; maybe eml could play a similar role for continuous mathematics. The paper itself admits there’s no settled definition of “elementary functions,” so the author picks a list of 36 common primitives and attempts to express each as a finite composition of eml and 1. But it has been reported that the work relies on floating-point numerical evaluation and heuristic filters rather than formal symbolic proofs; the supplement even calls symbolic verification “intractable.” He’s candid that the methods prioritise speed and exhaustiveness over proof-level rigor.

Reaction

The internet has been atwitter — Hacker News hosts a brisk and skeptical thread — and for good reason. Numerical evidence can be suggestive. It is not a substitute for a rigorous proof that every member of a proposed class can be generated. The author has yet to say whether the paper will be submitted for peer review, and anyone can read the PDF and “kick the tires,” as the article notes. Allegedly, the idea could reshape how we think about encoding and evaluating mathematical expressions if it withstands scrutiny, but that’s a big if.

Bottom line

If this turns out to be more than a clever trick, the payoff would be neat: uniform “circuits” for continuous math, simpler hardware or software primitives, new ways to search for formulas. But extraordinary simplicity demands extraordinary evidence. For now, it’s an enticing claim — one part elegance, two parts provocation — waiting for the slow, sometimes painful work of verification.

Sources: The Register