Mathematical Minimalism

It has been reported that a surprising bit of math economy is making the rounds: Andrzej Odrzywolek allegedly posted an arXiv paper showing that you can obtain all the elementary functions from a single base function — referred to in the write-up as the "elm" function — together with the constant 1. The paper’s supplement reportedly lays out explicit equations that bootstrap addition, subtraction, multiplication and division from that one primitive. Neat trick. Elegant, too.

The claim

According to the supplement, once you take that one function and the constant 1 as primitives, you can algebraically build constants like π and standard operations such as square, square root, and the familiar circular and hyperbolic functions. It has been reported that the derivations are constructive: not just existence proofs but explicit formulas showing how the usual toolbox can be assembled from very little. If true, it’s the kind of result that delights people who like seeing complexity reduced to a single, tidy origin.

Why it matters

Why should anyone care? Because this is the same urge that produced universal gates and minimalist instruction sets: find a small, complete foundation and you get insight into structure, implementation and sometimes surprising efficiencies. Could this change how we build math libraries? Probably not overnight. But for theoretical computer scientists, numerical analysts and people who love the elegance of minimalism, it’s a sweet reminder that big systems can sometimes be reconstructed from very small kernels.

What’s next

The paper and its supplement are the place to look for details and verification; community vetting will tell us how robust and practical the constructions are. For now, treat the result as an intriguing theoretical feat — a little like finding a single Lego that, in principle, can build the whole model. Will it be used to rewrite numerical libraries? Maybe not. Will it spark fresh thinking about foundations and implementation? Almost certainly.

Sources: johndcook.com, Hacker News