Mathematicians Ernst Zermelo and Abraham Fraenkel used set theory to give mathematics a foundation at the beginning of the 20th century. Before then subfields such as geometry, analysis, algebra and stochastics were largely in isolation from each other. Fraenkel and Zermelo formulated nine basic rules, known as axioms, on which the entire subject of mathematics is now based.

One such axiom, for example, is the existence of the empty set: mathematicians assume that there is a set that contains nothing; an empty bag. Nobody questions this idea. But another axiom ensures that infinitely large sets also exist, which is where finitists draw a line. They want to build a mathematics that gets by without this axiom, a finite mathematics.

And yet there are physicists who follow this philosophy, including Nicolas Gisin of the University of Geneva. He hopes that a finite world of numbers could describe our universe better than current modern mathematics. He bases his considerations on the idea that space and time can only contain a limited amount of information. Accordingly, it makes no sense to calculate with infinitely long or infinitely large numbers because there is no room for them in the universe.

This effort has not yet progressed far. Nevertheless, I find it exciting. After all, physics seems to be stuck: the most fundamental questions about our universe, such as how it came into being or how the fundamental forces connect, have yet to be answered. Finding a different mathematical starting point could be worth a try. Moreover, it is fascinating to explore how far you can get in mathematics if you change or omit some basic assumptions. Who knows what surprises lurk in the finite realm of mathematics?