The Radical Rejection of Infinity

Most mathematicians accept infinity as a core reality, but finitism argues that truly infinite objects simply do not exist. In this view, numbers are only real if they can be reached through a finite process of counting.

Finitists believe that math should be grounded in what we can actually construct or calculate. Because we can never physically finish counting to infinity, they argue that concepts like infinite sets are just useful fictions rather than objective truths. This challenges the foundation of much of modern science, which relies on the idea that space and time are infinitely divisible. It is a bold reminder that our most basic mathematical rules are choices, not necessarily laws of nature.