Paradoxical Math: A Study of Inconsistent Consistency

Welcome to the Banach–Tarski Paradox page, where the lines blur between reality and madness.

Dive deeper into the depths of mathematical inconsistency Back to Paradoxical Math Home

What is the Banach–Tarski Paradox?

In 1924, Polish mathematicians Stanisław Banach–Tarski and Stefan Banach discovered that a sphere is a subset of the plane, and a plane is a subset of the sphere.

This paradoxical finding challenged the fundamental understanding of topology at the time, forcing mathematicians to re-evaluate their understanding of dimensions.