Georg Cantor proved that infinity comes in different sizes — that there are more real numbers than whole numbers, even though both sets are infinite. The idea was so counterintuitive that it drove him into repeated nervous breakdowns, provoked the most vicious academic feud in the history of mathematics, and was called a “disease” by his rival Leopold Kronecker. Cantor spent his final years in a psychiatric hospital, and the mathematics that put him there is now considered one of the foundations of modern logic.

This episode traces Cantor from his Russian-German childhood through the diagonal proof that shattered intuitions about infinity, the Kronecker persecution, and the mental illness that consumed a mind too original for its own era.

• Cantor’s diagonal argument — the elegant proof that some infinities are larger than others
• The concept of transfinite numbers and the continuum hypothesis that remains unresolved
• Leopold Kronecker’s campaign to destroy Cantor’s career and block his publications
• The recurring breakdowns, the psychiatric hospitalizations, and Cantor’s death in an asylum