What If Cantor Was Wrong?

A blog post about infinity, categories, and a mathematical mystery. Cantor showed that not all infinities are equal: the infinity of the natural numbers (ℵ₀) is genuinely smaller than the infinity of the real numbers (called c, the continuum). He then asked what seems like a natural follow-up: is there anything in between? His conjecture that the answer is no became known as the Continuum Hypothesis (CH). He spent years trying to prove it. He failed. He had a breakdown. He died without knowing t