Georg Cantor

German mathematician who created set theory and the theory of transfinite numbers — proving that infinite sets come in different sizes and that the continuum cannot be put into bijection with the natural numbers.

Cantor's theorem: for any set, its power set is strictly larger — there is no largest infinity. The diagonal argument proves there are more real numbers than natural numbers — uncountably many. Defined ordinal and cardinal arithmetic for infinite sets. The Continuum Hypothesis: is there a cardinality between ℵ₀ and 2^ℵ₀? (Independent of ZFC, proven by Gödel and Cohen).