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Mathematics tamed infinity, at least partially. In the nineteenth century, Georg Cantor developed a rigorous theory of infinite sets, showing that infinity is not one thing but many. Some infinities are larger than others. The natural numbers, one, two, three, and so on, form an infinite set. But the real numbers, including all decimals, form a larger infinity. Cantor proved there is no way to match every real number to a natural number; the reals are uncountably infinite, while the naturals are only countably infinite. This was revolutionary and disturbing. Cantor showed there is an infinite hierarchy of infinities, each larger than the last, with no top. Infinity is not a ceiling; it is an endless ladder. Some mathematicians of his time thought Cantor was mad. Today his ideas are foundational.