You can't get any bigger than infinite, right? Well, kind of.

Late in the 19th century, German mathematician Georg Cantor showed that infinite comes in different types and sizes.

Scientific American doesn't do the best job of making Cantor's math understandable, but the last time I received a math grade higher than a D was in high school – so it might not be their fault.

The bottom line: by using a neat little trick called diagonalization, Cantor showed that there are fewer possible whole numbers – i.e., non-decimal – than there are possible decimal numbers between zero and one. And that's not all: he also showed

... that the set of integers had an equal number of members as the set of even numbers, squares, cubes, and roots to equations; that the number of points in a line segment is equal to the number of points in an infinite line, a plane and all mathematical space....

At the time, studying infinity was a radical, almost heretical choice:

mathematicians were discouraged from treating infinity as having an actual value. Henri Poincare – a mathematician so influential that even I've heard of him – said that future generations would consider

Cantor's work a "disease." And he was one of the nice critics.

Cantor was personally and professionally attacked, his papers suppressed. He spent the last three decades of his life wracked by nervous breakdowns, shuttling in and out of mental institutions. But even as he weakened, his math gained acceptance. Cantor's set theory is, along with logic and predicate calculus, central to modern mathematics: anything that involves high-level equation-crunching, from economics to physics to biology to computer engineering, owes a debt to

Cantor.

It's a sad story ... but at least Cantor was still alive when science changed its mind about him. Contrast that to Ignaz Semmelweis, who had the misfortune of telling doctors to wash their hands decades before Pasteur made it fashionable.

Strange but True: Infinity Comes in Different Sizes [Scientific American]

Bert Wachsmuth's Biography of Georg Cantor