German mathematician who built a hierarchy of infinite sets according to their cardinal number. By one-to-one pairing, he showed that the set of real numbers has a higher cardinal number than does the set of rational fractions. However, he found every class of algebraic numbers has the same cardinal number as the integers. Such considerations led to his Mengenlehre (theory of assemblages) and Mannigfaltigkeitslehre (theory of manifolds). He also invented the Cantor set.

Cantor's highly original views were vigorously opposed by his contemporaries, especially Kronecker. The attacks contributed to the nervous breakdowns he suffered throughout the final 33 years of his life. Cantor died in a mental institution.

Kronecker

Additional biographies: MacTutor (St. Andrews)