Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor was a German mathematician whose astonishing creative vision invented modern set theory and tamed the concept of mathematical infinity. Born in Saint Petersburg and educated at the University of Berlin under Karl Weierstrass and Leopold Kronecker, Cantor spent his academic career at the University of Halle.

In 1874, Cantor published a paper demonstrating that the set of real numbers cannot be put into one-to-one correspondence with the set of natural numbers. Using his famous diagonal argument, he proved that infinity is not a single monolith: there are multiple, hierarchically distinct sizes of infinity, showing that the continuum of real numbers is strictly larger than the infinity of integers. He introduced transfinite cardinal numbers (aleph numbers: א₀, א₁...) and formulated the Continuum Hypothesis. Fiercely attacked by contemporaries like Kronecker who denounced him as a 'corrupter of youth', Cantor suffered bouts of severe depression, but was defended by David Hilbert, who famously proclaimed: 'No one shall expel us from the paradise that Cantor has created for us.'