Georg Cantor

Georg Cantor created set theory and established one-to-one correspondence between sets, proving the real numbers outnumber the natural numbers and implying an infinity of infinities. He defined cardinal and ordinal numbers and their arithmetic. His theory of transfinite numbers struck contemporaries as counter-intuitive: Leopold Kronecker called him a "scientific charlatan" and "corrupter of youth," while decades later Ludwig Wittgenstein dismissed set theory as "utter nonsense." A devout Lutheran, Cantor believed God had communicated the theory to him; some theologians saw it as a challenge to divine uniqueness, though Cardinal Johann Baptist Franzelin accepted it. Cantor suffered recurring depression from 1884 until his death in 1918, blamed by some on the hostility, by others on bipolar disorder. In 1904 the Royal Society awarded him its Sylvester Medal, and David Hilbert later declared, "No one shall expel us from the paradise that Cantor has created."