
The Deepest Uncertainty
Georg Cantor died in 1918 in a sanatorium in Halle, Germany. A preeminent mathematician, he had laid the foundation for the theory of infinite numbers in the 1870s. At the time, his ideas received hostile opposition from prominent mathematicians in Europe, chief among them Leopold Kronecker, once Cantor’s teacher. In his first known bout of depression, Cantor wrote 52 letters to the Swedish mathematician Gösta MittagLeffler, each of which mentioned Kronecker. But it was not just rejection by Kronecker that pushed Cantor to depression; it was his inability to prove a particular mathematical conjecture he formulated in 1878, and was convinced was true, called the Continuum Hypothesis. But if he blamed himself, he did so needlessly. The debate over the conjecture is profoundly uncertain: in 1940 Kurt Gödel proved that the Continuum Hypothesis cannot be disproven (technically speaking, that the negation of the Hypothesis cannot be proven), and in 1963 Paul Cohen proved that it cannot be proven. Poor Cantor had chosen quite the mast to lash himself to.In his first known bout of depression, Cantor wrote 52 letters to the Swedish mathematician Gösta MittagLeffler, each of which mentioned Kronecker.
How is it possible, though, for something to be provably…Read More…