Kurt Gödel

The family called him Herr Warum, Mr. Why, for the questions. His father managed and part-owned a textile firm in Brünn, and the house was German-speaking and comfortable. At six or seven the boy had rheumatic fever, recovered completely, read up on the disease, and concluded that his heart had been permanently damaged — a belief he kept for the rest of his life. At 12 the empire dissolved and he became a citizen of Czechoslovakia without moving house, which he resented. He went to Vienna at 18 meaning to study theoretical physics, sat in with the Vienna Circle, and turned to logic after a seminar on Bertrand Russell. Logic, he decided, came before every other science.

At 23 he proved that first-order logic is complete: whatever is true in every model can be derived. Then he showed where that stops. His 1931 paper on formally undecidable propositions found a way to encode statements about arithmetic as numbers inside arithmetic, and built a formula asserting its own unprovability. Any consistent system strong enough for ordinary number theory contains truths it cannot prove, and cannot prove its own consistency. Hilbert's program for complete, self-certifying foundations was over. Gödel went on to show that the axiom of choice and the continuum hypothesis are consistent with standard set theory, and in 1949 he gave Einstein a birthday present: solutions to the field equations describing a rotating universe in which a traveller can reach his own past.

In June 1936 Moritz Schlick, whose seminar had pulled him into logic, was shot dead on the university stairs by a former student. Gödel collapsed, developed a fear of being poisoned, and spent months in a sanatorium. After the Anschluss the University of Vienna refused his application for a paid post, the German army found him fit for conscription, and he and Adele left the long way round, by the Trans-Siberian Railway and a ship from Japan, reaching San Francisco in March 1940. At his citizenship hearing in 1947 he began explaining to the judge the inconsistency he had found in the United States Constitution that would let the country turn into a dictatorship legally. Einstein and Oskar Morgenstern, his witnesses, had come along precisely to prevent this. The judge changed the subject.

He ate only what Adele cooked. When a stroke put her in hospital late in 1977 he stopped eating, and on January 14, 1978 he died at Princeton Hospital weighing 65 pounds — the certificate said malnutrition and inanition caused by personality disturbance. Adele left his papers to the Institute for Advanced Study when she died in 1981, thousands of pages in an obsolete shorthand still being edited. The theorems escaped the discipline: into Hofstadter's Gödel, Escher, Bach in 1979, into arguments about minds and machines, and into a great deal of nonsense. In 2014 two computer scientists ran his proof of God through theorem provers. The corrected version held. Two years later they showed the original axioms were inconsistent.

Kurt Gödel's life against the full span of the corpus.

• On the Completeness of the Calculus of Logic article
  His doctoral dissertation, written at 23 1929
• On Formally Undecidable Propositions of Principia Mathematica and Related Systems article
  The incompleteness theorems, and the end of Hilbert's program 1931
• The Consistency of the Continuum Hypothesis book
  The constructible universe, from his Princeton lectures 1940
• Russell's Mathematical Logic article
  His statement of mathematical realism 1944
• The Gödel metric discovery
  A rotating universe with closed timelike curves, made for Einstein at 70 1949
• The ontological proof other
  A formalization of Anselm by way of Leibniz, circulated among friends 1970

• April 28, 1906 aged 0 Born at Brünn to a textile manufacturer's family
• 1924 aged ~18 Goes to the University of Vienna at 18 to study physics He switched to logic after a seminar on Russell's Introduction to Mathematical Philosophy.
• 1929 aged ~23 Proves the completeness theorem for first-order logic It was his dissertation, under Hans Hahn.
• 1931 aged ~25 Publishes the incompleteness theorems Von Neumann called the achievement a landmark visible far in space and time.
• June 22, 1936 aged 30 Moritz Schlick is murdered by a former student in Vienna Gödel suffered a severe nervous crisis and lasting fear of poisoning.
• September 1938 aged 32 Marries Adele Nimbursky, six years his senior His parents had objected to her for a decade.
• March 4, 1940 aged 33 Reaches San Francisco by way of Siberia and Japan The couple had left Vienna rather than face conscription into the German army.
• December 5, 1947 aged 41 Argues constitutional logic at his own citizenship hearing Einstein and Morgenstern were his witnesses. The judge moved on.
• January 14, 1978 aged 71 Dies at Princeton Hospital weighing 65 pounds He had stopped eating when his wife was hospitalized.

• Albert Einstein 1879–1955
  German-American theoretical physicist whose theory of relativity revolutionized modern physics. walked home with
• John von Neumann 1903–1957
  Hungarian-American mathematician and engineer whose computer architecture remains the basis of modern computing. championed by
• J. Robert Oppenheimer 1904–1967
  Theoretical physicist who led the Manhattan Project and became known as the father of the atomic bomb. colleague at the Institute
• Claude Shannon 1916–2001
  Mathematician and engineer who founded information theory, the basis of all digital communication. built on his encoding
• Richard Feynman 1918–1988
  Theoretical physicist known for his work in quantum mechanics and his accessible teaching style. Princeton contemporary