Godel was a mathematician, logician, and philosopher whose theorems provided the foundation for theoretical computer science

Kurt Godel was a mathematician, logician, and philosopher born in April 1906 in what is now Brno, Czech Republic. Godel was a sickly child who suffered from rheumatic fever as a six-year-old. It’s said that Godel’s early illness left him paranoid about things like cleaning eating utensils obsessively, and about the purity of his food. Godel went to Austria in 1924 to study at the University of Vienna, where he earned a doctorate in mathematics before joining the faculty in 1930.

The Completeness Theorem

Godel’s doctoral thesis, Über die Vollständigkeit des Logikkalküls (On the Completeness of the Calculus of Logic), proved the completeness theorem. Godel showed that: “…classical first-order logic, or predicate calculus, is complete in the sense that all of the first-order logical truths can be proved in standard first-order proof systems.”

The Incompleteness Theorem

In 1931, Godel published Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme (On Formally Undecidable Propositions of Principia Mathematica and Related Systems).  The incompleteness theorem showed that: “…in any consistent axiomatic mathematical system there are propositions that cannot be proved or disproved within the system and that the consistency of the axioms themselves cannot be proved.” To put it another way, Godel proved that there are mathematical statements out there which are true, but which can not be proven.

It’s so hard to understand that it must be important. Godel’s work, particularly his Incompleteness Theorem, has been described as one of the most remarkable mathematical or logical achievements of the 20th century. Godel has been described as the founder of theoretical computer science.

Godel and Einstein, intellectual peers

Publication of the incompleteness theorem brought Godel international fame. Godel lectured extensively in the United States, including at Princeton University, where he met Albert Einstein. Godel and Einstein would become and remain friends until Einstein died in 1955.

Einstein and Godel were very different men. In The New Yorker’s February 20, 2005 article, Time Bandits, described them this way:

Whereas Einstein was gregarious and full of laughter, Gödel was solemn, solitary, and pessimistic. Einstein, a passionate amateur violinist, loved Beethoven and Mozart. Gödel’s taste ran in another direction: his favorite movie was Walt Disney’s “Snow White and the Seven Dwarfs,” and when his wife put a pink flamingo in their front yard he pronounced it furchtbar herzig—“awfully charming.” Einstein freely indulged his appetite for heavy German cooking; Gödel subsisted on a valetudinarian’s diet of butter, baby food, and laxatives.

But there was an undeniable kinship, too. Einstein is said to have told people that he went to his office “just to have the privilege of walking home with Kurt Godel.”

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The accolades

In 1951, Godel was awarded the first Albert Einstein Award, along with Julian Schwinger. (The photograph above is of Einstein presenting that award to his colleague.) Godel was awarded the National Medal of Science in mathematics and computer science from President Ford in 1974. The citation for the 1974 prize says: “For laying the foundation for today’s flourishing study of mathematical logic.” An annual award for outstanding papers in theoretical computer science, The Godel Prize, was named after him.

Beyond mathematics

Godel transitioned from mathematics and logic to philosophy in later years. He was particularly interested in the idea of Mathematical Platonism. He argued that “sentences” like 2+2=4 truly described non-physical and non-mental collections of objects that existed outside of time and space in a mathematical realm called “Platonic Heaven.” Godel’s philosophical views, though tied to his accepted mathematical and logical theorems, were not widely accepted.

 A fascinating and comprehensive source for all things Godel, including his philosophical work, is the Stanford Encyclopedia of Philosophy.

Godel’s paranoia progressed with age. Godel would not eat unless his wife, Adele, tasted his food first out of certainty he was being poisoned. Adele was hospitalized for a time due to her own illness. As a result, Godel stopped eating and starved to death.

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