# Post, Emil Leon, 1897-1954

Alternative names## Biographical notes:

Emil L. Post was a mathematician who worked in logic, set theory, and computation theory.

From the description of Papers, 1888-1994. (Unknown). WorldCat record id: 86138611

Emil L. Post was born in Poland in 1897. At the age of seven he emigrated with his mother and sisters to New York, where his father worked in the successful family clothing and fur business.

As a child growing up in Harlem, Post was especially interested in astronomy. Tragically, before age thirteen he lost his left arm in an accident. Post wrote to several observatories asking whether his handicap would exclude him from the profession of astronomy. While the response from Harvard College Observatory was encouraging ("there is no reason why you may not become eminent in astronomy"), the superintendent of the U.S. Naval Observatory wrote that "in my opinion the loss of your left arm would be a very serious handicap to your becoming a professional astronomer. In observational work with instruments the use of both hands is necessary in all the work of this observatory." Discouraged, Post turned his intellect away from the heavens and toward mathematics.

After graduating from Townsend Harris High School, Post entered City College of New York. By the time he received a B.S. in mathematics in 1917, Post had already done much of the work for a paper on generalized differentiation that was eventually published in 1930. From 1917-1920 Post was a graduate student at Columbia University. His doctoral dissertation involved the mathematical study of systems of logic, specifically the application of the truth table method to the propositional calculus of Whitehead and Russell's Principia Mathematica . Post was able to show that the axioms of propositional calculus were both complete and consistent with respect to the truth table method. This dissertation was to help form the foundation of modern proof theory.

Post spent the 1920-1921 academic year at Princeton on a post-doctoral fellowship. It was during this period that he continued to analyze the Principia Mathematica and began to grapple with a revolutionary idea that would become famous in the 1930s: the fundamental incompleteness of any formal logic. Unfortunately for Post, his early formulations were fragmentary and as he struggled to work them out, Kurt Gödel, who had no knowledge of Post's work, announced his landmark "incompleteness theorem" in 1931. When Alonzo Church published "An Unsolvable Problem of Elementary Number Theory" in 1936, Post's work, which remained unpublished, lost its claim to originality. In a 1938 letter to Gödel, a disappointed but gracious Post remarked that "any resentment I may have is at the Fates if not myself.... I have the greatest admiration for your work, and after all it is not ideas but the execution of ideas that constitute a mark of greatness."

In 1921 Post suffered his first attack of manic-depressive illness, a condition which was to reoccur throughout his life, often at the peak of creative periods. He recovered from this first occurrence well enough to begin teaching at Cornell, but after another collapse he found himself unemployed and unwanted in academia. For years he survived by teaching high school in New York. In 1932, Post began teaching at City College of New York, where he stayed for the rest of his career. Despite a treatment regimen that limited research time and a teaching load of sixteen hours per week, he continued to produce important papers.

In 1936 Post contributed a paper to the first issue of the Journal of Symbolic Logic entitled "Finite Combinatory Processes--Formulation I." This paper had much in common with Alan Turing's work on a universal computing machine. While Turing's work described the mechanics of such a machine, Post focused on the instructions, or "software," that would make the machine work. Post was able to prove that all computational processes could be reduced to a set of instructions that manipulated two symbols, "0" and "1."

Post's most influential mathematical work arose out of an address given to the American Mathematical Society in 1943. His paper on recursively enumerable sets, published in 1944, spawned a series of investigations on completeness and simplicity in set theory.

As a teacher at City College during the 1930s and 1940s, Post had a reputation as a demanding yet fair instructor. His classes were organized to the minute, and he did not encourage questions from his students. Still, he was a popular teacher who had many students go on to become professional mathematicians.

Post continued to struggle with manic depression throughout his career. In 1954, after a period of fairly good health, he became ill for the last time. He died of a heart attack shortly after being treated with electro-shock therapy in an upstate New York hospital. He was survived by his wife, Gertrude Singer Post (1900-1956) and his daughter, Phyllis Post Goodman.

From the guide to the Emil Leon Post Papers, 1927-1991, (American Philosophical Society)

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#### Subjects:

- Logic, Symbolic and mathematical
- Eugenics--United States
- Algorithms
- Set theory