Karl Menger Biography

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World of Mathematics on Karl Menger

One of the foremost mathematicians of the twentieth century, Karl Menger was especially recognized for his work in curve and dimension theory.

Menger was born on January 13, 1902 in Vienna, Austria, the son of eminent economist Carl Menger and novelist Hermione Andermann. From 1913 to 1920 he attended the Doblinger Gymnasium (a classical college-preparatory school), where in his last year he decided that he wanted a career in literature. Menger seems to have formulated this goal in the face of discouragement from his teachers, however, who thought he had far more talent in mathematics and physics. One of his teachers at the gymnasium described Menger as "not quite normal," megalomaniacal, and "a strange fellow."

Menger entered the University of Vienna later in 1920 and began studying physics. A year later his academic interests shifted to mathematics when he heard a lecture in which the professor mentioned that at the time there was no satisfactory definition of a curve. Menger was intrigued by this statement and immediately went to work on the problem. Within a few days, he had found a solution and presented it to the stunned lecturer. It was apparently this incident that led to Menger's further work in the area of curves and dimension.

Severe tuberculosis slowed Menger down considerably during the rest of his undergraduate career. In 1921 doctors sent him to a sanatorium in the Austrian Alps to recover. He remained there until 1923, but during that time did much of his fundamental mathematics work. Menger finally returned to the University of Vienna, receiving his doctorate in mathematics in 1924.

A year later, he moved to Amsterdam to begin research work with Egbertus Jan Luitzen Brouwer. Although the two did not get along particularly well, Menger did more valuable work there on curve and dimension theory as well as gaining a deeper understanding of logic and the foundations of mathematics. Meanwhile, he served as a docent in mathematics for nearby university students. Menger earned his teaching credential in 1926 and returned to the University of Vienna as chair of the Geometry Department.

Menger's prestige as a mathematician received a major boost in 1927 when he was chosen as a member of the elite Vienna Circle, a group of some three dozen scientists from wide-ranging disciplines. He remained at the University of Vienna for the next decade, except for the time he spent in 1930-1931 as a visiting professor at Rice and Harvard universities. He decided to resign from Vienna in 1937 and accepted a position at the University of Notre Dame in Indiana to avoid the worsening political situation in his homeland.

Once he had settled into his new position in the United States, Menger established the Mathematical Colloquium as a rival to the Vienna Circle. However, World War II soon began to affect the United States as well, and the group never gained the momentum it needed to make it as influential as the older body. Menger's passion for mathematics continued unabated, however, and he found his interests broadening to include probabilistic and hyperbolic geometry as well as the algebra of functions. Also, much of his work at the university was centered on teaching calculus to Navy cadets as part of the war effort.

Menger remained at Notre Dame until 1946, when he joined the new Illinois Institute of Technology (IIT) in Chicago. Because of his work during the war, which had convinced him that there must be a better way to teach basic mathematics, he expended great effort during the 1950s and 1960s to bring about changes in mathematics education. He wrote a textbook on calculus to this end.

After becoming an emeritus professor at IIT in 1971, Menger dedicated more time to leisurely pursuits. He enjoyed trying new foods, taking long walks, and listening to music. Menger and his wife, an actuarial student, had married in 1934 and had four children together. He died in his sleep on October 5, 1985 in Highland Park, Illinois.