# Dirk Jan Struik

Dirk Struik, a highly respected analyst and geometer, and an internationally acclaimed historian of mathematics, was a good friend of the Mathematics Department at Tufts, and of the Tufts alumnus Norbert Wiener. The two were colleagues at MIT from 1926 until Wiener's death. Struik was born in the Netherlands in 1894. He attended school and obtained his doctorate there and married in 1923. The Struiks went to Rome and Göttingen where they met Norbert Wiener, who in 1926 got Struik to come to MIT.

## Education

Dirk Struik was born in Rotterdam on September 30, 1894, the same year as Norbert Wiener. In 1906 he entered the Hogere Burgerschool, which allowed entry to the university system after passing additional examinations. In 1912 he entered the University of Leiden, becoming the first in his family to attain a University education. He studied mathematics and physics with the intention of becoming a high school teacher. He took courses from H. A. Lorentz and de Sitter. Lorentz retired in 1912, and Paul Ehrenfest was appointed to his chair. It was he who pulled Struik into the academic world. Struik was strongly influenced by Ehrenfest and attended his weekly seminar. At this time mathematics and physics had close ties, and aside from being exposed to world class faculty (Lorentz and Kamerlingh Onnes were Nobel laurates by then) Struik heard guest speakers such as Curie, Rutherford, and Einstein. Indeed, Ehrenfest was Einstein's closest friend among physicists, and therefore he was aware of the importance of tensor calculus. Thus, Leiden became a center of research on general relativity, which Einstein visited frequently. In 1917, while working on a dissertation, his funds ran out and he left the university to take up a post teaching mathematics at the Hogere Burgerschool in Alkmaar, north of Amsterdam.

However, in November of that year he received a letter from J. A. Schouten in Delft asking if he would like to become his assistant. He did, and in 1922 he earned his doctorate with J. A. Schouten in tensor analysis and differential geometry. He was an assistant at the Technical University in Delft from 1917 to 1924.

## Career

From 1924 to 1926 a Rockefeller Fellowship enabled him to visit Rome, where he worked with Levi-Civita, who had collaborated with Einstein to develop the differential geometry for the general theory of relativity. From there he went to Göttingen, which was then the mathematical center of the world. There he interacted with Cartan, Courant, Hilbert, Landau, Noether, and Norbert Wiener. They took to each other from the start and talked a great deal of shop. They drank beer together and took walks on the nearby hills. When Wiener learned that Struik's plans for the future were rather vague he suggested that Struik come to MIT, where Wiener was an assistant professor. Dirk and Ruth Struik both liked the idea, and when he was offered a lectureship at MIT in the fall of 1926 (as well as a tempting job in Moscow), he accepted. Struik became assistant professor there in 1928, associate professor in 1931, and professor in 1940. He retired from MIT in 1960 as Professor Emeritus of Mathematics. His work at MIT contributed significantly to building up differential geometry there.

## Family

Soon after finishing his dissertation Struik met Dr. Saly Ruth Ramler, a Czech mathematician (and accomplished modern dancer). She had obtained a doctorate on the axiomatics of affine geometry under G. Pick and G. Kowalewski at the University of Prague in 1918 (making her, Struik remarked, possibly the first woman at that venerable University to receive a doctorate in mathematics). In 1923 they were married in Prague. She schemed to get him out of the Netherlands and from under the watchful eyes of Schouten. She made sure he encountered Levi-Civita and Courant at dinner during a mathematics meeting in Jena, and these men arranged for a Rockefeller Fellowship.

When they were in Rome she worked with Federigo Enriques, preparing a Italian edition of the tenth book of Euclid's *Elements*. They also had the chance to meet many other mathematicians (Amaldi, Castelnuovo, Volterra and Bianchi) who were working in Rome as well as Hadamard, Zariski and Aleksandrov, who were visiting there. While she was an accomplished mathematician, she was kept out of mathematics by illness for much of her adult life. She struggled with the tension between raising three daughters and wanting to do mathematics. She found it unfair that women cannot have a career and a family, and she resented and suffered from the discrimination bred out of the traditional expectation that a married woman do nothing but attend to the family. However, in later years she became mathematically active again, attending meetings and publishing. The Kovalevskaya Fund at the Gauss School in Peru was endowed in her memory.

Struik was a member of the Appalachian Mountain Club and enjoyed hiking in New England. Every year a led a group to Thoreau's cabin on Walden Pond and gave a brief talk on Thoreau and the land. He religiously drank a glass of sherry at 4pm. Also with guests present; he would note that it was 4pm "Time for a sherry. -- Would you like to have one?" This and his pipe were his only possible vices.

The Struiks had three daughters: Ruth Rebekka Struik, a mathematics professor at the University of Colorado; Anne Macchi of Arlington, MA, a teacher; and Gwendolyn Bray of New Zealand, an ecologist. Anne Macchi took care of her parents for many decades, and showed great judgement in allowing them their independence whenever possible. They had been married for 70 years at the time of his wife's death (at 99) on November 26, 1993. Having retired from MIT in 1960, he remained intellectually active, and lived to the age of 106. He died peacefully at his home in Belmont, MA on Saturday, October 21, 2000.

## Research

Struik had a productive career in differential geometry with much research based on collaboration with Wiener and Schouten. One accomplishment is the 1950 text *Lectures in Classical Differential Geometry*.

Since his time in Rome he had been interested in the history of mathematics. There he had encountered the historians of mathematics Ettore Bortolotti and Giovanni Vacca as well as the director of the Dutch archeological institute in Rome, G. J. Hoogewerff. He induced Struik to study the Dutch renaissance mathematician Paul van Middelburg, who had been an Italian bishop and advisor on calendar reform. Struik's historical interest came into focus just after their arrival in Göttingen, when Klein died. Courant asked Struik to prepare an edition of Klein's lectures on the history of 19th century mathematics for publication. Struik's approach to history was radical because he focused on people and circumstances rather than tracing ideas in isolation. In 1948 Struik published *A Concise History of Mathematics, Volumes I & II*, which, according to a review, "takes care to distinguish between established facts, plausible theories, wild hypotheses and traditional ideas", and remains a classic (as well as in print in a 1987 Dover edition). Also in 1948 Struik published *Yankee Science in the Making*, in which he studies how navigation and surveying were developed in America to serve trade and industry in New England. In a centennial tribute to Struik in 1994 Evelyn Simha, the Executive Director of the Dibner Institute for the History of Science and Technology, said:

As an historian of mathematics, he is particularly important...because of his great and influential book, A Concise History of Mathematics, beautifully balanced between technicalities and generalities, translated into uncountable languages, most recently Persian. With this book and his historical scholarship, Struik has become the instructor responsible for half the world's basic knowledge of the history of mathematics.

## Marxism and McCarthy

Struik developed left wing views while at the Hogere Burgerschool, being influenced by one of the teachers. He greeted the rise and observed the fall of communism in the Soviet Union. Throughout his life he maintained an active interest in Marxist socialism (as opposed to communism), and he was considered a major Marxist scholar. He edited the 100th anniversary edition of the works of Marx and Engels issued in Moscow, the main edition of the Communist Manifesto in the US, the works of Marx and Engels, and arranged to have Marx's doctoral dissertation published. These activities led to trouble in the McCarthy era, which he described as "half reminiscent of Nazi Germany, half of Alice in Wonderland." In 1951 he was denounced as a traitor by FBI informant Herbert Philbrick before the House Un-American Activities Committee. By July he was charged with being a member of the Communist Party and having taught Marxism. He was brought before the Committee and invoked the Fifth Amendment, refusing to answer each of over 200 questions that were put to him. In September 1951 he was indicted by a Middlesex County grand jury on charges of breaking an "Anti-Anarchy Law" by advocating the overthrow of the United States and Massachusetts governments. This prompted MIT to suspend him from teaching duties, but with full pay and benefits. During this time he continued his scholarly work, but also traveled nationwide with his wife to give public addresses on freedom of speech. After five years, the indictment was dropped for lack of evidence and because of a U.S. Supreme Court ruling that states do not have jurisdiction in such matters. In May 1956, MIT reinstated him, although not without grumbling about his "unbecoming" conduct of invoking the Fifth Amendment.

These political views and circumstances informed his approach to history, focusing his interest on the relationship between abstract thinking and the conditions of life in society. He liked a quote by Horkheimer: Science can be ideological in what it shuts its eyes to. Evelyn Simha of the Dibner Institute noted in 1994:

From the very beginning, personally and professionally, and continuing even now, Professor Struik's great concern for people in oppressed situations has been the backdrop for all his activities -- has informed his life and work, in fact, even when it brought him hard times.

He wanted to link mathematics with the socio-economic background against which mathematics developed -- questioning the weight of social and economic forces in the development even of the `pure math' of the Greeks, for example. He is now interested in ethno-mathematics and remains unshaken in his social and political beliefs.

## Retirement

Professor Struik continued his scholarly and teaching work after his retirement in 1960. In 1972 he was made an honorary research associate in the History of Science Department at Harvard University. In 1975 he was awarded a Gold Medal of Achievement by the National University of Mexico "for his services to the teaching and development of mathematics in Mexico over the years." In March and April that year, Professor Struik gave a series of lectures on the History of Mathematics to the MIT Concourse Forum. In Hamburg, Germany in May 1989, he was awarded the first Kenneth Ownsworth May Prize for History of Mathematics by the International Commission on the History of Mathematics & International Union of the History and Philosophy of Science. Well into his 90s he regularly drove to his MIT office to continue his research and scholarly work. In his centennial year he traveled far and wide and lectured to rapt audiences about "Mathematicians I have known". In these lectures he combined his remarkably detailed recollections with his inimitable wit to produce an unequaled impression of early 20th century mathematics and physics.

## Tufts

Well into his 90s he visited Tufts regularly, giving guest lectures in Lenore Feigenbaum's course on the history of mathematics at least every other year. Tufts faculty and alumni remember him, at well over 100, standing in front of the blackboard facing the audience and producing, without notes, a sweeping account of 19th century mathematics, providing literature references from memory as needed. For Christmas 1999 he was presented with a large portrait of himself that now hangs in the James A. Clarkson Conference room in the Bromfield-Pearson Building on Tufts campus, facing that of his friend Norbert Wiener.

When asked what he had done to achieve such longevity he was given to retorting that he simply had not died. At other times he attributed it and his happiness to 3M: Marriage, Mathematics, and Marxism. "Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts." Asked on his 100th birthday what he missed most, he replied: "My wife."*This page includes information obtained from a biography at St. Andrews College, obituaries in the MIT Mathematics **web pages**, the Boston Globe and the New York Times, and a 1987 interview with Struik (by David Rowe) published in the Mathematical Intelligencer in 1989.**If you have comments, suggestions, or further information, please contact **Professor Boris Hasselblatt**.*