"Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do."— Dirk Jan Struik |

Dirk Jan Struik, Professor Emeritus of mathematics at the Massachusetts Institute of Technology, died peacefully on Saturday, 21 October 2000 at his home in Belmont, Massachusetts. He had just turned 106, on September 30. In celebration for what was to be his last birthday, friends from around the world presented him with many multicolor posters containing expressions of admiration and gratitude for the depth and rigor of his academic scholarship and the boldness of his political stances, moving tributes attesting to how he enriched their lives, and words of hope for the worldwide struggle for justice and peace that he championed.

Struik's life spanned many eras. He was born in 1894 in Rotterdam, Holland, where he studied from grammar through high school. In a recent interview, he speculated that from his father, who was a schoolteacher, he inherited a love of mathematics and history (Powell and Frankenstein, 1999, p. 421). In 1912, Struik entered Leiden University to study mathematics and physics. In contrast to his high school notions, he attributed his understanding of the spirit of mathematics and science to the theoretical physicist Paul Ehrenfest at Leiden: "All the science I had learned before was static. Ehrenfest showed me how science is a living and growing field" (Powell and Frankenstein, 1999, p. 442).

In 1922, Struik received a doctorate with a dissertation on applications of tensor methods to Riemannian manifolds (Struik, 1922). However, even before receiving a doctorate, he had already embarked on publishing his many mathematical reflections (Schouten and Struik, 1918). Struik and Jan Arnoldus Schouten carried on an important and fruitful collaboration (Rowe, 1994, contains an extensive bibliography of their technical papers, as well as of Struik's other works). Throughout his life, Struik did considerable work in and kept current with the mathematical ideas of tensor calculus, Riemannian manifolds, differential geometry, and absolute differential calculus. He wrote a large number of mathematical papers and books, including, in 1950, his *Lectures on Classical Differential Geometry*. At age 101, he published a review (1995a) of Karin Reich's (1994) history of tensor calculus and a few years earlier had contributed his own account of the emergence of tensor calculus (1989).

A year after completing his doctorate, Struik married Saly Ruth Ramler, a native of Czechoslovakia, who also became an accomplished mathematician. She died in 1993 at age 99. From 1924 to 1926, with Struik's Rockefeller fellowship, he and his wife traveled to several other European countries and studied, met, and collaborated with many of the great mathematicians and scientists of the Twentieth Century, including Tullio Levi-Civita, Richard Courant, and David Hilbert.

Nevertheless, by 1926, Struik found himself unemployed in Holland and with limited opportunities in Europe. After an inquiry from Norbert Wiener, Struik accepted a teaching post from Samuel Stratton, the president of MIT.

From then until 1960, Struik taught and researched at MIT and became internationally acclaimed as a mathematician and historian of mathematics and science. His* A Concise History of Mathematics*, which has been translated into more than seventeen languages, was first published in 1948 (Struik, 1948a). The fourth revision appeared in English in 1987. The book "has probably done more to promote interest in and appreciation for the rich diversity of mathematical ideas and cultures than any other single volume on the history of mathematics" (Rowe, 1994, p. 245).

Perhaps not as well known as his other academic achievements is the fact that Struik was a founding editor (in 1936) of the Marxist-oriented journal, *Science and Society*, and the editor of books on Marxism (Struik 1964a and 1971). He was a scholar-activist whose work exemplifies a commitment to unite theory and practice in the struggle for social and economic justice. Internationally, he influenced scholars from diverse disciplines — mathematicians, philosophers of mathematics and science, and historians of mathematics and science — as well as inspiring practical activities.

His research for his book, *Yankee Science in the Making* (1948b, reprinted 1991, New York: Dover) helped lead to the restoration of several of the sites he studied, including the old manufacturing section of Lowell, Massachusetts, and some sections of the Middlessex Canal.

*Dirk Jan Struik in his home, April 1998
Photograph by Marilyn Frankenstein*

As the above indicates, the influence of Struik's work was not just confined to the academy. With other left and liberal activists, from 1944 to 1948, Struik founded and taught at the Samuel Adams School, where, on a volunteer basis, individuals taught courses on labor laws, international conditions, science, and so on. The school filled a need for centers that would promote progressive and militant citizenship among adult workers and an interest in trade unions and leftwing political parties, goals thought unattainable in public schools and colleges.

From 1951 to 1956, Struik suffered an interruption in his MIT professorship. He became a victim of the anti-democratic political witch-hunt of communists and their fellow travelers that was led by Senator Joseph McCarthy and the House Un-American Activities Committee. The Commonwealth of Massachusetts charged him with three counts of sedition, and MIT suspended him with pay. In 1951, though denounced by FBI informant Herber Philbrick, using the right awarded under the Fifth Amendment, Struik refused to "name names," which led him to be branded a Fifth Amendment communist. Eventually, the Supreme Court accepted Struik's plea that the Commonwealth's anti-sedition laws were unconstitutional. In 1956, MIT reinstated Professor Struik, restored his tenure, but censured him "for conduct unbecoming" an MIT professor, basing its judgement on his use of the Fifth Amendment before the House Un-American Activities Committee and "lack of candor with members of the [MIT] administration." Four years later he retired from MIT. Struik's personal experience of persecution led him to lecture widely on freedom of speech issues.

A major theme of Struik's life work consisted of attempting to combine his mathematics and his Marxism. The result was to reconcile the two into a new discipline: the sociology of mathematics (Struik, 1942 and 1986). Besides his purely mathematical preoccupations, he concerned himself with discovering whether and in what ways social and institutional forces influence mathematical research. As Alberts (1994) notes, Struik asserted "that mathematical conceptions can better be understood in conjunction with larger social and intellectual processes" (p. 280). He has used the analytical tools of dialectical and historical materialism to examine and understand the unfolding of mathematical ideas. However, Struik went beyond assertions and demonstrated that social context interacts with the production of mathematical knowledge. Unlike historians before him, he believed that an understanding of the operative forces within a society was indispensable for knowing and doing historical work on mathematics. In this way, Struik reconciled mathematics and politics by shaping a new sociology of mathematics and science and made significant contributions to the history of these disciplines. These included a study of how philosophical notions decisively influenced Marx's theoretical ideas on the foundation of the calculus (Struik, 1942, 1948c [reprinted in Powell and Frankenstein, 1997]; for more of his work on the sociology of mathematics and science, see 1964b, 1984a, 1984b, 1986). Interestingly, as Alberts (1994) states, Struik's "numerous contributions to the history of mathematics were largely undertaken as a complement to his own mathematical production, and were only rarely self-reflexive in the sense of touching on the latter" (p. 290).

Throughout his life, Struik remained an active intellectual. In recent years, Struik extended his scholarship in the sociology of mathematics to include written and oral commentary on the nascent field of ethnomathematics. He published articles in *Monthly Review* (1995b), "Multicultural Mathematics and the History of Mathematics," and in *Technology Review* (1995c), "Everybody counts: Toward a broader history of mathematics." Even more recently, he spoke about research in ethnomathematics at conferences at the University of Massachusetts in Boston (1997) and then at a pre-session of the joint mathematics meetings in Baltimore, Maryland (1998). He was especially keen on the academic and political program of ethnomathematics, which aims to connect mathematics to its origins in culture (including social and productive contexts) and to link mathematics education to social justice.

Struik had a fascinating career whose motive force was his pitiless intellectual curiosity. During one of our last visits with him, after we remarked on how sharp his memory still was for details, Struik pointed to a spherical, crystal bowl given to him in Holland at a celebration of his 100^{th} birthday with the etching *M* + *M* + *M* = 100. He said that equation symbolized what was responsible for his stamina and continued intellectual acuity: "Marriage, Mathematics, and Marxism."

See also the obituary on the MIT web site and the biography of Struik at the St. Andrews history of mathematics site.

Alberts, Gerard (1994). On Connecting Socialism and Mathematics: Dirk Struik, Jan Burgers, and Jan Tibergen*, Historia Mathematica*, 21, 280-305.

Powell, Arthur B. and Frankenstein, Marilyn, Eds. (1997). *Ethnomathematics: Challenging Eurocentrism in Mathematics Education*. New York: State University of New York.

Powell, Arthur. B. and Frankenstein, Marilyn. (1999). In His Prime: Dirk Jan Struik Reflects on 102 Years of Mathematical and Political Activities. *The Harvard Educational Review*, 69, 4: 416-445.

Reich, Karin (1994). *Die Entwicklung des Tensorkalküls. Vom absoluten Differentialkalkül zur Relativtätstheorie*. Berlin: Birkhäuser Verlag.

Rowe, David E. (1994). Dirk Jan Struik and His Contributions to the History of Mathematics, *Historia Mathematica*, 21, 245-273.

Schouten, Jan Arnoldus and Struik, Dirk J. (1918). On the Connection between Geometry and Mechanics in Static Problems, *Proceedings Koninklijke Akademie van Wetenschappen Amsterdam*, 27: 801-809.

Struik, Jan Dirk (1922). *Grundzüge der mehrdimensionalen Differentialgeometrie in direkter Darstellung* (Doctoral Dissertation, University of Leiden), Berlin: Springer-Verlag, 1992.

__ __. (1942). On the Sociology of Mathematics. *Science and Society*, 6, 58-70.

__ __. (1948a). *A Concise History of Mathematics*. New York: Dover, 2nd rev. ed., 1951; 3rd rev. ed., 1967, 4th rev. ed. 1987.

__ __. (1948b). *Yankee Science in the Making*. Boston: Little, Brown; reprinted, New York: Dover, 1991.

__ __. (1948c). Marx and Mathematics. *Science and Society*, 12, 118-196; reprinted in Arthur B. Powell and Marilyn Frankenstein (1997), pp. 173-192.

__ __. (1950). *Lectures on Classical Differential Geometry*. Cambridge, MA: Addison-Wesley; 2^{nd} ed., Reading, MA: Addison-Wesley, 1961.

__ __. Ed. (1964a). *Economic and Philosophic Manuscript of 1844 by Karl Marx*. New York: International Publishers.

__ __. (1964b). The Influence of Mercantilism on Colonial Science in America. *Organon* (*Warsaw*), 1, 157-163.

__ __. Ed. (1971). *Birth of the Communist Manifesto*. New York: International Publishers.

__ __. (1984a). Early Colonial Science in North America and Mexico, *Quipu*, 1 25-54.

__ __. (1984b). Early Colonial Science in North America and Mexico, *Quipu*, 2, 323-325.

__ __. (1986). The Sociology of Mathematics Revisited. *Science and Society*, 50, 280-299.

__ __. (1989). Schouten, Levi-Civita, and the emergence of tensor calculus. In D. E. Rowe and J. McCleary (Eds.), *The History of Modern Mathematics*, 2 vols. Boston: Academic Press, 2:99-105.

__ __. (1995a). Reviews. *Historia Mathematica*, 22, 323-330.

__ __. (1995b). Multicultural Mathematics and the History of Mathematics. *Monthly Review*, 28-33.

__ __. (1995c, August-September). Everybody Counts: Toward a Broader History of Mathematics. *Technology Review*, 36-42, 44.

*Arthur B. Powell is Associate Professor of Mathematics and Mathematics Education at Rutgers University-Newark; Marilyn Frankenstein is Professor at the College of Public and Community Service of the University of Massachusetts-Boston. *

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Saturday, October 21, 2000