Dirk J. Struik

Interview with Dirk Jan Struik

Dirk J. Struik was born in Rotterdam in 1894, where he attended the Hogere Burger School from 1906-1911 before enter ing Leiden University. At Leiden he studied algebra and analysis with J. C. Kluyver, geometry with P. Zeeman, and physics under Paul Ehrenfest. After a brief stint as a high school teacher at Alkmaar, he spent seven years at Delft as the assistant to J. A. Schouten, one of the founders of tensor analysis. Their collaboration led to Struiks dissertation, Grundziige der mehrdimensionalen Differentialgeometrie in direkter Darstellung, published by Springer in 1922, and numerous other works in the years to follow. From 1923 to 1925 Struik was on a Rockefeller Fellowship while s tudy ing in Rome and G6tt ingen. During these years he and his wife Ruth, who took her degree under Gerhard Kowalewski at Prague, met many of the leading mathematicians of the era--LeviCivita, Volterra, Hilbert, Landau, et al. After befriending Norbert Wiener in G6ttingen, Struik was invited to become his colleague at M.I.T., an offer he accepted in 1926. He taught at M.I.T. until his retiremen t , except for a f ive-year per iod dur ing the McCarthy era when he was accused of having engaged in subversive activities. He has also been a guest professor at universities in Mexico, Costa Rica, Puerto Rico, and Brazil. Beyond his work in differential geometry and tensor analysis, Professor Struik is widely known for his accomplishments as a historian of mathematics and science. His Concise History of Mathematics (recently reissued with a new chapter on 20th century mathematics) has gone through several printings and has been translated into at least sixteen languages. His Yankee Science in the Making, a classic account of science and technology in colonial New England, is considered by many to be a model study of the economic and social underpinnings of a scientific culture. As one of the founding editors of the journal Science and Society, Professor Struik has been one of the foremost exponents of a Marxist approach to the historical analysis of mathematics and science. At the present time he is completing a study on the history of tensor analysis while working on his autobiography. He is a passionate devotee of Sherlock Holmes. This interview is excerpted from a December 1987 conversation.

Schouten, Levi-Civita, And the Emergence of Tensor Calculus

Publisher Summary The flowering of the tensor calculus and its application to differential geometry, mechanics, and physics was primarily because of the impact of Einsteins general theory of relativity. Einstein took from this chapter the mathematical inspiration he needed, baptizing this new tool the tensor calculus. Like Kepler, who found the mathematics required for his planetary theory in Apolloniuss Konika, Einstein had come across a treasure trove that proved to be invaluable for his general theory of relativity. This geometrical interpretation appealed strongly to persons with an engineering mind like Schouten; it also was quite attractive to mathematicians of the Monge–Darboux school, accustomed as they were to thinking of analytical expressions (that is, differential equations) in geometrical form. To this school can be counted Elie Cartan, who contributed so much to differential geometry and tensor calculus. Geometrical interpretations of analytical expressions have more than once proven extremely productive in the history of mathematics.

Cauchy and Bolzano in Prague

No reference has ever been made, as far as we know, to the fact that CAUCHY and BOLZANO, both creators of modern exact criticism in mathematics, lived near each other for some years, from I833 to I835. At that time the banished king of France, CHARLES X, had appointed the catholic and royalist CAUCHY tutor in mathematics to the young duke of Bordeaux (later HENRY OF CHAMBORD). CHARLES had his splendid residence in the royal castle of Hradchin above the old capital of Bohemia, Prague. BOLZANO, the catholic preacher and professor of theology at the University of Prague lived at that time also in or near Prague, in Techobuz. It is of interest to inquire whether these men of science were known to each other, and exchanged ideas. In consequence of the following facts however, it seems rather improbable that there existed any such personal acquaintance. CAUCHY, whose life is described by VALSON (i), and about whose Prague period interesting and amusing details are mentioned by the General

Into the Age of Boerhaave

With Ruysch, Witsen, Merian, van Leeuwenhoek and Rumphius we have already left the Golden Century behind us and have entered the period we can associate with Herman Boerhaave, the Leiden professor of medicine. This “Age of Boerhaave” was no Golden Century and the Regents were no longer the sturdy “boys of Jan De Witt” deciding on the fate of Europe. Yet the age should not be underestimated. It was not only the time of overfed rentiers living on their investments in their town houses and country homes along rivers like the Vecht with their formal gardens, arbors and pretty vistas, a maximum of obsequious poor on charity and a minimum of picturesque sea dogs. It was also a time of continued scientific life at the universities, especially those of Leiden and Utrecht, and though contributions to exact science diminished in value after Huygens’ death in 1695 and the departure of Johann Bernoulli from Groningen in 1705, medicine, experimental physics, botany and chemistry flourished and attracted students from all over the world.

The Dutch Teachers of Mathematics and Navigation

We should not think that during the centuries preceding the rise of the Dutch Republic, the Northern Netherlands were inhabited only by semi-illiterates in the service of feudal princes always at each others’ throats. We only have to look at the noble lines of the Knights Hall (Ridderzaal) in The Hague or the townhalls of Middelburg and Gouda to understand how much taste existed in the Holland and Zeeland of these days, not to speak of the beauty of some of the churches. Dutch prosperity depended to a considerable degree on the herring fishery that flourished because an invention called haringkaken, a special conservation method of gutting, salting and barreling ascribed to Willem Beukelsz. of Biervliet in Zeeland around 1300. The coastal trade was a good school for the training of skippers and shipbuilders, the preserving of dykes and drainage for that of mill builders and engineers. Connections with the Hansa broadened vision and the sense of toleration. We may be sceptical of the story that not Gutenberg in Mainz, but Laurens Jansz. Coster in Haarlem invented printing with movable type, but it illustrates the fact that this process was developed in the Netherlands at an early date (after ca. 1450). Literacy was widespread.

The Period of Transition

Towards the end of the fifteenth century the Latin-speaking world of scholars was pretty well acquainted with much of the best of the Greek and Arabic heritage, but was as yet unable to go beyond its level. If somebody like Avicenna or Omar Khayyam,1 scientists from the eleventh and twelfth centuries, had reappeared in the Nuremberg or Venice of the time of Columbus, he would not have found much in the way of novelty except perhaps the admirable way of printing with movable type, the despicable way of spreading destruction and death with gun powder, or some other technical inventions, but new to them would have been the spirit of restless progress, not only among merchants, but also among craftsmen and men of learning, an atmosphere of fresh ideas on discovery and invention, on achieving more than their fathers, in sharp contrast to the more tradition-bound intellectual climate of the Orient.

The Young Republic

The rise and growth of the Dutch Republic1 will always fill us with amazement and a desire for understanding. Here was a people of artisans, shopkeepers, sailors and merchants that defeated the best armies of Europe, had created a land of industrious and growing cities, with a mighty fleet and an excellent transportation system, a flourishing agriculture and horticulture, an exemplary financial condition, a country that created an art which in its way has never been surpassed. Natives and strangers were impressed. “How is it done?” they asked abroad. An Englishman who, in 1614, witnessed the departure of the herring fleet from Amsterdam, a fleet of a thousand sail, exclaimed that “no king on earth has ever seen a fleet such as this being equipped by his subjects.” The French Duke De Rohan, visiting Amsterdam in 1600, said that nobody could believe it who had seen it, but there were from three to four thousand sailing vessels on the quays, twice a year fleets of between four hundred and five hundred ships arrived with wheat from Danzig, wine and salt from France and Spain and, moreover, other ships laden with spices and other precious commodities from India and the newly discovered countries.

The New Science

The Republic, that turned clerks into magistrates, skippers into naval heroes, schoolteachers into scholars and painting apprentices into artists also turned the Orange princes, who in their old country probably would never have been more than petty serenissimi, into generals and statesmen of the first rank. All have contributed by their intense interest in military technique to the development of those sciences and engineering practices connected with warfare — and the Republic, during the whole Golden Century, knew only a few years of peace. Maurice, of all these princes, achieved much more in this respect than we can conclude from his relation to Stevin alone. He was interested in the University of Leiden where he was a student at the time of his father’s assassination, and in 1600 he sponsored, as already mentioned, the “Dutch” engineering school at Leiden with able men as teachers. We also noted his interest in Plancius and scientific navigation in general. Several books dedicated or referring to him bear witness to the respect he enjoyed in scientific circles. He had a reputation of being the ablest general of his time, and men from all parts came to his army to learn the novel art of warfare. True, among those men were plenty of swashbuckling characters of the kind immortalized by Dumas in his Three Musketeers, but also serious students like Maurice’s youthful relative Johan Maurits, the later “Brazilian”, and the young Rene Descartes.

The Living World

At the time of Jan De Witt there were already five universities. The oldest was that of Leiden, founded in 1575 after the triumph over the Spanish. This was in Holland. Then followed those of Franeker in Frisia in 1585, of Harderwijk in Gelderland in 1603, of Groningen in the province of Groningen in 1614 and of Utrecht in the province of Utrecht in 1636. In addition there were Latin schools and Athenaea, as those of Dordrecht, Breda and Deventer. The most famous Athenaeum was in Amsterdam and its status almost equalled that of a university. It dated from 1632 and is the forerunner of the present university. The astronomical observatory at Leiden was founded in 1633, that of Utrecht in 1642.1 Lectures were given, and textbooks written, in Latin.

Der Alte Orient

Wahrend des funften, vierten und dritten Jahrtausends vor unserer Zeitrechnung entfalteten sich an den Ufern groser Strome in Afrika und Asien, in subtropischen oder fast subtropischen Gebieten, neuere und fortgeschrittenere Staatsformen aus den festgefugten steinzeitlichen Gemeinwesen. Diese Strome waren der Nil, der Tigris und Euphrat, der Indus, spater der Ganges, der Hoangho und noch spater der Jangtsekiang.