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Dirk Struik admired Mannoury's intellectual style and robust spirit. But despite all this. Sometimes a party worker brought it up: I remember Metscher asking me why I wanted to study all that "bourgeois science. But he was disappointed by Mannoury's lecture delivered before a forum of socialist students in Leiden in His search for a way to accommodate mathematics and politics led to a balance between.
An additional factor was that. It was a question all young intellectuals in the movement have to face some time or another. Brouwer's early ideas on intuitionism. I did not relish the prospect of working permanently under it. The intemperate words "Den Mann.
The results were correct and some of them even of central importance. Although Schouten did invoke such terms as "structural schema"--hinting that the notion of mathematical modeling was in the air in Delft as well--the tradition in which he and his student Struik worked developed no new notion to express a more intricate relationship between pure mathematics and its applications.
Schouten's Grundlagen der Vektor.
Schouten was a modern research leader. Considering that Schouten's mathematics was largely motivated by its potential applications to physics. Schouten's style of mathematics was by no means modernist. Struik's professional career began under the wing ofJ. Schouten's work confirmed his position as a leader at the forefront of international mathematical research [ Together they coauthored a series of articles and finally two books on the subject .
Schouten In conducting research through teamwork and in designing a research program. Schouten's geometrically tuned direct analysis produced a totally inaccessible formalism.
Schouten's zeal for his research program stemmed in large part from the need for a well-developed geometric framework within which general relativity theory and unified field theories could be studied.
Even with the advantages of hindsight. In Struik defended his thesis in Leiden. The physicists Hertz. By contrast.
Jahrhundert [ By the early 's. In Struik became Schouten's assistant. Sch 5]. Struik was one of a series of assistants with whom Schouten coauthored several articles. The following year he married. Struik's interest in political matters continued unabated and politics filled every spare moment of his time.
Struik eventually sought to reconcile. While in the United States. In doing so. Struik had been lecturing on probability theory at MIT. Struik's numerous contributions to the history of mathemat- ics were largely undertaken as a complement to his own mathematical production. After pondering the possibility of working on a scientific project in the Soviet Union. The only major exception to this was his "Outline of the History of Differential Geometry" .
But this was not to be. Marcel Minnaert. Struik's Concise History. The pinnacle of his political activity in the Netherlands came in the mid s. In a similar popular vein came the work of Lancelot Hogben. Struik eventually went far beyond mere popularization with contributions to the history of mathematics and science that reached a high scholarly standard. This is only to say that a long-standing tradition of interest in the history of science was evident within leftist circles.
During this period he published a set of two introductory booklets for CPN training courses on historical and dialectic materialism that appeared under the pseudonym O. In view of the fact that the Netherlands generally lacked expertise in this rapidly emerging field.
These writings were produced during the very sabbatical leave from MIT in More- over. A strong tradition of popularizing science. Schouten's wish to bring Struik back to Delft in was quite understandable. He reached a resolution through three stages. Verborg [ Mathematics for the Million .
The second stage in Struik's resolution of scientific and political interests came through his work in history. Dialectical material-. The transition Struik made over these years is well illustrated by his quarrel with Lancelot Hogben. Struik gained considerable inspiration from this new approach. His assertion that "[o]ur mathematical conceptions were formed as the result of a long social and intellectual process. In Jeremy Bentham's phrase.
In fact this notion received its first more elaborate Marxist treatment when Boris Hessen addressed this theme at the International Congress of the History of Science and Technology held in London in The writer.
These conclusions hint at the third and final stage of Struik's undertaking to harmonize his mathematical and political concerns. Struik struck back.. The notion that even science is shaped and influenced by social and economic factors would appear only "natural. Struik countered Hogben's contention that his materialism was rubbish by insisting that the Englishman's notion of materialism was obsolete.
Struik has maintained that the material basis is decisive. Far from denying that mathematics exists side by side with the arts. It is disappointing to find this obsessional Germanophilia obtruding in an otherwise sugges- tive article [.
As with all his other historical publications. These ideas also helped to inspire Struik and other Marxist scholars when in they founded the journal Science and Society.
Insofar as he achieved a synthesis of academic and political endeavours in his life. If Struik did refer to Engels' Dialektik und Natur  repeatedly.
Merton's work not only opened new vistas in the history of science but also helped inspire Struik both to formulate a general program for the sociology of mathematics  and to undertake a major study within the context of that program.
Full of cogent social analysis and vivid details. At the same time. He completed the manuscript in Struik spent much of his time pursuing an entirely new research project: Some of the professors were involved in research for the military. Hessen's paper of on the "Social and Economic Roots of Newton's Principia"  had broken new ground for him.
In the s Struik's writings--as Verborg as well as his essays in Science and Society--show a somewhat formal or cerebral reception of the idea that science is influenced by social and economic factors. Technology and Society in Seventeenth Century England . This appeal to the influence of different types of social structures in order to gain a better understanding of the prevalence of certain styles or stages of development in an intellectual discipline had.
During the war years much of the normal mathematical research activity at MIT came to a standstill.. Robert Merton published his now classic study. In Even more significantly. His article on "Sociology of Mathematics" in brought this approach to bear on Struik's own subject. Aside from this. The sociology of mathematics. Sch 2]. That acceptance was in turn instrumental in formulating the possibility of a sociology of mathematics.
Upon their return to Delft in This meeting turned out to be the first in a still ongoing series of international conferences. It was through contacts made at the conference in Delft that Dirk Struik and his wife Ruth made plans to study with Levi-Civita in Rome and with Courant in G6ttingen soon thereafter.
Delft restricted itself to the theoretical side of the field. That was just shortly after Struik's arrival in Delft to serve as assistant to Schouten. His interest in the discipline's history may well have issued from his own political concerns. Four years after he had begun his studies. Burgers played a leading role in launching it. World War I had shown that aeronautics would play a decisive role in future military conflicts.
For the time being. One year younger than Struik. Cornelis Biezeno. The result helped spawn a new subdiscipline. In he and his Delft colleague in applied mechanics. Burgers advanced from being a student to heading a newly established research institute. Burgers completed his dissertation. Burgers participated in political activities at that time.
Also after the war. Burgers' tastes ran more in the philosophical direction. ESC ]. He had broad intellectual interests and read a good deal of the cultural critics so popular during the interwar years.
In the United Kingdom in particular. Such a committee was installed in Burgers was well aware of contemporary opinion with regard to the role and function of science in society. Through his widespread international contacts during the 's. Whereas Struik pursued historical interests to complement his mathematical research. These events. ESC The war prevented the founding of such an institute. Crowther had expressed arguments in favor of directing science so as to benefit society as a whole.
The Dutch chemist H. Kruyt acted as vice president of the International Council from to With the help of these prior developments. Burgers incorporated Whitehead's ideas into his own scientific vision which he set forth in several articles dealing with topics ranging from entropy and life. He personally considered his book. Kruyt and Burgers proposed that the Council appoint a committee to coordinate work in relation to the social responsibilities of science and scientists. Petersburg to lecture on aerodynamics at the institute of Ehrenfest's friend Joffe [ Ervaring en conceptie .
Along with a group of concerned scientists that included Jan Tinbergen. Burgers took the initiative in establishing an institute for the study of the implications of science for the development of social relations in the Nether- lands . He was also a visible spokesman within the Dutch scientific community when the debates over the proper role of scientific research really heated up just before the outbreak of World War II.
Through the Dutch Academy of Science. Burgers was very active in this Committee for Science and its Social Relations. In the International Council of Scientific Unions. The very titles of the articles reveal the emerging new role of mathematics: Burgers took a theoretical. One cannot really assert that Jan Burgers sought to resolve. Conscious that he did not have the latter in hand. Burgers presented. His reflections on the role of science in society led to innovation in the practice of science.
Burgers showed few signs of slowing down. In the Netherlands such innovations. Burgers' social conscience had led him to participate in political activity during his student years and.
Burgers had already been a research leader. I believe I may say that with my simplified model I am able to attain more principal results. The connection between Burgers' thinking and Ehrenfest's views can perhaps be seen most clearly by referring to the famous survey article written in by Paul Ehrenfest and his wife Tatyana on the conceptual foundations of the statistical view of mechanics for the Encyclopiidie der mathematischen Wissenschaften [ 16].
This latter aspect is most characteristic of the views of Ehrenfest. But what has not been reached is. While many physicists preferred to approach the ontological problems raised by physical theories from the comfortable position offered by positivism. In this study they took a firm stance in favor of physical insight.
This entailed a profound reassessment of the nature of the contributions which mathe- matics could offer to physics.
Burgers summarized this approach as follows: Along different lines a lot has been reached which I. Since the 's thermodynamics had been based on a kinetic theory of gases. In his retrospective valedictory lecture. Burgers was very precise in his wordings. In fact. The struggle to create the concepts of 20th-century physics involved more than physical insight per se. Ehrenfest's teachings eventually enabled Burgers. The theory of so-called "isotropic homogeneous turbulence" may to some extent show how a given turbulence evolves.
The crude analogy of bouncing billiard balls had shaken the classical Laplacean ideal of physical truth. For Burgers. During the early 20th century. Ehrenfest avoided such easy solutions. Burgers' notion of mathematical 4 There is an awkward connection between the debates in the 's over relativism in science and relativism in socialist ideology. Burgers showed respect for the technical a c h i e v e m e n t s attained by researchers who pursued more pragmatic approaches.
Lenin in his Materialism and Empirio-criticismof sided with Boltzmann against Mach and the epistomological relativism of the "Machists. Burgers held on to the search for a d e e p e r truth in his studies of the statistical theory of turbulence. The Austrian social democrats were judged to be contaminated with Machian thought and.
What at first would a p p e a r as a conservative position in the evolution of scientific research. Such was the situation concerning the relation of mathematics and physics in the early twentieth century.
Ehrenfest stuck to the search for a d e e p e r truth and rejected Gibbs' " m o d e s t y. M a x w e l l ' s formulation of the theory of electromagnetism dealt a further blow to the mechanical worldview. In the same vein. Difficulties of this kind have deterred the author from attempting to explain the mysteries of nature and have forced him to be contented with the more modest aim of deducing some of the more obvious propositions relating to the statistical branch of mechanics.
WiUard Gibbs went e v e n further than Mach in advocating a pragmatic position " a s long as the theory works to derive the main results" or e v e n a pragmatist view " t h e truth of the theory is in its w o r k i n g " with regard to the ontological status of the statistical theory of gases.
The term image. In their Encyclopiidie article.
Explanations turn into pictures and h y p o t h e s e s into arbitrary statements. Tinbergen belonged to a new generation of Social Democrats. Tinbergen helped to found a club for social democratic studentsqjust as Struik had done ten years before--as well as a student journal. Its participants. Together with Hein Vos. These initiatives were taken without reference to the earlier efforts of Dutch social democrats.
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