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Title —
Marie Evert Bruins (1909-1990): intelligent, productive and controversial

Authors:  Peter van Emde Boas 

DOI: http://doi.org/10.18352/studium.9295
Volume: 6,  Issue: 3

Published on 01 Dec 2013   Peer Reviewed  CC BY 3.0

Marie Evert Bruins (4 January 1909-20 November 1990) studied between 1927 and 1932 natural sciences at the University of Amsterdam. He then worked as an assistant and deputy director at the Amsterdam Physics laboratory. In 1938 he graduated with honors under Jacob Clay thesis on cosmic rays in the Earth's magnetic field. During the war he joined the Mathematical Institute. After teaching in the analysis he was appointed in 1943 as lecturer in applied mathematics and foundation year. This professorship he held until 1969, in which year he was appointed extraordinary professor of History of Mathematics. This position he held until his retirement in 1979. In between, he was between 1953 and 1956 visiting professor in Baghdad, Iraq (at that time still a friendly Arab kingdom). After his retirement he remained active as a writer and editor. He was a long time editor of the science history journal Janus - a magazine that after his death no longer appeared. A biography by Eberhard Knobloch with an extensive bibliography of Jan P. Hogendijk published in Historia Mathematica 18 (1991) 381-389.

The earliest articles Bruins go on chemistry. Importantly, his research on cosmic rays in which he calculated, based on measurements taken during a sea voyage, which at 2.5 to 4 terrestrial radiation from electric currents in space occur later elaborated in his thesis. 1 This, he predicted the existence of the 'discovered' in 1958 all belts, something for which he received just recognition during his lifetime. The mathematical Bruins dealt with many topics. He was an admirer and practitioner of the invariant theory of R. Weitzenböck. His interest in the history of mathematics goes back to his youth as a high school student when he was out of his pocket money bought a book about the cuneiform.

The most important publications on the history of mathematics are the publication of a collection of clay tablets from Susa and the Codex Constantinopolitanus Palatii Veteris. 2 He has dealt with a wide variety of subjects and periods, ranging from Egyptian times to logaritmenberekeningen in the Renaissance. His approach was to carefully monitor the sources and many computations. For example, he showed that the known 2 / n table in the Rhind Mathematical Papyrus is not the result of centuries of research but a capable Egyptian reckoner this table may have figured in one day. 3 Bruins railed repeatedly against fellow historians who, because of lack for language skills are not the sources consulted and therefore only concerned with the (mis) interpret each other (mis) interpretations. He demanded of his only Amsterdam PhD student Y. Dold Samplonius (upgraded in 1977) that they would learn Arabic before she could begin her research on the Book of assumption by Aqatun. Fg001

A notable contribution to the geometry (which Bruins Nor has received recognition) is the Zeno geometry. By opting in projective geometry of the plane a special tripartite implementation group created a model that meets the five axioms of Euclid but in which virtually every theorem in Euclidean geometry is invalid. The set of degenerate points at infinity (in the standard Euclidean geometry a double straight line and in the traditional non-Euclidean geometry a real or imaginary conic for resp. The elliptical and hyperbolic geometry) is the Zeno geometry formed by a pair of intersecting lines. In this geometry, the circles are the lines through the point of intersection of this line pair and applies that each center point of each circle. The angle concept is meaningless and become reflections not exist.

That this result has not penetrated to the mathematical canon is related to the way in which the Bruins had been published. He showed them how the Euclidean geometry as an axiomatic preconceived theory fails. Not the parallels postulate but the third postulate of the circles is the core problem. Also practice to assume an independent additive linear and angular size is inadmissible. It proves the superiority of the Babylonian about Greek geometry, because the Babylonians did not use corner understanding. The clearest treatise on geometry Zeno I can find the article in Euclid, 4 but it is also described in the major review article on Babylonian mathematics in Physis. 5 The only mathematicians intended primarily for article he wrote in 1977. 6

When your author in 1962 went to study mathematics at the University of Amsterdam was this the final year students of mathematics 'little exam Bruins' had to take. This was the first semester of his first year teaching based on his textbook Introduction to Mathesis. 7 Treated was a collection of techniques, presented in a classical style, set well on what the former students were supposed to have learned in high school and the high school. Later that year I took another six weeks course in the second semester for non-mathematicians on differential equations, and the following year the Bruins course on the history of mathematics.

At that time you heard that Bruins was a controversial figure. Partly on the basis of complaints about his teaching at the chemists his teaching job was eroded systematically; finally put the chemists with the means to come to an Institute of first-year mathematics under the guidance of the lecturer Herman van Rossum which took over all remaining tasks of teaching Bruins, with the exception of his education in history. The Bruins thought about it you can read in his inaugural lecture as Professor Extraordinary:
It is now taken from me the education of chemists against my will and against my advice. In a few years, the chemist can not 'count'. He will not know. 8

Also played the controversy over the behavior of Bruins during the war. The position he took in 1943 would concern the place of Freudenthal who as a Jew had been fired before, and after the war Bruins unwilling to make available to his position. Details were never mentioned. Meanwhile, however, we have the biography of Brouwer Van Dalen which the history of the Mathematical Institute in Amsterdam this is discussed extensively in the period and the official war history of the University of Amsterdam Knegtmans. This creates a more nuanced picture.

Freudenthal was appointed a curator position. Bruins this between his teaching in 1941 and his research group held a short time in 1943, but formally he was in 1945 no longer in the position of Freudenthal (which certainly aspired to a professorship). During the purification after the war are the signatories of the notice boards advising the students to sign the declaration of loyalty, LEJ Brouwer, A. Heyting and EM Bruins, all three reprimanded.

Bruins describes in his farewell speech how he based on inside information, the efforts of the Board for Reconstruction to persuade him to keep the honor to themselves and to resign resisted. 9 was Bruins seen as not 'fouter "than his former colleagues. Moreover, the biography of Brouwer obvious that the return of Freudenthal in Amsterdam at any position is primarily blocked by Brouwer himself. Bruins was a protege of Brouwer, which does not prevent that he had a conflict in 1959 with Brouwer on a publication.
Why then was the Bruins for the Amsterdam mathematicians always getting picked on? In my opinion, this is not by war past, but it's because of the behavior of Bruins: his limitless desire to want to be right in all circumstances, and that same never get through its setup.

Personally, I remember how the Bruins at the end of his lecture on differential equations effortlessly fifteen minutes explaining how good course it worked. He also peppered his lectures with interesting stories; how, for example, during the war the Mathematical Institute helped to triple coal quota by the placement of partitions in the coal shed (cf. his valedictory lecture). 10

Many of his historical considerations degenerated into tirades against his fellow historians who have made ​​a mistake. A representative example do you encounter in discussing the biography of Hilbert by Constance Reid appeared in Janus 57 (1970) 222-228 (book reviews sadly lacking in the bibliography of Hogendijk): Bruins resented a caveat to which Brouwer pro- German sympathies were attributed and would not rest until he in a survey of four pages (more than half of the discussion) had demonstrated that this piece of misinformation had come of BL van der Waerden, or someone from his environment.

Personally, I've always had a good relationship with Bruins among other things resulted in many reprints of Bruins I can consult when writing this piece. Unfortunately, its articles, thanks to the archaic language and to understand the outdated mathematical terminology tricky. I should have just read the book of Weitzenböck on invariant theory.

Notes

1E.M. Bruins & J. Clay, ‘Magnetic storm and variation of cosmic rays’, KNAW Proceedings Science 41 (1938); E.M. Bruins, Cosmische stralen in het aardmagnetisch veld (Amsterdam 1938).
2 E. M. Bruins & Rutten, mathematics texts from Susa: Memoirs of the Archaeological Mission in Iran, 34 (Paris 1961); EM Bruins (ed.) Codex Constantinopolitanus Palatii Veteris, 3 vols. (Leiden 1964).
3E.M. Bruins, ‘Ancient Egyptian arithmetic: 2/N’, Indagationes Mathematicae 14 (1952) 81–91.
4 E. M. Bruins, Non-Euclidean Euclidean geometry ', Euclid 39 (1963) 1-15.
5E.M. Bruins, ‘Interpretation of cuneiform mathematics’, Physis 4 (1962) 277–341.
6E.M. Bruins, ‘Does “ds = du” characterize the isotropic planes?’, Periodica Mathematics Hungarica 8 (1977) 91–102.
7E.M. Bruins, Inleiding in de Mathesis (Amsterdam 1951, 19622).
8 E. M. Bruins, Science develops further outside the university, unless. . . ! (Inaugural address Amsterdam, Leiden, 1969).
9 E. M. Bruins, ANAГKH (valedictorian University of Amsterdam, Amsterdam 1982)
10 Ibid.

Figure

Evert Marie Bruins (1909–1990)