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The Scholar and the State: In Search of Van der Waerden

Alexander Soifer
Publication Date: 
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[Reviewed by
Frank Swetz
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B. L.[Bartel Leendert] Van der Waerden (1903–1996) was an eminent mathematician of the twentieth century. Trained as an algebraic geometer, he did important work in many fields of mathematics and was a recognized historian of the discipline. He is best remembered for his influential two volume Moderne Algebra, (1930–31), his formulation of the “Van der Waerden Theorem”, and for his publications in history, including Science Awakening (1954) and Geometry and Algebra in Ancient Civilizations (1983). Born in Holland, he remained a Dutch citizen throughout his life, although he spent much of his working career in Germany during the Nazi period. His residency in Germany has been a source of much concern and controversy. It is this aspect of his life that Alexander Soifer has researched, documented and examined in this book.

How can science and evil exist side-by-side: one the arbiter of truth and hope, the other the purveyor of desolation and damnation? Can a man with good intentions — the preserving and strengthening of mathematics — live and function in a malevolent environment and not be tainted by it? These are some of the complex questions Soifer confronts in this book. He has undertaken over twelve years of dogged research, securing the archival evidence from official documents and correspondence and seeking out of witnesses and personal interviews. The material has been organized and culled to serve as the basis for this examination. Indeed, in this aspect, the author’s efforts have been very thorough and revealing.

Issues of nationalism, loyalty, patriotism, pride, moral integrity, hypocrisy, personal survival, dedication to mathematics and ‘What is “correct and just behavior” in an abhorrent situation?’ — all intermingle and conflict, making judgments difficult. Alexander Soifer’s prosecutorial modus operandi also raises questions: Is he objectively relating history or a “man with a mission?” Of course, the later stance is acceptable, and possibly even warranted, but this objective should be made clear.

Little consideration is given to van der Waerden’s mathematical accomplishments. A rich landscape of contemporary mathematical and scientific personages is presented, however: Emil Artin, Richard Courant, L. E. J. Brouwer, Emmy Noether, Richard Brauer, Issai Shur, Werner Heisenberg, Niels Bohr, and many others. The impact of Nazi anti-Semitic purges on this community is made clear. Van der Waerden openly protested these actions, much to his own peril. Portraits and photographs of many of the main players enhance various chapters. An instance on page 137, where a photograph of the physicist Werner Heisenberg is juxtaposed next to a picture of SS Reichfüher Heinrich Himmler to emphasize an implied association, seems (to this reviewer) as inappropriate and in poor taste.

Some exceptionally nice historical research is evident in Chapters 37 and 38 where issues concerning Van der Waerden’s Theorem are examined and resolved. The theorem in combinatorics had been already presented and discussed in Chapter 7 of the book. Formulated in 1926, it can be stated thus:

For any positive integers k, l, there is an N = N(k, l) such that the set of positive integers {1,2, ..., N}, partitioned into k classes, contains an arithmetic progression of length l in one of the classes.

Van der Waerden had acted upon a conjecture he attributed to an unknown mathematician, “Baudet”; other available evidence attributed the relevant conjecture to the well-known algebraist, Issai Schur (1875–1941). Soifer unraveled the truth and traced the conjecture to the brilliant but short lived Pierre Joseph Henry Baudet (1891–1921). Also in investigating the origins of the proof, he found a more elegant version published in 1948 by another unknown, M.A. Lukomskaya. Once again, his diligent research identified the person, Lukomskaya Mira Abramovna, who graduated in mathematics from Leningrad University and worked for many years teaching at the Belarus State University. She died in 1976. How nice that that “unknowns” sometimes become recognized for their work!

In 1935, Werner Heisenberg sought the counsel of the eminent physicist Max Planck (1868–1947) regarding the deteriorating moral and political situation in Germany-“Should he leave or stay?” Planck advised “... I think that all of us who have a job to do and who are not absolutely forced to emigrate for racial or other reasons must try to stay on and lay the foundation for a better life once the present nightmare is over.”(p.129) Van der Waerden endured this nightmare. He also emerges unscathed from Soifer’s rhetorical inquisition. Bartel Leendert Van der Waerden was a talented mathematician, a gifted teacher and an obstinate and complex man who perhaps made some bad decisions, but was no villain.

It is obvious that Alexander Soifer collected much material during his quest to clarify B.L. Van der Waerden’s association with Nazi Germany and its policies. Unfortunately, a little too much of this material is foisted upon the reader with excessive editorializing and accompanying moralizing. Five honorary forwards introduce the text, which seems excessive. Despite these overzealous efforts, this is a valuable book for the story it tells and the, sometimes uncomfortable, questions it asks, specifically “Is it ever justifiable to allow the desire for professional or scientific achievement to cloud moral prerogatives?” — a question that remains most relevant today!

Frank Swetz, Professor of Mathematics and Education, Emeritus, The Pennsylvania State University, is the author of several books on the history of mathematics. His research interests focuses on societal impact on the development, and the teaching and learning, of mathematics.

Greetings to the Reader: What is History?
Why Van der Waerden and Why Me?

The Family
The Joys of Young Bartel
Van der Waerden at Hamburg
The Story of The Book
The Theorem on Arithmetic Progressions
From Göttingen to Groningen
Transformations of The Book
The Algebraic Revolution That Produced Just One Book
On to Germany
The Dawn of the Nazi Era
The Princeton Offer
Eulogy for the Beloved Teacher
One Faculty Meeting at Leipzig
A Cloud of Suspicion
Mathematische Annalen
Germany Treacherously Invades Holland
Barrau’s Succession at Utrecht
A Dream of Göttingen
“Furniture and Scientific Books”
Home, Bittersweet Home
The New World or Old?
“The Defense”
Van der Waerden and Van der Corput: Dialog in Letters
One Heartfelt Letter to a Friend
A Rebellion in Brouwer’s Amsterdam
The Het Parool Affair
Job History 1945–1947
“America! America! God shed His grace on thee”
Van der Waerden, Goudsmit and Heisenberg: A Letteral Triangle
On Active and Passive Opposition in the Third Reich
Van der Waerden in Defense of Heisenberg
Professorship at Amsterdam
Escape to Neutrality
The Theorem Becomes Classic
Whose Conjecture Did Van der Waerden Prove?
Zurück nach Zürich
Reunions of Old Friends: Van der Waerden and Heisenberg
The Drama of Van der Waerden
The Scholar and the State
Farewell to the Reader: “I Hope and I Hope”.