The Early Background of Genius

July 10, 2008

Alexander Grothendieck, at the International Congress of Mathematicians, Nice, France, 1970;

Book Review
Philip J. Davis

Wer Ist Alexander Grothendieck? Anarchie, Mathematik, Spiritualität: Teil I: Anarchie. By Winfried Scharlau, 2007, available from the author, 180 pages,
12€ plus 2€ shipping and mailing in Germany, 3€ elsewhere in Europe. (In German. An English translation is in preparation.)

Out of the crooked timber of humanity no straight thing was ever made.---Immanuel Kant, quoted by Sir Isaiah Berlin in his essay on the proto-fascist Joseph de Maistre (1753–1821).

Alexander Grothendieck (AG), now more than a mathematical genius and phenomenon, has been transfigured into an industry, with epigones constructing, deconstructing, elaborating, glossing, probing, psychologizing, historicizing, moralizing, even apotheosizing his life, his works, his eccentricities. There are festschrifts, seminars, conferences, a Grothendieck Circle, a tremendous Nachlass, and, of course, an immense amount of Web material. AG occupies a seat in the Mathematical Valhalla.

A micro-treatment of AG's life story would read as follows: Born in Berlin on March 28, 1928, as Alexander Raddatz. Father: Alexander Schapiro, a.k.a. Sascha Tanaroff; mother: Johanna (Hanka) Grothendieck Raddatz, a German writer and journalist. Parceled out, young AG survived the Nazi regime and ultimately, at the end of the war, found his way to mathematics. There he set algebraic geometry on its ear with brilliant new concepts and methods. Around 1970, AG abandoned mathematics, believing it to be morally corrupt, and became an anti-war polemicist and speaker. He subsequently selected isolation as a way of life and later descended into religious mania.

In his book Winfried Scharlau is concerned largely with AG's father, mother, other relatives (even unto grandparents), friends, and ancillary characters. Their stories are of interest and concern precisely because of AG's importance to the mathematical community and his subsequent notoriety to a general audience. The book also deals with the historic background in Europe, circa 1905–1945, particularly with the activities, thoughts, ideals, and difficulties experienced by the anarchists of that period. AG's father and mother were both anarchists. There is some material on AG's boyhood and youth, up to the time he began to study mathematics. His mental collapse is mentioned briefly.

Scharlau has made a deep study of this background, relying on the total Nachlass, which includes an unpublished autobiographical novel by AG's mother titled Eine Frau, letters and autobiographical material written by AG, and interviews with relatives, friends, and mathematical colleagues. Both mother and son were facile, copious, and outspoken writers. Scharlau has provided substantial clips from Eine Frau and from AG's published non-mathematical, political and ethical writings. The future mathematical brilliance of AG is not really Scharlau's concern in this volume.

The story of Grothendieck's parents, fraught with significance, is a period piece---one of thousands of poignant, heartbreaking stories of human suffering during this period. To read them we must steel ourselves. In a way, they are all the same---the slaughter of innocents or of those considered misguided or undesirable---and yet, each individual deserves to be treated as an individual and not as a piece of statistical data.

Consider, briefly, the story of Alexander Schapiro, AG's father. Born in 1890 in Novozybkov, a town near the three-cornered meeting of Russia, White Russia, and the Ukraine, into a Chassidic (i.e., mystic, anti-rational) background, an atmosphere in which disciples huddled around a rabbinic guru. Reacting to the pogroms of 1905 attendant on the failed revolution in Russia in that year, Schapiro left his birthplace, chucked the religion of his ancestors, and joined a group of anarchists, ultimately adopting a new name. The activities of the group landed him in a Russian jail in about 1907, where he remained until his release in 1917, in the aftermath of the October Revolution. In an early attempt to escape, he was shot in the left arm, which was later amputated. He tried suicide and failed.

In a paragraph set in bold type, Scharlau considers anarchism as a philosophic and political idealism. Later, he describes the lives, ideals, and the doings of some of the prominent anarchists of the period, including N.I. Machno, Vsevolod Eichenbaum, Emma Goldman, and Alexander Berkman, the latter two active in the United States. Yet, without government, we would "swallow up one another alive," to paraphrase Samuel Johnson.

I do not elaborate here the subsequent path of Alexander Schapiro/Tanaroff, which led him to Paris, to Berlin, to a meager living as a street photographer during good weather, and to Johanna Raddatz, née Grothendieck, to the Spanish Civil War in the mid-1930s, and ultimately, around 1942, to annihilation in Auschwitz. Read his history and shudder.

Consider briefly, too, the story of Hanka Grothendieck, AG's mother. Born to a middle-class Hamburg family on August 8, 1900, she was apparently a very difficult person with numerous masculine tendencies. A good student in school, she broke at around the age of 17, for reasons that are not clear, with her "bourgeois" life and began to live as an emancipated young woman, taking acting lessons and revealing considerable literary talent in her poetry, essays, and journalism. Through her work for the weekly periodical Der Pranger, she came in contact with ordinary workers, the unemployed, prostitutes, ex-prisoners, alcoholics, and was exposed to domestic violence and unwanted pregnancies. She also encountered communists and anarchists.

In Hamburg around 1921, Hanka took up with Johannes Raddatz (1897–1958), a journalist for left-wing publications, a bit of a scatterbrain, in and out of jail on minor charges, but an intelligent, witty, and charming individual. Both believing in free love (how quaint and archaic this sounds in 2008), they lived together for a while and then married in 1922. The marriage essentially broke up in 1926 but lasted formally until 1929, after which Raddatz enter-ed into a second marriage.

Around 1926, Schapiro/Tanaroff walked into Hanka's life. AG, born in 1928 and recorded initially as Alexander Raddatz, was a legally legitimate child. Very soon afterward, however, Johannes Raddatz took the question of paternity to court, and Tanaroff acknowledged that he was AG's father. Tanaroff and Hanka never married.

We are indebted to Winfried Scharlau, a professor emeritus of mathematics at the University of Münster and a novelist, for this stark, dark, and yet greatly illuminating picture of the early background of a genius. Scharlau has spent many years amassing Grothendieck-iana and has incorporated many significant clips into this volume. His book will grip general readers and keep them turning the pages. It may upset those specialists who advocate: Forget sensation and look only at a person's professional accomplishments, leaving unexplored the subject's background and non-professional character and opinions.

As if in contradiction to the statement of Kant quoted at the beginning of this article, new mathematics, said to have revolutionized certain areas of the subject, did emerge from the crooked timber of the frightful forests of 20th-century Europe. And then . . . between the creation and the emotion fell the shadow. What predisposes genius to a "descent into Avernus" without return, a release of the darkness said to reside in all souls? In a forthcoming book (Loving and Hating Mathematics: Inside Mathematical Life), Reuben Hersh and Vera John-Steiner raise the question of whether an absolute rigidity of excessive logic, combined with the rigidity of excessive social idealism and utopian hopes, conduces to mental disturbance or destruction of the self. Along with Grothendieck, they cite Theodore Kaczynski, the Unibomber, André Bloch, the Mad Mathematician of Charenton, and Kurt Gödel. Given the strong mathematical as-pects of the game of chess, they might also have cited the brilliant chess master Bobby Fischer. Is it possible that intense involvement with logic can actually be a sanity-preserving device for individuals who are either born with extreme sensitivity or in whom sensitivity has been implanted by events totally out of their control?

Sigmund Freud is quoted as saying that the minds of poets and novelists were beyond his understanding. If, as is often asserted, mathematics is an art form with a pronounced aesthetic, the wellsprings of mathematical creativity may be beyond ultimate understanding. As regards AG's mental collapse, did genetics play a role? Did the blandishments of admiring disciples, swarming around the Master and feeding him ego-food, like bees feeding the Queen royal jelly, exacerbate matters?

During episodes of advanced religious mania, AG received a delegation of angels and a personal message from God that the final trumpet would be sounded on such and such a date. We might regard this as a mystic and recidivist return to the Chassidic world of his paternal ancestors. But in the long run, the crooked timber of civilization and of the individual will fade from memory, and the history of science will judge the mathematical contributions of Alexander Grothendieck on their own abstract merits.

Philip J. Davis, professor emeritus of applied mathematics at Brown University, is an independent writer, scholar, and lecturer. He lives in Providence, Rhode Island, and can be reached at [email protected].

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