amples (e.g., lack of uni form integra- bility, p. 414), or to inconsistencies of notat ion which reveal some difficulties, as with condit ional probabi l i t ies (pp. 258-260). Condit ional probabi l i t ies are indeed the Ar iadne thread of the whole book, as I h inted above with the Gauss- Cauchy example.

Let us now go through the overall structure of the book. The first five chapters, roughly 150 pages, are de- voted to the fundamenta l not ions of probabi l i ty, which are systemat ica l ly presented in cor respondence with those of statist ics. There fol low three chapters, roughly 200 pages, on statis- tics: conf idence intervals, bayes ian sta- tistics, l inear models (this topic takes up the whole of Chapter 8, 100 pages in itself). Then the author returns to probabi l i ty in Chapter 9 on condit ional expectat ions, mart ingales, and Poisson processes; and Chapter 10 is devoted to quantum probabi l i ty.

The book ends with four appendices, concerning a number of technical points (for example, the ax iom of choice!) which were sk ipped over in the main text; the solutions of the principal exer- cises (Appendix B); and an invitation to and overview of the l i terature (Appen- dix D). The book contains a great num- ber of exercises, updates (sometimes with Star-trek-type adventures), discus- sion of some classical questions: the bus paradox (p. 434), the prob lem of mo- ments, for which B. Simon's 2000 article is exploited, and so on.

This book is often remin iscent of the classic Volume 1 by W. Feller; still, the discussion is much more directed at the reader, as I have said. It is re- p lete with pedagogica l tr icks, and con- stantly is on the lookout for the sim- p lest solution. Often the author leads the reader to a wrong path, then re- turns later to the good road; in Chap- ter 10, the reader is in i t iated to quan- tum probabi l i ty in a ser ies of steps, leading to a good understanding. Many notes of humour are scat tered through the text; I enjoyed, for instance, the Sobs notat ion (p. 170) supposed to bring sta- t ist ic ians to tears.

In summary, while progressing through the book, the reader evolves from elementary questions of heads and tails toward a global vis ion of probabi l -

ity and statistics, with the author vow- ing (see, e.g., the first lines of the Pref- ace) to reconci le these two domains, which have separated, then divorced. It is a goldmine of information in both do- mains, giving access to the most ad- vanced knowledge and techniques. I recommend it as a working tool for a specif ic class of French students just be low the graduate level: those who are preparing for the "agrdgation de Math- dmatiques: option probabilitds et sta- tistiques" and who in the future will teach candidates for the Ecole Poly- technique, Ecoles Normales, etc. (There are plenty of potential readers through- out the world, but this reviewer can be

The author leads the reader to a

wrong path, then returns later to the good road.

most precise in describing a natural readership in France.)

Bravo, David, for this new tour de force! Many readers will be looking for- ward to your next volume, but this should not d ist ract you from l'art d'etre grand-pD'e, especial ly in the bicenten- nial year of Victor Hugo.

Laboratoire de Probabilites et Modeles

Aleatoires

Universite Paris Vl

175, rue du Chevaleret

75013 Paris

France

e-mail: deaproba@proba,jussieu.fr

From Trotsky to GGdel: The Life of Jean van Heijenoort by Anita Burdman Feferman

NATICK, MASS.: AK PETERS, 2001

PAPERBACK 416 pp, US $24.95 ISBN 1 56881-148-9

REVIEWED BY JOHN W. DAWSON, Jr.

T his is a paperback reissue of the bi- ography of Jean van Hei jenoort

or iginal ly publ ished in 1993 under the tit le Politics, Logic, and Love. It is to be hoped that the new title will attract greater attent ion to this vivid portra i t of the life of a remarkable and complex mai l .

Within the mathemat ica l commu- nity van Hei jenoort is best known as a h istor ian of modern logic, whose From Frege to Gddel: A Source Book in Math- ematical Logic, 1879-1931 (Harvard Univers i ty Press, 1967) remains an ex- emplar of what a source book should be. Some are also famil iar with his edi- t ion of Jacques Herbrand 's ~,crits Logiques (P resses Univers i ta i res de France, Paris, 1968), but re lat ive ly few are aware of his later book With Trotsky in Exile: From Prinkipo to Coyoacdn (Harvard, 1978), in which he recounted the seven years from 1932 to 1939 during which he lived with Leon Trotsky as his bodyguard, secretary, and translator.

After those turbulent years van Hei- jenoor t entered upon a life of scholar- ship. He left Trotsky's circle not long before the latter 's assassination, ob- ta ined a doctorate in mathemat ics in 1949 from New York University (for a d issertat ion in differential geometry), and stayed on as a professor there un- til 1965, when he moved to Brandeis Univers i ty to teach logic. In the 1950s he became an archival consultant for the Trotsky papers at Harvard, and dur- ing the last four years of his life he held a half-t ime appointment at Stanford, where he served both as an archival ass istant to the Hoover Inst itut ion (whose Trotsky holdings complement those at Harvard) and as a co-editor of Kurt G6del 's Collected Works.

Feferman's b iography is based on extensive persona l interviews she had with van Hei jenoort during his years at Stanford. It is a sensit ive account that opens with his chi ldhood memory of his father coughing up blood. The year was 1914: the Germans had occupied the smal l F rench town of Creil where young Jean had been born two years before, and in the wake of the German invasion all medica l personnel had gone away. Van Hei jenoort 's father, a Dutch citizen, was not subject to F rench mi l i tary service and had re- ma ined in Creil with his wife and son,

78 THE MATHEMATICAL INTELLIGENCER

where he worked as a decorat ive pa inter of metal safes. But he devel- oped a gastr ic ulcer that began to he- morrhage, and with no one with med- ical knowledge to turn to, he became a casualty of the war.

That searing event left van Heijenoort without any male ancestor to serve as a role model and caused a series of fltr- ther calamities. Without a provider in the fantily, van Heijenoort's mother H61bne was forced to seek employment. Her family had lived in Creil for genera- tions, but by marrying a foreigner she had lost her French citizenship and "was required to carry papers designating her as an alien" (p. 9). As a Dutch widow she was further ineligible for "almost every . . . j ob . . , except private domestic work" and had "to report to the police once a week , . . . [and] refrain from leav ing . . . Creil [without] a special permit for each departure" (p. 16).

When she eventual ly found work as a hotel chambermaid , H61~ne had to send her son to live with an aunt. The result ing separat ion was painful, and the only way she could escape from her pred icament was to marry a French- man. When she did so, her cit izenship rights were fully restored, but Jean jealous ly resented the new roan in her life and never accepted him as a step- father.

AS Fe ferman notes, such possess ive at tachments were character ist ic of all of van Hei jenoort 's re lat ionships with women. As with his mother, he at first put all his lovers on a pedestal; but "when the honeymoon was over and the re lat ionship came down to earth, there was a lways ser ious trouble" (p. 21). He was "the quintessential roman- tic Frenchman," who in his affairs with women "forgot about logic and reason" and consequent ly suffered "pain, re- morse, and eventua l ly . . . [a] violent end" (p. xiii). (He was murdered in 1986 by his last w i fe - -h i s fourth or fifth, "depending," he said, "on how you count.")

For van Hei jenoort, "almost every- thing was an all or nothing affair" (p. xiii). As a youth he turned abrupt ly away f rom an early devot ion to rel igion and "reappl ied his zealousness to his studies" (p. 30). He was a bri l l iant stu- dent, f irst in Creil, then at the coll~ge

in Clermont and finally at the lycde Saint-Louis in Paris. But he resented the regimentat ion of the F rench school system, and, dis i l lus ioned with the world polit ical situation, became ac- tive in a secret Marxist society. There his linguistic abi l i t ies impressed his companions and he was recru i ted to jo in Trotsky as a translator. Accord- ingly, with little hesitat ion, he forsook his scholast ic ach ievements and prospects and became a revolut ionary.

Van Hei jenoort fo l lowed Trotsky from Prinkipo, an is land in the Sea of Marmora, through France, Norway, and finally to Coyoac~in in Mexico. But intrigues within Trotsky's circle, in-

Recruited to join Trotsky as a translator, he forsook his scholastic

prospects and became a

revolutionary. cluding a c landest ine affair between van Hei jenoort and Fr ida Kahlo, the wife of Diego Rivera, eventual ly led to confl icts. Van Hei jenoort left Coyoac~ in November of 1939, less than a year before Trotsky's murder (an event van Hei jenoort bel ieved he could have thwarted, had he heard the speech pat- terns of the Spanish assassin, who c la imed to be a Belgian). At the mo- ment he learned of the assassinat ion, van Hei jenoort felt that "darkness set in." He remained active in the Trot- skyite cause for seven more years, but eventual ly his growing awareness of the evils of Stalinism led him to become disil lusioned with Marxist-Leninist ide- ology.

Part III of Feferman's b iography is devoted to van Hei jenoort 's return to the world of scholarship. As a non- mathematician, she focuses more on his personal life and relat ionships than on his mathematical work. But an appen-

dix at the end of the volume, wr i t ten by her husband, the dist inguished logician Solomon Feferman, provides an over- view of van Hei jenoort 's contr ibut ions to mathemat ics and phi losophy.

The last two chapters of the book chronic le van Hei jenoort 's on-again, off-again re lat ionship with Ana Mar ia Zamora, the daughter of Adolfo Zamora, who had been a comrade of van Hei- jenoor t ' s during his days with Trotsky and had served as Trotsky's and Rivera's lawyer. Van, as he was by then known among his mathemat ica l col leagues, became reacquainted with Ana Mar ia (whom he had first known as a chi ld) in 1958, while assist ing the Harvard li- brary in its negot iat ions to acquire Trotsky 's papers. The two quickly fell in love, and a tempestuous re lat ionship ensued. They were marr ied, d ivorced, and eventual ly remarr ied, but could not live happi ly either together or apart. Eventual ly Ana Mar ia began to show signs of ser ious menta l distur- bance, culminat ing in suic idal and homic ida l depression. Bel ieving he could somehow contro l her impulses, van Hei jenoort returned to be with her in her home in Mexico City; and there, while he slept, she shot f irst h im and then herself.

At the t ime of his death, I was work- ing with Van on the G6del Project . He was a vital contr ibutor to that effort, a fr iendly col laborator , and a met icu lous scholar. But as Fe ferman st resses throughout her book, he was also a very pr ivate person whose life was careful ly compartmenta l i zed. I knew nothing of his pr ivate life and was s tunned by his murder. Only posthu- mously, through this book, d id I be- come aware of how complex his per- sonal i ty real ly was.

Van Hei jenoort is bur ied in the Zamora family crypt in Mexico City, but there is no outward ind icat ion of the fact. Should an epi taph ever be in- scr ibed for him, it ought to be one of Pascal 's Pensdes that he part icu lar ly appreciated: "The heart has its reasons reason knows nothing about."

Department of Mathematics

Pennsylvania State University York, PA 17403-3398 USA e-mail: jwd7@psu.edu

VOLUME 25, NUMBER 2, 2003 79