Jean van Heijenoort

Passion and Structure

Review of Politics, Logic, and Love: The Life of Jean van Heijenoort
By Anita Burdman Feferman
AK Peters, Wellesley, Massachusetts, 1993. 415 pages. $29.95

One day in the summer of 1945, a man of 33 enrolled at New York University to study for an advanced degree in mathematics. Although older by far than the average graduate student, he worked hard over the next four years under the demanding supervision of J.J. Stoker and earned a doctor's degree with a thesis entitled "On Locally Convex Surfaces''. For the next four decades he was professor of mathematics at a variety of colleges in the U.S.; during that time he became editor of the Journal of Symbolic Logic, and he produced a major scholarly contribution in his From Frege to Gödel: A Source Book in Mathematical Logic.

This man, before walking through the doors of NYU, had been Leon Trotsky's gun-carrying bodyguard; he had held that position from October 1932 until Trotsky's assassination in August 1940, after which he became one of the principal promoters of Trotsky's "Fourth International".

Anita Feferman, who know Jean van Heijenoort (1912-1986) personally for many years, has written the absolutely spellbinding story of a man who lived two lives --- in series, but not entirely without connection. I began to read the book by dipping in here and there, held initially by the gossip and then by my desire to understand a life that was so split. It became clear that later I would read it through from title page to index.

Let me begin with a few words about Lev Davidovitch Bronstein, whom the world cam to know as Leon Trotsky (1879-1940). One of the principal actors in the Russian Revolution and in the early Soviet government, a brilliant orator and writer, a charismatic politician and personality, an interpreter and creator of his own version of theoretical and applied Marxism, Trotksy was, when van Heijenoort first met him, living in exile on the Turkish island of Prinkipo in the Sea of Marmara. He had been expelled from Russia by Stalin in February 1929 and came to be regarded by the Stalinist Faithful of the World as the antichrist of Marxism.

Why did Van (as he was known to his friends), a young man of 20, forsake the complex variables and abstract algebra he was studying at the Ecole Normale and in 1932 join the world-renowned Trotsky as part of Trotsky's court? Why did he then follow Trotsky to his various refuges in France, Norway, and finally Mexico?

Van Heijenoort was born in the small village of Creil, 50 kilometers north of Paris; his first memories were of military action in World War I and of his father bleeding to death in the absence of doctors. With these memories as background and with the worsening of the world economic depression in the early 1930's, it was probably inevitable that this bright village star would turn to Marxism as a source of salvation. He joined Trotskyist circles in France and was selected because of his intelligence and language skills to join the Master in exile. Explaining later why he had turned to Trotsky and not to Stalin, van Heijenoort said, "It was almost a question of style, of literary style, even. It was enough to read five sentences of one and five sentences of the other."

Ultimately, at the invitation of President Cardenas of Mexico, the court established itself in Cayoacan, where Trotsky wrote furiously, plotted world revolution, defended himself against both Stalin's trumped-up accusations and his murderers. Van Heijenoort, for his part, acted as personal secretary, as secretary of the Fourth International, as one of the bodyguards; in his spare time he developed an intimate relationship with Frida Kahlo, whose prominence as an artist seems now to overshadow that of her husband, Diego Rivera.

With the assassination of his surrogate father in August 1940, a major part of van Heijenoort's psychological world collapsed and he looked into the darkness of the future. But retaining the memory and the ideals of the Old Man. he pulled himself together and carried on with his political activities in the U.S. In 1948, however, when he must have been well into his Ph.D. thesis, his full recantation and refutation of Marxism was published pseudonymously in the Partisan Review.

It is interesting that mathematics played a not insignificant role in van Heijenoort's arrival at this refutation, as pointed out clearly in an appendix written by mathematician Solomon Feferman, the author's husband. It is fairly well known that both Marx and Engels wrote on the philosophy of mathematics. In their desire to establish the doctrines that became known as Marxism and even to provide a scientific basis for them, they pulled in mathematics as part of the demonstration. When van Heijenoort examined closely what Marx and Engels had written, he found it both uninformed and puerile. If the gods had written such junk about mathematics, an area where van Heijenoort felt himself on absolutely firm ground, what was the guarantee that their other writings had any value?

We need structure in our lives. When one structure collapses, we must turn to another, else we wander as lost children. The turn or return to well-structured religious doctrines and rituals by former Communists or Marxists has been well documented. In recent years, dedicated Marxists of Central Europe have turned to Green politics or to mild forms of Luddism. Ven Heijenoort turned to mathematics as a structure in which certainty reigned, beyond the grasp of time and historical event --- or so it was claimed. He even moved from differential geometry to symbolic logic, a part of the subject that was more abstract, and further removed from the interests of his professors, who were members of the world-renowned group that came to be known as the Courant Institute.

Van Heijenoort, says the author, pursued logic with passion: "Almost everything Van did was an all or nothing affair." So also with mathematics. Mathematics, particularly logic, is perceived by many as an all or nothing affair. A statement is either true or false. In contrast to life, there is nothing in between.

Van Heijenoort pursued love with passion. Shy and reclusive with men, he blossomed in the presence of women and had no difficulty in finding them. Was he looking for a stable, warm, soul-nourishing structure based on love? If so, his quest seems to have come to naught, and his life ended during his fourth marriage in a tragedy that ironically paralleled that of his master.

According to Jean-François in The Postmodern Condition, our age has discarded one ideal after another, and all attempts at arriving at a "big picture" are met with skepticism. All structures, while supportive, are restrictive; all knowledge is local and hence limited. Mathematics itself has not been immune from these tendencies. The last attempts at a big picture cam from the Ecole Bourbaki, whose efforts are now seen as a period piece, and within emerging philosophies of mathematics, the existence of local truths and global ambiguities can now be contemplated.

It is the great merit of this book to be a part of the history of ideas. Van Heijenoort's life, a life both of intellectual idealism and of tragedy, in its way paradigmatic for the 20th century, provides firm documentation of how we have come to think as we now do think.

Philip J. Davis, is an independent writer, scholar, and lecturer based in Providence, Rhode Island.