"WEN DE CHEEPS are down," Hannah Arendt used to tell her American students, "you must make some choices." She knew whereof she spoke. Essentially a philosophical prodigy who had been taken under the wing of the major German philosophers of her time-- Edmund Husserl, Martin Heidegger and Karl Jaspers-- Arendt sacrificed her first love to become a fighting political theorist. The Nazis saw to that when they started putting the boot to the Jews, and in the bargain detonated a huge hole in Arendt's ivory tower that could never be mended. From her mid-20s on, she was exiled from her beloved "deep" German culture, but used the instruments it gave her to do radical surgery on the political nightmares of our age.

Elisabeth Young-Bruehl, a former student of Hannah Arendt's at New York's New School for Social Research-- once a refuge for brilliant Jews who had been kicked out of Germany--has done the first biography of this formidable and controversial lady (1906-1975), and it is very solid stuff. If it has a flaw for the general reader, it is one readily acknowledged by the author in her preface: "A biography abundant in novelistic descriptions of places, people, and periods would not be appropriate for someone like Hannah Arendt. What must be shown are the historical bases for her generalizations, the particular experiences that launched her thought."

In other words, our biographer takes a rather strict approach for those who like their super-intellectuals clothed in flesh and anecdote as well as pure thought; but even so a couple of startling facts break through: Hannah Arendt's father died of syphilis in 1914, and the great poet W. H. Auden (who was homosexual) seriously proposed marriage to Arendt after she was widowed in 1970. Ponder that.

Apart from these zingers, however, Young-Bruehl does a very steady, thorough job in showing us what shaped Hannah Arendt. If she was considered fearless and unyielding in later years, much of this inner steel has to be attributed to her very secure German-Jewish roots in the East Prussian city of Konigsberg. Except for her father's tragedy, the result of a youthful indiscretion known to his compassionate wife who believed the disease had been halted, Arendt apparently had a happy childhood. The life of the mind was fostered at home and she in turn took giant leaps like a high-IQ kangaroo. Any American educator would bow his or her head before the kind of pre-university learning Arendt thrived on--Greek, Latin, philosophy, poetry, her mother boasting that "she knows everything by heart." As a matter of fact, the young Hannah Arendt was something of a holy terror, already a leader and a threat to authority: at 15 she was temporarily expelled from the local gymnasium for leading her schoolmates in the boycott of a rude teacher's class!

Many years later, in New York, poet Delmore Schwartz spluttered to friends after losing an argument to Arendt at a party: "That Weimar Republic flapper!" As usual, he was shrewdly on target. Hannah Arendt represented everything that was self-confident and exciting about pre- Hitler Germany, with pictures in this book showing an intense-eyed, good-looking woman with a perpetual cigarette smoldering between the first two fingers of her right hand. The high point of the Republic, the years 1924 to 1929, was the time when Arendt put the seal on her education by studying advanced philosophy at the universities of Marburg and Heidelberg; she fell in love (and went to bed) with Martin Heidegger at the former and became a life- long friend of Karl Jaspers at the latter. She also began her first book, The Philosophy of Love in St. Augustine, which was published in Berlin when she was all of 23.

But that was the end of pure philosophy for Hannah Arendt until just before her death, when she wrote the uncompleted The Life of the Mind. Hitler made a Jew out of her, so to speak, rather than a philosopher, and for the next 45 years she saw her role as one of using her natural passion for thought on the life-and-death politics of our time. This existential involvement led to the two books for which she is most widely known today: The Origins of Totalitarianism (1951) and Eichmann in Jerusalem: A Report on the Banality of Evil (1963). Yet original as both books are, one always senses the unfulfilled daughter of Hegel, Kant and the contemporary German existenz philosophers chafing inside the political harness. But it was a choice she deliberately willed, in keeping with her own uprooted destiny.

Young-Bruehl takes us through the years of exile in Paris, 1933-41, when Arendt worked night and day trying to find refuge for young German Jews in Palestine. And although she labored unstintingly for Zionist organizations, she believed to her death that the Jewish and Arab homelands should be under a joint federation --something that never endeared her to fanatics on either side. It was in Paris, also, that she married the Brechtian man who was to firm up her political thinking, German ex-Communist Heinrich Blucher. Together, they constituted a "Dual Monarchy" in the eyes of writers who came to call on them in New York, after they had immigrated in '41.

Major poets like Robert Lowell and W.H. Auden threw themselves at Arendt's feet--or at least on her living-room sofa--but not everyone was spellbound. Saul Bellow was outraged when madame presumed to lecture him about William Faulkner. Partisan Review co-editor William Phillips let it be known that: "I think of Hannah as a very handsome man." And even such an objective observer as William Barrett tells us in The Truants: Adventures Among the Intellectuals that her arrogance was particularly unbridled towards "raw and uncultured" American intellectuals.

We therefore owe a lot to Elisabeth Young-Bruehl for putting it all in context. We see that Hannah Arendt couldn't really help being what she sometimes was, an abrasive mixture of some of the elitist qualities of Prussian general and Jewish prophet combined. But what she made of these genetic/environmental factors, how she used them as a ladder to the truth, is a strong part of this story about an intellectual conquistador who wrote secret love poems on the side.