He was born in Moscow and grew up in Paris, where he graduated from the cole Centrale in 1905 with a degree in mechanical engineering. Following the accident, in 1910 he won a fellowship in mathematics at Clark University and gained his Ph.D. there after only one year. He came to Princeton in 1924 from the University of Kansas, was named Fine Professor in 1933 and appointed department chairman in 1945; he continued in both offices until his retirement in 1953.

Lefschetz was brought to Princeton by Dean Fine as part of a continuing effort to develop a first-rate mathematics department. After the newly founded Institute for Advanced Study took James W. Alexander II, Oswald Veblen, and John von Neumann from the University in the early 1930s, Lefschetz supplied the creative drive that maintained the department's research strength and the energy and imagination that led it to new heights. As chairman, the University Orator later said in presenting him for an honorary degree, he ruled ``with some pepper, much salt, and an invigorating and impetuous impishness.'' Under Lefschetz's dynamic guidance the *Annals of Mathematics,* which he edited for twenty-five years, became one of the world's foremost mathematical journals.

In his early research in algebraic geometry Lefschetz made innovative use of topological methods, winning the Bordin Prize of the Paris Academy of Sciences in 1919 and the Bcher Prize of the American Mathematical Society in 1924. In the twenties he began to concentrate on topology itself, proving his famous ``fixed point formula'' and the ``Lefschetz duality theorem.'' ``Topology'' is a word he coined in 1930 as the title for a monograph that brought this subject to the forefront of pure mathematics. During the Second World War, he turned his attention to more applied mathematics -- nonlinear differential equations, stability theory, and control theory -- in which he continued to work the rest of his life. He wrote over 100 papers, as well as a number of books and monographs.

On his retirement from the University in 1953, he embarked on a period of strenuous activity that lasted almost a score of years. He helped organize at Martin Company's Research Institute for Advanced Study in Baltimore a Mathematics Center which, when it moved to Brown University, became known as the Center for Dynamical Systems. His efforts to make known recent Soviet advances in mathematics and his leadership in developing an American school in nonlinear differential equations and kindred subjects were of strategic importance to American space technology. At the same time, he helped build a school of pure mathematics at the National University of Mexico, and in recognition of this achievement received Mexico's Order of the Aztec Eagle. Two international conferences in his honor were held, one on algebraic geometry and topology in Princeton in 1954 on the occasion of his retirement and the other on differential equations and dynamical systems in Puerto Rico in 1965.

His distinction in his field brought him the presidency of the American Mathematical Society, membership in the American Philosophical Society and the National Academy of Sciences, and foreign membership in the Royal Society of London and the Academies of Sciences in Madrid, Milan, and Paris. He received honorary degrees from Mexico, Paris, and Prague, as well as from Brown, Clark, and Princeton. In 1956 he received the Feltrinelli Prize of the Academia dei Lincei. In 1965 when he was eighty-one, he was awarded the National Medal of Science ``for indomitable leadership in developing mathematics and training mathematicians.'' And his colleagues in Fine Hall, on his death in 1972 at age eighty-eight, added to the many honors he had received in his long career a final tribute which only they could make, when they cited as qualities they would always remember, his love of life, his courage, vigor, and humor, his incessant curiosity, and his ``towering genius.''

From Alexander Leitch, A Princeton Companion, copyright Princeton University Press (1978).