Henri Léon Lebesgue

1875-1941

French Mathematician

Like many another mathematical innovator, Henri Lebesgue was not immediately recognized for his principal achievement, in his case a new approach to integral calculus. As so often happens with groundbreaking ideas, his integration theory offended prevailing sensibilities. In time, however, Lebesgue would see his ideas accepted—not only in Poland and America but even in his homeland.

Born in the town of Beauvais on June 28, 1875, Lebesgue was the son of a typographical worker and an elementary school teacher. In 1894 he entered the Ecole Normale Supérieure, where he became distinguished both for his sharp mind and for his rather cavalier approach to his studies—an early sign of the unorthodox attitude that would characterize his work on integrals. After graduating in 1897, he worked for two years at the school's library before going on to a teaching position at the Lycée Central in Nancy.

During the period between his graduation and the end of his time at Nancy in 1902, Lebesgue conducted some of his most important work with regard to integral calculus. The integral, which relates to the limiting case of the sum of a quantity that varies at every one of an infinite set of points, is fundamental to the study of calculus. Typically, the integration of a function is represented as a curve; some kinds of functions, however, reveal a non-continuous curve, a curve with jumps and bumps along its trajectory. Half a century earlier, Bernhard Riemann (1826-1866) had attempted to extend the concept of integration to apply to these discontinuous curves, but the Riemann integral did not apply adequately to all functions.

It was Lebesgue's achievement to transcend the difficulties of the Riemann integral, and in this aim he was aided by the contributions of Emile Borel (1871-1956), with whom he became personally acquainted. Borel's theory of measure helped Lebesgue define the integral geometrically and analytically, thus making it possible to include more discontinuous functions in his theorem than Riemann had earlier. He presented his findings in his 1902 doctoral dissertation, a paper that has been highly praised. That praise, however, came later. In the early twentieth century, Lebesgue's work shocked many other scholars.

After receiving his doctorate at the Sorbonne, Lebesgue took a position at the University of Rennes and in 1906 went on to the University of Poitiers. As his reputation grew, he was asked to return to the Sorbonne, and later he became a professor at the Collège de France. The following year saw his recognition by the French academic community with his election to the Académie des Sciences. The adoption of his integration concepts in France, however, was slower. By 1914, however, students at Rice University in the United States were already studying his work, and Polish schools at Lvov and Warsaw adopted his ideas just after World War I.

Lebesgue published some 50 papers, along with several books, and in the last two decades of his life saw his integral become widely accepted as a standard tool for analysis. He died in Paris on July 26, 1941, leaving behind a wife, son, and daughter.

JUDSON KNIGHT