Émile Picard

French mathematician

• Born: July 24, 1856
• Birthplace: Paris, France
• Died: December 11, 1941
• Place of death: Paris, France

Picard’s work with differential equations led to his having a theorem named after him. His theories advanced research into analysis, algebraic geometry, and mechanics.

Early Life

The mother of Émile Picard (ay-meel pee-kahr) was the affluent daughter of a doctor from France’s northern provinces. His father, from Burgundy, was a textile manufacturer who died during the Franco-Prussian War of 1870. Picard demonstrated brilliance early in his life. While in school, he developed interests in varied subjects such as literature, languages, and history. His accomplishments in these areas of scholarship were enhanced by his love for books and reading and by his exceptionally powerful memory. One theme that appears throughout Picard’s life is his broad range of interests. He was an athlete as well as a scholar. Throughout his life, he maintained a love for such rigorous physical activities as gymnastics and mountain climbing.

Given the fact that Picard was a generalist, it was difficult for him to choose any one field in academics on which to focus. In fact, he only decided to study mathematics at the end of his secondary studies. The reason for this decision came from his having read an algebra book. After making the decision to study mathematics, Picard committed himself to this pursuit with a devotion that is rarely matched. Indeed, by 1877, at age twenty-one, he had already made a major contribution to the development of a portion of mathematics that focused on the theory of algebraic surfaces. He had also received, by this time, the degree of doctor of science.

Picard’s scholarship was recognized by many important members of the academic community. One of the great French mathematicians of the time, Charles Hermite, became his mentor and lifelong friend. In fact, Picard’s development as a mathematician was strongly guided by Hermite. In 1881, with support from Hermite, he was appointed to a professorship at the Sorbonne, and during the same period he married Hermite’s daughter.

Life’s Work

The diversity that marked his life also marked his professional development. His early career emphasized research and focused on algebra and geometry. Some of his major contributions came in the field of algebraic geometry. He soon, however, began to pursue other interests in mathematics. By 1885, he had begun to pursue work in the field of differential and integral calculus. Picard was elected to the chair of this subject at the Sorbonne during this period.

Picard’s most famous work came from his investigations of differential equations. Indeed, one theorem for which he is still remembered in modern texts of all languages is Picard’s theorem, a method for approximating the solution to a differential equation. More important, however, is the work that Picard did in trying to develop a general framework for finding solutions to differential equations.

In addition to his work in differential equations, Picard did work in complex analysis. In this area, he helped to extend the research of his colleague Henri Poincaré. The work on which he focused involved functions of two complex variables. Picard termed these functions hypergeometric and hyperfuschian. The work that he did here was collected in a two-volume set entitled Théorie des fonctions algébriques de deux variables indépendantes (1897, 1906). This work was coauthored by the mathematician Simart.

At the turn of the century, Picard was engaged in the study of algebraic surfaces. This series of investigations was inspired by his previous work on the nature of complex functions. One of the interesting side effects of Picard’s career as a generalist is the fact that his investigations frequently led him into other areas of study.

Another interesting facet of Picard’s career is the fact that it touched so many areas that one would not expect. For example, he was the chair of many government commissions, including the Bureau of Longitudes. Also, the quality and the variety of his scholarship led to his permanent election as the secretary to the Academy of Sciences. Picard’s wide-ranging scholarship reached even into areas such as physics and engineering. His researches included the application of mathematical methods to physics problems of elasticity, heat, and electricity. One subject to which Picard added significantly was the way in which electrical impulses moved along wires. In engineering, Picard, who had originally begun as a theoretician in mathematics, developed into an excellent teacher and eventually became responsible for training ten thousand French engineers between 1894 and 1937.

It should be emphasized that the quality of Picard’s scholarship did not suffer because of its variety. During the course of his career, he was responsible for the development of more than three hundred papers on various subjects. His Traité d’analyse (1891-1896) is considered a classic book on mathematics. At one time, this monumental work was considered required reading for obtaining a thorough background in mathematics.

Picard also published materials that were, strictly speaking, outside the realm of mathematics. He was, for example, responsible for collecting and editing the works of Charles Hermite, his mentor. In addition, he published a number of works on the philosophy of science and the scientific method, the majority of these after 1900.

Picard’s career was long as well as productive. Many mathematicians find their most productive years early. Picard was a notable exception to this pattern. Again following his early path of intellectual diversity, he made significant contributions to the development of mathematical concepts such as similarity and homogeneity well after he was eighty years old. These concepts are important in algebra and engineering.

Picard’s investigations were particularly significant in their effects on his fellows and successors in his field. Among those influenced by him were Henri-Léon Lebesgue, Émile Borel, and Otto von Blumenthal. Picard was one of the most honored scientists of his generation. In 1924, he was elected to the Academy of France. In 1932, he received the Gold Cross of the Legion of Honor. In 1937, he received the Mittag-Leffler Gold Medal from the Swedish Academy of Sciences. All told, he was awarded honorary doctorates by universities in five foreign countries.

In contrast to his almost unbroken string of professional successes, Picard had a personal life that was filled with tragedy. War was a common theme in the litany of misery that filled his personal existence. Besides the death of his father in the Franco-Prussian War, he lost a daughter and two sons during World War I. During World War II, his grandsons were wounded in the invasion of France. The personal tragedy under which Picard lived was emphasized by the fact that he died while France was still under German occupation. Yet he had lived as one of the most productive and honored mathematicians in a period known for the brilliance of its mathematical researchers.

Significance

Émile Picard was, in all ways, a generalist. Many would have termed him a Renaissance man. This diversity of interests was reflected in his work both in and out of mathematics. In mathematics, his research involved such varied areas as geometry, algebra, differential equations, and complex analysis. It is extremely rare to encounter mathematicians in the modern world who make significant contributions in more than one specialty. Picard’s most significant work was in differential equations. It is here that the mathematical world outside France most commonly remembers the great Parisian. Modern works still make reference to Picard’s theorem for approximating solutions to differential equations, and these new efforts still mention Picard groups as a way of categorizing the transformations that can occur in linear differential equations.

In areas outside mathematics, Picard was known as a teacher, writer, editor, and administrator. He published an important survey of mathematics in France. He headed both the Academy of Sciences and the Society of Friends of Science, a group interested in helping needy scientists. Picard was not only a great mathematician and scientist but also a great man. In an age that is characterized by the specialist, it is good to reflect that men such as Picard have lived.

Bibliography

Bell, Eric T. The Development of Mathematics. New York: McGraw-Hill, 1940. This is a particularly good discussion of the history of mathematics from a developmental standpoint. Consequently, Picard gets fairly good treatment. This book also discusses Hermite fairly extensively.

‗‗‗‗‗‗‗. Men of Mathematics. New York: Simon & Schuster, 1937. Picard is mentioned only slightly in this text. Yet it provides an excellent look at one of his most famous colleagues, Henri Poincaré. It gives a view of the flavor of the times and the problems that were faced by mathematicians.

Considine, Douglass M., ed. “Picard’s Theorem.” In Van Nostrand’s Scientific Encyclopedia. New York: Van Nostrand Reinhold, 1976. This includes a good discussion of Picard’s theorem.

Griffiths, Phillip. “Œuvres de Émile Picard, Tome II.” Dialog Math-Sci Database, February, 1989. A review of the collected works of Picard. It discusses the material addressed by Picard during his researches. It also includes a discussion of his life. The review is in English. Unfortunately, the book that it covers is not.

Hadamard, J. “Émile Picard.” Journal of the London Mathematical Society 18 (1943). This biographical sketch, published not long after Picard’s death, is the best description of his life.