Vallée Poussin, Charles-Jean Gustave Nicolas baron de la (1866-1962)

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Mathematician and professor, known for his proof of the prime number theorem (PNT). Born in Leuven on 14 August 1866 and died in Watermaal-Bosvoorde on 2 March 1962.
Son of Charles Louis de la Vallée Poussin.

Biography

Born in Leuven on 14 August 1866, Charles-Jean de La Vallée Poussin grew up in a family of intellectuals. In reality, his father, Charles Louis de la Vallée Poussin, was a renowned geologist and professor at the University of Leuven. The family included several other eminent university professors, including Louis Philippe Gilbert, who had a strong influence on his young cousin's new orientation towards the mathematical sciences.

Charles-Jean began his education at the Collège de la Sainte-Trinité in Leuven with the Josephite Brothers, before continuing at the Collège Saint-Stanislas in Mons, which was run by the Jesuits. He joined the university of Leuven to study engineering for the Arts and Manufactures, Civil Engineering and Mining. Despite obtaining his degree in 1890, the passion for mathematics instilled in him by Louis Philippe Gilbert took over and led him to a doctorate in Physical Sciences and Mathematics under the guidance of his cousin and mentor. During this period, de La Vallée Poussin studied for a time in Paris with renowned mathematicians such as Camille Jordan, Charles Hermite, Gaston Darboux and Henri Poincaré. A year later, in 1891, he obtained his doctorate in physical sciences and mathematics. In October of the same year, he deputised for Louis-Philippe Gilbert for the mathematics course at the University of Leuven. After the untimely death of his cousin Gilbert in 1892, de La Vallée Poussin succeeded him in the chair of mathematics. He was promoted to extraordinary professor in 1893 and ordinary professor in 1897. He was also appointed to the chair of mathematics at the University of Leuven.

During this early period, de La Vallée Poussin's research focused on integrals and differential equations. His first publications had already attracted the attention of the Belgian scientific community, and more particularly of Paul Mansion. In fact, de La Vallée Poussin's early work was awarded a prize by the Académie royale des Sciences et Belles-Lettres in Brussels. In 1896, the demonstration of his prime number theorem brought him international renown.

On 19 April 1900, he married Marie Caroline Frédérique Joséphine Dhanis, whom he had met on holiday in Norway and who "constantly kept the brambles and thorns out of my way".

In 1914, de La Vallée Poussin managed to leave Belgium safely with his family. His first port of call was the United States (1915), where he was invited to lecture at Harvard University and Cambridge University (Mass.). Like many scientists, he then travelled to Paris (1916), where he was warmly welcomed at both the Collège de France and the Sorbonne. De La Vallée Poussin gave a number of lectures and filled in for professors called up for military service. These lectures, given at Harvard University, the Collège de France, the Sorbonne and the University of Geneva, were followed by several monographs on the integration and approximation of functions, which have become classics. Around the common themes discussed in Paris, de La Vallée Poussin had forged a sincere friendship with the mathematicians Henri Lebesgue and Paul Montel.

When the war was over, de La Vallée Poussin returned to Belgium to resume his work as a teacher. In the years following the end of the war, he travelled to several universities across Europe (Strasbourg, 1921; Madrid, 1923; Sorbonne, 1924 and 1925) and the United States (Chicago, Columbia, Berkeley, Wisconsin, Minnesota, Yale, Princeton, Rice Institute, Brown and Philadelphia). At Louvain, de La Vallée Poussin had Gustaaf Verriest as one of his students. He also supervised Georges Lemaître's thesis. Despite the vast scientific network of mathematicians, de La Vallée Poussin conducted his research in isolation. He did not found any school of mathematics at the University of Louvain, and had few students around him apart from Gustaaf Verriest and Georges Lemaître, whom he later accompanied on their respective doctorates. Although he reached retirement age in 1936, he kept the mathematical analysis course at the University of Louvain until 1943. In the end, he taught for 60 years.

He was elected a corresponding member of the Académie royale des Sciences et Belles-Lettres de Bruxelles on 15 December 1898, then a member on 6 June 1908, he became President of the Class of sciences in 1923, serving in the Académie for no less than 64 years. General Secretary of the Société scientifique de Bruxelles, he contributed to its Annales, publishing several works including his prime number theorem At international level, he was also a member of the Instituto de Coïmbra, the Koninklijke Hollandsche Maatschappij der Wetenschappen in Haarlem, the Royal Scientific Societies of Utrecht and the Lower Rhine, the Mathematical Union of France and Spain, the Accademia Pontificale de' Nuovi Lincei, the Accademia nazionale dei Lincèi, the Real Academia de Ciencias Exactas, Físicas y Naturales in Madrid (1923), the Società Nazionale di Scienze, Lettere e Arti in Naples (1916) and the American Academy of Arts and Sciences in Boston. He was also made an associate member of the Institut de France. At the end of the First World War, the International Mathematical Union was created, and de La Vallée Poussin became its president and then honorary president.

His list of honours did not end there! In fact, he also received honorary doctorates from the Universities of Paris, Toronto, Strasbourg and Oslo. He was awarded the title of Grand Cordon of the Order of Leopold II and Commander of the Légion d'Honneur. De La Vallée Poussin also won numerous prizes, including twice the Decennial Prize of the Belgian Government for Pure Mathematics for the periods 1894 to 1903 and 1914 to 1923. In 1928, King Albert I made him a baron. Finally, at the Catholic University of Louvain (UCL), a La Vallée Poussin chair offers a mathematician the opportunity to teach there.

Works

Historians of science generally regard Charles-Jean de La Vallée Poussin as one of the greatest mathematicians in Belgian history. He was best known for his brilliant proof of the prime number theorem in 1896. The greatest mathematicians of the 19th century tried unsuccessfully to demonstrate the asymptotic distribution of prime numbers. This gives an approximate description of the measure of the average distance of large prime numbers. Aided by the pioneering work published 40 years earlier by the German mathematician Bernhard Riemann, de La Vallée Poussin succeeded in transforming the conjecture into a theorem. De La Vallée Poussin's theorem, immediately known as the Prime Number Theorem (PNT), was distinguished by its elegance, concision and clarity. De La Vallée Poussin also considered mathematics to be an art form, and as with art, he attached great importance to individual sensitivity and aesthetics. In constructing his theory, a mathematician like de La Vallée Poussin reveals something of himself. He allows himself to be guided by a certain instinct for beauty, which eludes analysis. At the same time, and independently of de la Vallée Poussin, the Frenchman Jacques Hadamard also demonstrated the prime number theorem. Like de la Vallée Poussin, he used complex methods of analysis. His success in 1896 gave him an international reputation, which was subsequently confirmed by important work on the theory of integration of Riemann and Lebesgue ("La Vallée Poussin integrability test"), the approximation of functions ("La Vallée Poussin kernel"), harmonic analysis ("La Vallée Poussin convergence and summation test"), conformal representation and potential theory..

He also wrote numerous notes on non-Euclidean geometry, probability theory, special relativity, the motion of a solid body, and the theory of linear inequations, which later became known as linear programming Joseph Marie De Tilly's work on non-Euclidean mechanics was a source of inspiration for Charles-Jean de La Vallée Poussin. He demonstrated that De Tilly's kinematic considerations used to prove the existence of only three types of geometry existing with a common system of rectilinear and planar notions, can be replaced by purely geometric axioms.

Courses

In the tradition of Gilbert, de La Vallée Poussin wrote and published his course in analysis. The course went through twelve editions between 1903 and 1959, and was translated into Russian and republished by Dover in the United States. Many European and American mathematicians acknowledged that they had drawn inspiration from de La Vallée Poussin's work. The second edition of 1909 was, moreover, the first work on elementary analysis to develop the "Lebesgue integral", while the third edition of 1914 already expounded the notion of the "total differential" of a function of several variables.

Publications on de La Vallée Poussin

The scientific works of Charles de La Vallée Poussin were published by Jean Mawhin (UCL), Paul Butzer (Rheinisch-Westfaelische Technische Hochschule Aachen) and Pasquale Vetro (University of Palermo). The first volume, devoted to biographical aspects and contributions to number theory, was published in 2000. It was a joint publication of the Académie royale de Belgique and the Circolo matemático di Palermo. The second volume dealt mainly with the theory of measurement, integration and differential equations. The third volume was devoted to the theory of approximation and the fourth volume to conformal representation and potential theory.

Publications

Lists with his publications can be found in:

• Butzer,P. ; Mawhin, J. and Vetro, P. eds., Charles-Jean de La Vallée Poussin. Collected Works. Oeuvres Scientifiques, Vol. I, Académie Royale de Belgique, Bruxelles, and Circolo Matematico di Palermo, Palermo, 2000.
• Godeaux, Lucien, "De la Vallée Poussin, Charles-Jean (1866-1962)", in: Annuaire ARB, (1967), 132-144.

Bibliography

• "Biographie de Charles de La Vallée Poussin", sur: Website UCL Mathématique, consulté le 4/07/2016.
• Burkill, John Charles, "Vallée-Poussin, Charles-Jean-Gustave-Nicolas de La", in : Gillispie, Charles Coulston, Dictionary of scientific Biography, vol. XIII, 561-562.
• Butzer, Paul et Mawhin, Jean, "A biography of Charles-Jean de La Vallée Poussin", in: Charles-Jean de La Vallée Poussin. Collected Works. Oeuvres Scientifiques, Vol. I, P. Butzer, J. Mawhin and P. Vetro eds., Académie Royale de Belgique, Bruxelles, and Circolo Matematico di Palermo, Palermo, 2000, 3-9.
• P. Butzer et J. Mawhin, Charles-Jean de La Vallée Poussin and the Académie royale de Belgique, in: Charles-Jean de La Vallée Poussin. Collected Works. Oeuvres Scientifiques, Vol. I, P. Butzer, J. Mawhin and P. Vetro eds., Académie Royale de Belgique, Bruxelles, and Circolo Matematico di Palermo, Palermo, 2000, p. 27-34
• Ch. A. de La Vallée Poussin, Charles-Jean de La Vallée Poussin : l'homme, sa vie, sa pensée, in: Charles-Jean de La Vallée Poussin. Collected Works. Oeuvres Scientifiques, Vol. I, P. Butzer, J. Mawhin and P. Vetro eds., Académie Royale de Belgique, Bruxelles, and Circolo Matematico di Palermo, Palermo, 2000,p. 11-16
• Godeaux, Lucien, "De La Vallée Poussin, Charles-Jean (1866-1962)", in: Biographie Nationale, 37 (1971), 786-790.
• Godeaux, Lucien, "De La Vallée Poussin, Charles-Jean (1866-1962)", in: Florilège des Sciences en Belgique, 1968, 155-167.
• Godeaux, Lucien, "De La Vallée Poussin, Charles-Jean (1866-1962)", in: Annuaire ARB, (1967), 45-131.
• J. Mawhin, The mathematical environmen of Charles-Jean de La Vallée Poussin at the Université Catholique de Louvain,in: Charles-Jean de La Vallée Poussin. Collected Works. Oeuvres Scientifiques, Vol. I, P. Butzer, J. Mawhin and P. Vetro eds., Académie Royale de Belgique, Bruxelles, and Circolo Matematico di Palermo, Palermo, 2000, p. 17-26
• Mawhin, Jean, "De wiskunde", in: Robert Halleux, Geert Vanpaemel, Jan Vandersmissen en Andrée Despy-Meyer (red.), Geschiedenis van de wetenschappen in België 1815-2000, Brussel: Dexia/La Renaissance du livre, 2001, vol. 1, 103-105.
• Mawhin, Jean, The Cours d'analyse infinitésimale of Charles-Jean de La Vallée Poussin : from innovation to tradition, Jahresberichte Deutsche Math. Verein., 116 (2014) 243-259.