Introduction to the Correspondence
The book’s introduction presents the main mathematical themes considered by Paul Lévy and Maurice Fréchet in their correspondence to one another and examines the scientific and institutional context in which their letters were exchanged during their nearl
- PDF / 988,477 Bytes
- 54 Pages / 441 x 666 pts Page_size
- 19 Downloads / 230 Views
1 Borel and Hadamard The two great mathematicians, Jacques Hadamard (1865–1963) and Emile Borel (1871–1956), who were central in French mathematical life for many years, offered mathematical guidance and inspiration to both Maurice Fréchet and Paul Lévy and are frequently referred to in the correspondence. The books of Maz’ja and Shaposhnikova (1998) and Guiraldencq (1999), the article ‘Borel’ in the Encyclopedia Universalis written by Maurice Fréchet as well as the presentation of the life and work of Emile Borel in volume I of Borel (1972) contain extensive descriptions. Moreover, the exchanges between Lévy and Fréchet began just after the end of the First World War in which Borel and Hadamard had been deeply involved—consult Mazliak and Tazzioli (2009). Jacques Hadamard was born in Versailles in 1865. Heir to the great tradition of 19th century analysts, he threw himself into the investigation of analytic functions, focusing on theorems of analytic continuation and the systematic study of the radius of convergence. In particular he obtained what is now known as the Hadamard threecircle theorem, which affirms that the logarithm of the maximum modulus of an analytic function on a disk centered at O with radius r is a convex function. From his work, especially that on the Riemann ζ function, he drew important conclusions in analytic number theory. In 1896 he announced the remarkable prime number theorem (proven independently by de La Vallée-Poussin) showing that the number of primes less than a positive real number x grows asymptotically as lnxx . Under the influence of his illustrious predecessor Poincaré, Hadamard was eager to keep contact with physics, and was a promoter of the systematic study of partial differential equations. He introduced numerous methods for their solution, in particular a general solution for the case of hyperbolic equations. Hadamard was deeply involved in the scientific life of his time. He began a very active seminar at the Collège de France, which before the Second World War was the obligatory forum for any new results in mathematical analysis in France. In fact, Fréchet and Lévy indicate in their correspondence that this seminar was their natural meeting place. Hadamard was also politically engaged, like Borel as noted below, M. Barbut et al., Paul Lévy and Maurice Fréchet, Sources and Studies in the History of Mathematics and Physical Sciences, DOI 10.1007/978-1-4471-5619-2_1, © Springer-Verlag London 2014
1
2
Introduction to the Correspondence
but in a different spirit. A committed pacifist largely in sympathy with the goals of the Third International, Hadamard was an ardent partisan of rapprochement with the USSR. He was the guest of honor at the “Week of French science in the USSR” in 1934 (one of the first visits of a French scientist to the Soviet Union). A favorite of the regime, he returned to the Soviet Union several times. The dramatic developments beginning in 1940 found him an old man of 75, crowned in glory but nonetheless under the threat of racist persecution becau
Data Loading...
