Hadamard

Jacques Salomon Hadamard

Born: 8 Dec 1865 in Versailles, France
Died: 17 Oct 1963 in Paris, France

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Jacques Hadamard's most important result is the proof of the prime number theorem.

He proved this in 1896. It states that:-

The number of primes lte n tends to infinity as n/ln n.

This theorem was conjectured in the 18th century, but it was not proved until 1896, when Hadamard and (independently) Charles de la Vallée Poussin, used complex analysis.

The proof was outlined by Riemann in 1851, but the necessary tools had not been developed at that time. This problem was one of the major motivations for the development of complex analysis from 1851 to 1896 when Riemann's outlined proof was finally completed.

Hadamard's other contributions are to the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalisation of Green's functions in 1932.

In 1910 he published Lecons sur le calcul des variations which helped lay the foundations of functional analysis (he introduced the word functional). Other important work on determinants is used in the theory of integral equations.

References elsewhere in this archive:

Tell me about Hadamard's part in investigating prime numbers

Tell me about the Prime Number Theorem

Tell me about Hadamard's work on topology

References:

  1. Dictionary of Scientific Biography
  2. Biography in Encyclopaedia Britannica
  3. M L Cartwright, Jacques Hadamard, Biographical Memoirs of Fellows of the Royal Society of London 2 (1965).
  4. S Mandelbrojt and L Schwartz, Jacques Hadamard, Bull. Amer. Math. Soc. 71 (1965).
  5. J P Kahane, Jacques Hadamard, Mathematical Intelligencer 13 (1991), 23-29. 
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JOC/EFR February 1996