Charles Hermite
Charles Hermite | |
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Hermitian transpose Hermitian wavelet | |
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Charles Hermite (French pronunciation:
He was the first to prove that e, the base of natural logarithms, is a transcendental number. His methods were used later by Ferdinand von Lindemann to prove that π is transcendental.
Life
Hermite was born in
Hermite obtained his secondary education at Collège de Nancy and then, in Paris, at Collège Henri IV and at the Lycée Louis-le-Grand.[1] He read some of Joseph-Louis Lagrange's writings on the solution of numerical equations and Carl Friedrich Gauss's publications on number theory.
Hermite wanted to take his higher education at
In 1842, Nouvelles Annales de Mathématiques published Hermite's first original contribution to mathematics, a simple proof of Niels Abel's proposition concerning the impossibility of an algebraic solution to equations of the fifth degree.[1]
A correspondence with
After spending five years working privately towards his degree, in which he befriended eminent mathematicians Joseph Bertrand, Carl Gustav Jacob Jacobi, and Joseph Liouville, he took and passed the examinations for the baccalauréat, which he was awarded in 1847. He married Joseph Bertrand's sister, Louise Bertrand, in 1848.[2]
In 1848, Hermite returned to the École Polytechnique as répétiteur and examinateur d'admission. In July 1848, he was elected to the
Hermite died in Paris on 14 January 1901,[1] aged 78.
Contribution to mathematics
Number theory
An inspiring teacher, Hermite strove to cultivate admiration for simple beauty and discourage rigorous minutiae. His correspondence with
In 1858, Hermite solved equations of the fifth degree and, in 1873, he proved that e, the base of the natural system of logarithms, is transcendental.[2] Techniques similar to those used in Hermite's proof of e's transcendence were used by Ferdinand von Lindemann in 1882 to show that π is transcendental.[1]
Quintic equations
In 1858, Hermite showed that equations of the fifth degree could be solved by elliptic modular functions. In his famous work Sur la résolution de l'Équation du cinquiéme degré Comptes rendus he named the exact elliptical solution expression based on the theta function[3] the Bring Jerrard Normal form. In particular, he recognized how to determine the corresponding elliptic module and its Pythagorean complementary module for the given Bring-Jerrard form. The Bring-Jerrard form only contains the quintic, the linear and the absolute equation term:
All Bring-Jerrard equations can be normalized to this form by substituting the internal unknowns. If in the given form the value is a real number, then the equation in question has one real and four imaginary solutions. According to the
For the more accurate derivation, please watch the Article Lemniscate elliptic functions, section Elliptic Modulus and quintic equations!
These eccentricities are the corresponding elliptical module and its Pythagorean complementary counterpart in the Legendre's normal form or in the standard form. The two formulas now mentioned result directly from the formula which is at the top of page 258 in the Italian edition of the above-mentioned work Sulla risoluzione delle equazioni del quinto grado, which was further distributed by Francesco Brioschi. The expressions with the abbreviations for Tangens Lemniscatus Hyperbolicus and for Cotangens Lemniscatus Hyperbolicus as well as the elliptic integral for Areacosinud Lemniscatus Hyperbolicus represent the
Publications
The following is a list of his works:[1]
- "Sur quelques applications des fonctions elliptiques", Paris, 1855; page images from Cornell.
- "Cours d'Analyse de l'École Polytechnique. Première Partie", Paris: Gauthier–Villars, 1873.
- "Cours professé à la Faculté des Sciences", edited by Andoyer, 4th ed., Paris, 1891; page images from Cornell.
- "Correspondance", edited by Baillaud and Bourget, Paris, 1905, 2 vols.; PDF copy from UMDL.
- "Œuvres de Charles Hermite", edited by Picard for the Academy of Sciences, 4 vols., Paris: Gauthier–Villars, 1905,[6] 1908,[7] 1912[8] and 1917; PDF copy from UMDL.
- "Œuvres de Charles Hermite", reissued by ISBN 978-1-108-00328-5.
Quotations
There exists, if I am not mistaken, an entire world which is the totality of mathematical truths, to which we have access only with our mind, just as a world of physical reality exists, the one like the other independent of ourselves, both of divine creation.
— Charles Hermite; cit. by Gaston Darboux, Eloges académiques et discours, Hermann, Paris 1912, p. 142.
I shall risk nothing on an attempt to prove the transcendence of π. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort.
— Charles Hermite; letter to C.W. Borchardt, "Men of Mathematics", E. T. Bell, New York 1937, p. 464.
While speaking, M. Bertrand is always in motion; now he seems in combat with some outside enemy, now he outlines with a gesture of the hand the figures he studies. Plainly he sees and he is eager to paint, this is why he calls gesture to his aid. With M. Hermite, it is just the opposite, his eyes seem to shun contact with the world; it is not without, it is within he seeks the vision of truth.
— Henri Poincaré, INTUITION and LOGIC in Mathematics, Source: The Mathematics Teacher, MARCH 1969, Vol. 62, No. 3 (MARCH 1969), pp. 205-212
Reading one of [Poincare's] great discoveries, I should fancy (evidently a delusion) that, however magnificent, one ought to have found it long before, while such memoirs of Hermite as the one referred to in the text arouse in me the idea: “What magnificent results! How could he dream of such a thing?”
— Jacques Hadamard, The Mathematician's Mind: The Psychology of Invention in the Mathematical Field, p. 110
I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives.
— Charles Hermite; letter to Thomas Joannes Stieltjes about Weierstrass functions, Correspondance d'Hermite et de Stieltjes vol.2, p.317-319
Legacy
In addition to the mathematics properties named in his honor, the Hermite crater near the Moon's north pole is named after Hermite.
See also
- List of things named after Charles Hermite
- Hermitian manifold
- Hermite interpolation
- Hermite's cotangent identity
- Hermite reciprocity
- Ramanujan's constant
References
- ^ a b c d e f g h i j Linehan 1910.
- ^ a b c d e O'Connor, John J.; Robertson, Edmund F. (March 2001), "Charles Hermite", MacTutor History of Mathematics Archive, University of St Andrews
- ^
Literature Oral literature Major written forms Long prose fiction Short prose fiction - Novella
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Prose genres Fiction Non-fiction Poetry genres Narrative Lyric Lists Dramatic genres History Lists and outlines Theory and criticism Literature portal - ^ https://staff.math.su.se/mleites/ books/prasolov-soloviev-1997-elliptic.pdf
- arXiv:1510.00068 [math.GM].
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- Sources
- Linehan, Paul Henry (1910). Catholic Encyclopedia. Vol. 7. New York: Robert Appleton Company. . In Herbermann, Charles (ed.).
External links
- Charles Hermite at the Mathematics Genealogy Project
- (in French) Cours d'Analyse de l'École Polytechnique (Première Partie) by Charles Hermite (DjVu file on Internet Archive)
- (in French) Œuvres de Charles Hermite (t1) edited by Émile Picard (DjVu file on Internet Archive)
- (in French) Œuvres de Charles Hermite (t2) edited by Émile Picard (DjVu file on Internet Archive)
- (in French) Œuvres de Charles Hermite (t3) edited by Émile Picard (DjVu file on Internet Archive)
- (in French) Œuvres de Charles Hermite (t4) edited by Émile Picard (DjVu file on Internet Archive)
- Works by Charles Hermite at Project Gutenberg
- Works by or about Charles Hermite at Internet Archive
This article incorporates text from a publication now in the public domain: Herbermann, Charles, ed. (1913). "Charles Hermite". Catholic Encyclopedia. New York: Robert Appleton Company.