# Charles Hermite

Prof **Charles Hermite** (French pronunciation: [ʃaʁl ɛʁˈmit]) FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

Charles Hermite | |
---|---|

Charles Hermite circa 1887. | |

Born | |

Died | 14 January 1901 | (aged 78)

Nationality | French |

Alma mater | Collège Henri IV, Sorbonne Collège Louis-le-Grand, Sorbonne |

Known for | Proof that e is transcendental Hermitian adjoint Hermitian form Hermitian function Hermitian matrix Hermitian metric Hermitian operator Hermite polynomials Hermitian transpose Hermitian wavelet |

Scientific career | |

Fields | Mathematics |

Institutions | |

Doctoral advisor | Eugène Charles Catalan |

Doctoral students | Léon Charve Henri Padé Mihailo Petrović Henri Poincaré Thomas Stieltjes Jules Tannery |

Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré.

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.

In a letter to Thomas Joannes Stieltjes during 1893, Hermite remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives."

A crater near the north pole of the moon has been named in his honor.

## Contents

## LifeEdit

Hermite was born in Dieuze, The Moselle on 24 December 1822, ^{[1]} with a deformity in his right foot which would affect his gait for the rest of his life. He was the sixth of seven children of Ferdinand Hermite, and his wife Madeleine Lallemand. His father worked in his mother's family's drapery business, and also pursued a career as an artist. The drapery business relocated to Nancy during 1828 and so did the family.^{[2]}

He studied at the Collège de Nancy and then, in Paris, at the Collège Henri IV and at the Lycée Louis-le-Grand.^{[1]}

As a boy he read some of the writings of Joseph Louis Lagrange on the solution of numerical equations, and of Carl Friedrich Gauss on the theory of numbers.

Hermite wanted to study at the École Polytechnique and during 1841 he took a year preparing for the examinations and was tutored by Eugène Charles Catalan.^{[2]} During 1842 he was admitted to the school.^{[1]} However, after one year Hermite was refused the right to continue his studies because of his disability (École Polytechnique is to this day a military academy). He had to struggle to regain his admission which he won but with strict conditions imposed. Hermite found this unacceptable and decided to quit the École Polytechnique without graduating.^{[2]}

During 1842, his first original contribution to mathematics, in which he gave a simple proof of the proposition of Niels Abel concerning the impossibility of obtaining an algebraic solution for the equation of the fifth degree, was published in the "Nouvelles Annales de Mathématiques".^{[1]}

A correspondence with Carl Jacobi, begun during 1843 and continued the next year, resulted in the insertion, in the complete edition of Jacobi's works, of two articles by Hermite, one concerning the extension to Abelian functions of one of the theorems of Abel on elliptic functions, and the other concerning the transformation of elliptic functions.^{[1]}

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 during 1847. He married Joseph Bertrand's sister, Louise Bertrand, during 1848.^{[2]}

During 1848, Hermite returned to the École Polytechnique as *répétiteur and examinateur d'admission*. During 1856 he contracted smallpox. Through the influence of Augustin-Louis Cauchy and of a nun who nursed him, he resumed the practice of his Catholic faith.^{[3]} On 14 July, of that year, he was elected for the vacancy created by the death of Jacques Binet in the Académie des Sciences. During 1869, he succeeded Jean-Marie Duhamel as professor of mathematics, both at the École Polytechnique, where he remained until 1876, and in the Faculty of Sciences of Paris,^{[4]} which was a post he occupied until his death. From 1862 to 1873 he was lecturer at the École Normale Supérieure. Upon his seventieth birthday, on the occasion of his jubilee which was celebrated at the Sorbonne under the auspices of an international committee, he was promoted grand officer of the Légion d'honneur.^{[1]} He died in Paris, 14 January 1901,^{[1]} aged 78.

## Contribution to mathematicsEdit

An inspiring teacher, Hermite strove to cultivate admiration for simple beauty and discourage rigorous minutiae. His correspondence with Thomas Stieltjes testifies to the great aid he gave those beginning scientific life. His published courses of lectures have exercised a great influence. His important original contributions to pure mathematics, published in the major mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. During 1858 he solved the equation of the fifth degree by elliptic functions; and during 1873 he proved *e*, the base of the natural system of logarithms, to be transcendental. This last was used by Ferdinand von Lindemann to prove during 1882 the same for π.^{[1]}

## PublicationsEdit

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,
^{[5]}1908,^{[6]}1912^{[7]}and 1917; PDF copy from UMDL. - "Œuvres de Charles Hermite", reissued by Cambridge University Press, 2009; ISBN 978-1-108-00328-5.

## QuotationsEdit

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.

## See alsoEdit

## ReferencesEdit

- ^
^{a}^{b}^{c}^{d}^{e}^{f}^{g}^{h}^{i}Linehan 1910. - ^
^{a}^{b}^{c}^{d}O'Connor & Robertson 2001. **^**"CATHOLIC ENCYCLOPEDIA: Charles Hermite". Retrieved 18 August 2014.**^**See fr:Faculté des sciences de Paris.**^**Pierpont, James (1907). "Review:*Oeuvres de Charles Hermite*, publiées sous les auspices del'Académie des Sciences par EMILE PICARD. Vol. I" (PDF).*Bull. Amer. Math. Soc*.**13**(4): 182–190. doi:10.1090/S0002-9904-1907-01440-4.**^**Pierpont, James (1910). "Review:*Oeuvres de Charles Hermite*. Vol II" (PDF).*Bull. Amer. Math. Soc*.**16**(7): 370–377. doi:10.1090/s0002-9904-1910-01920-0.**^**Pierpont, James (1912). "Review:*Oeuvres de Charles Hermite*. Vol III" (PDF).*Bull. Amer. Math. Soc*.**19**(2): 83–84. doi:10.1090/s0002-9904-1912-02290-5.

- Sources

- Linehan, Paul Henry (1910). . In Herbermann, Charles.
*Catholic Encyclopedia*.**7**. New York: Robert Appleton Company. - O'Connor, John J.; Robertson, Edmund F. (March 2001), "Charles Hermite",
*MacTutor History of Mathematics archive*, University of St Andrews.

## External linksEdit

- 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)

*This article incorporates text from the public-domain Catholic Encyclopedia of 1913.*