Charles Hermite

Charles Hermite circa 1887
Born	December 24, 1822 Dieuze, Lorraine, France
Died	January 14, 1901 (aged 78) Paris, France
Residence	France
Nationality	French
Field	Mathematics
Institutions	Ecole Polytechnique Sorbonne
Alma mater	Collège de Nancy Collège Henri IV, Sorbonne Collège Louis-le-Grand, Sorbonne
Academic advisor	Eugène-Charles Catalan
Notable students	Henri Poincaré L. Bourguet Léon Charve Henry Padé Mihailo Petrovic Jules Tannery
Known for	Proof that e is transcendental

Charles Hermite (pronounced in IPA, [ʃaʁl ɛʁ'mit]) (December 24, 1822 – January 14, 1901) was a French mathematician who did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Image File history File links Size of this preview: 380 × 599 pixelsFull resolution (500 × 788 pixel, file size: 221 KB, MIME type: image/jpeg) File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... is the 358th day of the year (359th in leap years) in the Gregorian calendar. ... 1822 (MDCCCXXII) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day-slower Julian calendar). ... Dieuze is a town and commune in the Moselle département, Lorraine région in northeastern France. ... (Région flag) (Region logo) Location Administration Capital Regional President Departments Meurthe-et-Moselle Meuse Moselle Vosges Arrondissements 19 Cantons 157 Communes 2,337 Statistics Land area1 23,547 km² Population (Ranked 11th)  - January 1, 2006 est. ... is the 14th day of the year in the Gregorian calendar. ... Year 1901 (MCMI) was a common year starting on Tuesday (link will display calendar) of the Gregorian calendar (or a common year starting on Monday [1] of the 13-day-slower Julian calendar). ... City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) The Eiffel Tower in Paris, as seen from the esplanade du Trocadéro. ... Image File history File links This is a lossless scalable vector image. ... Image File history File links This is a lossless scalable vector image. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... For other Écoles Polytechniques, see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. ... Inscription over the entrance to the Sorbonne The front of the Sorbonne Building The name Sorbonne (La Sorbonne) is commonly used to refer to the historic University of Paris in Paris, France or one of its successor institutions (see below), but this is a recent usage, and Sorbonne has actually... The Lycée Henri IV (sometimes nicknamed HIV to be pronounced H4) is a public high school located in Paris. ... Inscription over the entrance to the Sorbonne The front of the Sorbonne Building The name Sorbonne (La Sorbonne) is commonly used to refer to the historic University of Paris in Paris, France or one of its successor institutions (see below), but this is a recent usage, and Sorbonne has actually... The Lycée Louis-le-Grand, in Paris is one of the most famous lycées providing preparatory classes for grandes écoles. ... Inscription over the entrance to the Sorbonne The front of the Sorbonne Building The name Sorbonne (La Sorbonne) is commonly used to refer to the historic University of Paris in Paris, France or one of its successor institutions (see below), but this is a recent usage, and Sorbonne has actually... Eugène Charles Catalan Eugène Charles Catalan (May 30, 1814 - February 14, 1894) was a Belgian mathematician. ... Jules TuPac Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [][1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ... Mihailo Petrovic-Alas - the famous Serbian mathematician and inventor Mihailo Petrović Alas (Serbian Cyrillic: Михаило Петровић Алас) (1868 - 1943), was a greatly influential Serbian mathematician and inventor. ... e is the unique number such that the value of the derivative of f (x) = ex (blue curve) at the point x = 0 is exactly 1. ... In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ... Articles with similar titles include the NATO phonetic alphabet, which has also informally been called the “International Phonetic Alphabet”. For information on how to read IPA transcriptions of English words, see IPA chart for English. ... is the 358th day of the year (359th in leap years) in the Gregorian calendar. ... 1822 (MDCCCXXII) was a common year starting on Tuesday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 12-day-slower Julian calendar). ... is the 14th day of the year in the Gregorian calendar. ... Year 1901 (MCMI) was a common year starting on Tuesday (link will display calendar) of the Gregorian calendar (or a common year starting on Monday [1] of the 13-day-slower Julian calendar). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ... In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. ... In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. ... In mathematics, an orthogonal polynomial sequence is an infinite sequence of polynomials p0(x), p1(x), p2(x) ... , in which each pn(x) has degree n, and such that any two different polynomials in the sequence are orthogonal to each other in the following sense: One can define an inner... In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ...

Hermite polynomials, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré. In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; and in physics, as the eigenstates of the quantum harmonic oscillator. ... In mathematics, a matrix is in reduced row echelon form (also known as row canonical form - the resulting matrix is sometimes called a Hermite matrix) if it satisfies the following requirements: All nonzero rows are above any rows of all zeroes. ... On a finite-dimensional inner product space, a self-adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose. ... In the mathematical subfield of numerical analysis a cubic Hermite spline, named in honor of Charles Hermite (Hermite is pronounced air MIT), is a third-degree spline with each polynomial of the spline in Hermite form. ... Jules TuPac Henri Poincaré (April 29, 1854 – July 17, 1912) (IPA: [][1]) was one of Frances greatest mathematicians and theoretical physicists, and a philosopher of science. ...

He was the first to prove that e, the base of natural logarithms, is a transcendental number. His methods were later used by Ferdinand von Lindemann to prove that π is transcendental. e is the unique number such that the value of the derivative of f (x) = ex (blue curve) at the point x = 0 is exactly 1. ... The natural logarithm, formerly known as the hyperbolic logarithm, is the logarithm to the base e, where e is equal to 2. ... In mathematics, a transcendental number is any complex number that is not algebraic, that is, not the solution of a non-zero polynomial equation with integer (or, equivalently, rational) coefficients. ... Carl Louis Ferdinand von Lindemann (April 12, 1852 - March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i. ... When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ...

In a letter to Thomas Stieltjes in 1893, Hermite famously remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives." Thomas Joannes Stieltjes (December 29, 1856 – December 31, 1894) was a Dutch mathematician. ...

Life

Born at Dieuze, Lorraine, 24 December, 1822 he was the son of a salt mine engineer, Ferdinand Hermite. His mother was Madeleine Lallemand. The family moved to run a drapers business in Nancy in 1828 and his father also pursued ambitions as an artist. Charles was the sixth of his parents seven children. Dieuze is a town and commune in the Moselle département, Lorraine région in northeastern France. ... (Région flag) (Region logo) Location Administration Capital Regional President Departments Meurthe-et-Moselle Meuse Moselle Vosges Arrondissements 19 Cantons 157 Communes 2,337 Statistics Land area1 23,547 km² Population (Ranked 11th)  - January 1, 2006 est. ...

Charles had a defect in his right foot which meant that from boyhood he moved around with difficulty.

He studied at the Collège de Nancy and then, in Paris, at the Collège Henri IV and at the Collège Louis-le-Grand. A building of Nancy-Université Nancy-Université federates the three universities of Nancy, in Lorraine : University Nancy I Henri Poincaré (UHP) : natural sciences, wrapping several faculty and engineering schools École Supérieure des Sciences et Technologies de lIngénieur de Nancy : general engineering École Supérieure dInformatique et... The Lycée Henri IV (sometimes nicknamed HIV to be pronounced H4) is a public high school located in Paris. ... The Lycée Louis-le-Grand, in Paris is one of the most famous lycées providing preparatory classes for grandes écoles. ...

Hermite wanted to study at the École Polytechnique and he took a year preparing for the examinations and was tutored by Catalan between 1841-42. Eugène Charles Catalan Eugène Charles Catalan (May 30, 1814 - February 14, 1894) was a Belgian mathematician. ...

In 1842 he entered the Ecole Polytechnique, where he remained as a student for a short time. After one year at the École Polytechnique Hermite was refused the right to continue his studies because of his disability. He had to fight to regain his place which he won but with strict conditions imposed. Hermite found this unacceptable and decided to leave the École Polytechnique without graduating. For other Écoles Polytechniques, see École Polytechnique de Montréal and École Polytechnique Fédérale de Lausanne. ...

As a boy he read some of the writings of Joseph Louis Lagrange on the solution of numerical equations, and of Carl Gauss on the theory of numbers. In 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". Joseph-Louis Lagrange, comte de lEmpire (January 25, 1736 – April 10, 1813; b. ... Johann Carl Friedrich Gauss or Gauß ( ; Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ... 1842 was a common year starting on Saturday (see link for calendar). ... Niels Henrik Abel (August 5, 1802–April 6, 1829), Norwegian mathematician, was born in Nedstrand, near Finnøy where his father acted as rector. ...

A correspondence with Carl Jacobi, begun in 1843 and continued in 1844, led to 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. Karl Gustav Jacob Jacobi (Potsdam December 10, 1804 - Berlin February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ... In mathematics, particularly in algebraic geometry, complex analysis and number theory, abelian variety is a term used to denote a complex torus that can be embedded into projective space as a projective variety. ... In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ...

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. Joseph Louis François Bertrand (March 11, 1822 - April 5, 1900, born and died in Paris) was a French mathematician who worked in the fields of number theory, differential geometry, probability theory, and thermodynamics. ... Karl Gustav Jacob Jacobi (Potsdam December 10, 1804 - Berlin February 18, 1851), was not only a great German mathematician but also considered by many as the most inspiring teacher of his time (Bell, p. ... Joseph Liouville (born March 24, 1809, died September 8, 1882) was a French mathematician. ... For other uses of Baccalaureate, see Baccalaureate (disambiguation). ...

He married Joseph Bertrand's sister, Louise Bertrand in 1848.

In 1848, Hermite returned to the Ecole Polytechnique as répétiteur and examinateur d'admission. In 1856, through the influence of Augustin Cauchy and of a nun who nursed him, he resumed the practice of his religion. On 14 July, of that year, he was elected to fill the vacancy created by the death of Jacques Binet in the Académie des Sciences. In 1869, he succeeded Jean-Marie Duhamel as professor of mathematics, both at the Ecole Polytechnique, where he remained until 1876, and in the Faculty of Sciences of Paris, which position he occupied until his death. From 1862 to 1873 he was lecturer at the Ecole 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. Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Jacques Philippe Marie Binet was a catholic mathematician. ... The French Academy of Sciences (Académie des sciences) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. ... The quadrangle at the main ENS building on rue dUlm is known as the Cour aux Ernests – the Ernests being the goldfish in the pond. ... Chiang Kai-sheks Légion dhonneur. ...

He died at Paris, 14 January, 1901, aged 78. City flag City coat of arms Motto: Fluctuat nec mergitur (Latin: Tossed by the waves, she does not sink) The Eiffel Tower in Paris, as seen from the esplanade du Trocadéro. ...

Contribution to mathematics

As a teacher Hermite was inspiring. His correspondence with Thomas Stieltjes testifies to the great aid he gave those entering scientific life. His efforts in teaching were directed not towards too rigorous minuteness, but towards exciting admiration for things simple and beautiful. His published courses of lectures have exercised a wide influence. His important original contributions to pure mathematics, published in the leading mathematical journals of the world, dealt chiefly with Abelian and elliptic functions and the theory of numbers. In 1858 he solved the equation of the fifth degree by elliptic functions; and in 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 in 1882 the same for pi. Thomas Joannes Stieltjes (December 29, 1856 – December 31, 1894) was a Dutch mathematician. ... e is the unique number such that the value of the derivative of f (x) = ex (blue curve) at the point x = 0 is exactly 1. ... Carl Louis Ferdinand von Lindemann (April 12, 1852 - March 6, 1939) was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i. ... When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ...

Publications

The following is a list of his works.

• "Cours professé à la Faculté des Sciences", edited by Andoyer, 4th ed., Paris, 1891
• "Correspondance", edited by Baillaud and Bourget, Paris, 1905, 2 vols.

• "Oeuvres de Charles Hermite" were edited by Picard for the Academy of Sciences, 2 vols., Paris, 1905 and 1908.

Quotation

" 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

External links

• O'Connor, John J; Edmund F. Robertson "Charles Hermite". MacTutor History of Mathematics archive.  
• Charles Hermite at the Mathematics Genealogy Project
• Charles Hermite at the Catholic Encyclopedia

This article incorporates text from the public-domain Catholic Encyclopedia of 1913. The MacTutor history of mathematics archive is a website hosted by University of St Andrews in Scotland. ... The Mathematics Genealogy Project is a web-based database that gives an academic genealogy based on dissertation supervision relations. ... This article needs additional references or sources for verification. ...