Charles Hermite
Overview
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
who did research on number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, quadratic form
Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables. For example,4x^2 + 2xy - 3y^2\,\!is a quadratic form in the variables x and y....
s, invariant theory
Invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties from the point of view of their effect on functions...
, orthogonal polynomials
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
, elliptic function
Elliptic function
In complex analysis, an elliptic function is a function defined on the complex plane that is periodic in two directions and at the same time is meromorphic...
s, and algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
.
Hermite polynomials
Hermite polynomials
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; in numerical analysis as Gaussian quadrature; and in physics, where...
, Hermite interpolation
Hermite interpolation
In numerical analysis, Hermite interpolation, named after Charles Hermite, is a method of interpolating data points as a polynomial function. The generated Hermite polynomial is closely related to the Newton polynomial, in that both are derived from the calculation of divided differences.Unlike...
, Hermite normal form
Hermite normal form
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z.-Nonsingular square matrices:...
, Hermitian operators, and cubic Hermite spline
Cubic Hermite spline
In the mathematical subfield of numerical analysis a cubic Hermite spline , named in honor of Charles Hermite, is a third-degree spline with each polynomial of the spline in Hermite form...
s are named in his honor. One of his students was Henri Poincaré
Henri Poincaré
Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and a philosopher of science...
.
He was the first to prove that e
E (mathematical constant)
The mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
, the base of natural logarithm
Natural logarithm
The natural logarithm is the logarithm to the base e, where e is an irrational and transcendental constant approximately equal to 2.718281828...
s, is a transcendental number
Transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
. His methods were later used by Ferdinand von Lindemann
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann was a German mathematician, noted for his proof, published in 1882, that π is a transcendental number, i.e., it is not a root of any polynomial with rational coefficients....
to prove that π
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
is transcendental.
In a letter to Thomas Stieltjes
Thomas Joannes Stieltjes
Thomas Joannes Stieltjes was a Dutch mathematician. He was born in Zwolle and died in Toulouse, France. He was a pioneer in the field of moment problems and contributed to the study of continued fractions....
in 1893, Hermite famously remarked: "I turn with terror and horror from this lamentable scourge of continuous functions with no derivatives
Weierstrass function
In mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere...
."
Born at Dieuze
Dieuze
Dieuze is a commune in the Moselle department in Lorraine in north-eastern France.-People:Dieuze was the birthplace of:*Charles Hermite, mathematician*Edmond François Valentin About, novelist, publicist and journalist*Émile Friant, painter...
, Moselle
Moselle
Moselle is a department in the east of France named after the river Moselle.- History :Moselle is one of the original 83 departments created during the French Revolution on March 4, 1790...
, 24 December, 1822 he was the son of a salt mine engineer, Ferdinand Hermite.
Unanswered Questions
