Alexandre-Théophile Vandermonde
Encyclopedia
Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French
musician
, mathematician
and chemist
who worked with Bézout and Lavoisier; his name is now principally associated with determinant
theory in mathematics
. He was born in Paris
, and died there.
Vandermonde was a violinist, and became engaged with mathematics only around 1770. In Mémoire sur la résolution des équations (1771) he reported on symmetric function
s and solution of cyclotomic polynomial
s; this paper anticipated later Galois theory
. In Remarques sur des problèmes de situation (1771) he studied knight's tour
s, and presaged the development of knot theory
by explicitly noting the importance of topological
features when discussing the properties of knots:
"Whatever the twists and turns of a system of threads in space, one can always obtain an expression for the calculation of its dimensions, but this expression will be of little use in practice. The craftsman who fashions a braid, a net, or some knots will be concerned, not with questions of measurement, but with those of position: what he sees there is the manner in which the theads are interlaced"
The same year he was elected to the French Academy of Sciences
. Mémoire sur des irrationnelles de différents ordres avec une application au cercle (1772) was on combinatorics
, and Mémoire sur l'élimination (1772) on the foundations of determinant theory. These papers were presented to the Académie des Sciences, and constitute all his published mathematical work. The Vandermonde determinant does not make an explicit appearance.
A special class of matrices
, the Vandermonde matrices are named after him, as is an elementary fact of combinatorics, Vandermonde's identity.
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...
musician
Musician
A musician is an artist who plays a musical instrument. It may or may not be the person's profession. Musicians can be classified by their roles in performing music and writing music.Also....* A person who makes music a profession....
, 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....
and chemist
Chemist
A chemist is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties such as density and acidity. Chemists carefully describe the properties they study in terms of quantities, with detail on the level of molecules and their component atoms...
who worked with Bézout and Lavoisier; his name is now principally associated with determinant
Determinant
In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...
theory in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. He was born in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, and died there.
Vandermonde was a violinist, and became engaged with mathematics only around 1770. In Mémoire sur la résolution des équations (1771) he reported on symmetric function
Symmetric function
In algebra and in particular in algebraic combinatorics, the ring of symmetric functions, is a specific limit of the rings of symmetric polynomials in n indeterminates, as n goes to infinity...
s and solution of cyclotomic polynomial
Cyclotomic polynomial
In algebra, the nth cyclotomic polynomial, for any positive integer n, is the monic polynomial:\Phi_n = \prod_\omega \,where the product is over all nth primitive roots of unity ω in a field, i.e...
s; this paper anticipated later Galois theory
Galois theory
In mathematics, more specifically in abstract algebra, Galois theory, named after Évariste Galois, provides a connection between field theory and group theory...
. In Remarques sur des problèmes de situation (1771) he studied knight's tour
Knight's tour
The knight's tour is a mathematical problem involving a knight on a chessboard. The knight is placed on the empty board and, moving according to the rules of chess, must visit each square exactly once. A knight's tour is called a closed tour if the knight ends on a square attacking the square from...
s, and presaged the development of knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...
by explicitly noting the importance of topological
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
features when discussing the properties of knots:
"Whatever the twists and turns of a system of threads in space, one can always obtain an expression for the calculation of its dimensions, but this expression will be of little use in practice. The craftsman who fashions a braid, a net, or some knots will be concerned, not with questions of measurement, but with those of position: what he sees there is the manner in which the theads are interlaced"
The same year he was elected to the French Academy of Sciences
French Academy of Sciences
The French Academy of 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...
. Mémoire sur des irrationnelles de différents ordres avec une application au cercle (1772) was on combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, and Mémoire sur l'élimination (1772) on the foundations of determinant theory. These papers were presented to the Académie des Sciences, and constitute all his published mathematical work. The Vandermonde determinant does not make an explicit appearance.
A special class of matrices
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
, the Vandermonde matrices are named after him, as is an elementary fact of combinatorics, Vandermonde's identity.