Alexandre-Théophile Vandermonde (28 February 1735 – 1 January 1796) was a French mathematician, musician and

chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...

who worked with Bézout and

Lavoisier Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS ( determinant In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if a ...

theory in mathematics. He was born in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. Si ...

, and died there.

Biography

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 In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f ...

s and solution of

cyclotomic polynomial In mathematics, the ''n''th cyclotomic polynomial, for any positive integer ''n'', is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any Its roots are all ''n''th primitiv ...

s; this paper anticipated later

Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems in field theory to ...

(see also

abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...

for the role of Vandermonde in the genesis of group theory). In ''Remarques sur des problèmes de situation'' (1771) he studied

knight's tour A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square exactly once. If the knight ends on a square that is one knight's move from the beginning square (so that it could tour the board again im ...

s, and presaged the development of

knot theory In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot ...

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 The French Academy of Sciences (French: ''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. It was at ...

. ''Mémoire sur des irrationnelles de différents ordres avec une application au cercle'' (1772) was on

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many a ...

, and ''Mémoire sur l'élimination'' (1772) on the foundations of determinant theory. These papers were presented to the ''

Académie des Sciences The French Academy of Sciences (French: ''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. It was at ...

'', and constitute all his published mathematical work. The

Vandermonde determinant In algebra, the Vandermonde polynomial of an ordered set of ''n'' variables X_1,\dots, X_n, named after Alexandre-Théophile Vandermonde, is the polynomial: :V_n = \prod_ (X_j-X_i). (Some sources use the opposite order (X_i-X_j), which changes the ...

does not make an explicit appearance. He was professor at the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

, member of the

Conservatoire national des arts et métiers A music school is an educational institution specialized in the study, training, and research of music. Such an institution can also be known as a school of music, music academy, music faculty, college of music, music department (of a larger ins ...

and examiner at the

École polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Savoi ...

Honors

* A special class of

matrices Matrix most commonly refers to: * ''The Matrix'' (franchise), an American media franchise ** ''The Matrix'', a 1999 science-fiction action film ** "The Matrix", a fictional setting, a virtual reality environment, within ''The Matrix'' (franchis ...

, the Vandermonde matrices are named after him, as is an elementary fact of combinatorics,

Vandermonde's identity In combinatorics, Vandermonde's identity (or Vandermonde's convolution) is the following identity for binomial coefficients: :=\sum_^r for any nonnegative integers ''r'', ''m'', ''n''. The identity is named after Alexandre-Théophile Vandermon ...

. * Vandermonde is the secret society of the

Conservatoire National des Arts et Métiers A music school is an educational institution specialized in the study, training, and research of music. Such an institution can also be known as a school of music, music academy, music faculty, college of music, music department (of a larger ins ...

.Vandermonde : secret society of the Conservatoire National des Arts et Métiers.
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Notes

External links

* {{DEFAULTSORT:Vandermonde, Alexandre Theophile 1735 births 1796 deaths Scientists from Paris 18th-century French mathematicians Linear algebraists Combinatorialists Members of the French Academy of Sciences

Biography

Honors

See also

Notes

Further reading

External links