Alexandre-Théophile Vandermonde
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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 graduated scientist trained in the study of chemistry, or an officially enrolled student in the field. Chemists study the composition of ...
who worked with Bézout and
Lavoisier Antoine-Laurent de Lavoisier ( ; ; 26 August 17438 May 1794),
CNRS (
determinant In mathematics, the determinant is a Scalar (mathematics), scalar-valued function (mathematics), function of the entries of a square matrix. The determinant of a matrix is commonly denoted , , or . Its value characterizes some properties of the ...
theory in mathematics. He was born in Paris, 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 prim ...
s; this paper anticipated later
Galois theory In mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field (mathematics), field theory and group theory. This connection, the fundamental theorem of Galois theory, allows reducing certain problems ...
(see also
abstract algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
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 topology, knot theory is the study of knot (mathematics), 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 be und ...
by explicitly noting the importance of
topological Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, wit ...
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 (, ) 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 method, scientific research. It was at the forefron ...
. ''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 as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...
, 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 (, ) 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 method, scientific research. It was at the forefron ...
'', 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 or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...
, member of the
Conservatoire national des arts et métiers The (; ; abbr. CNAM) is an AMBA-accredited French ''grande école'' and '' grand établissement''. It is a member of the '' Conférence des Grandes écoles'', which is an equivalent to the Ivy League schools in the United States, Oxbridge in th ...
and examiner at the
École polytechnique (, ; also known as Polytechnique or l'X ) is a ''grande école'' located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mat ...
.


Honors

* A special class of
matrices Matrix (: matrices or matrixes) or MATRIX may refer to: Science and mathematics * Matrix (mathematics), a rectangular array of numbers, symbols or expressions * Matrix (logic), part of a formula in prenex normal form * Matrix (biology), the ...
, the Vandermonde matrices are named after him, as is an elementary fact of combinatorics, Vandermonde's identity. * Vandermonde is the
secret society A secret society is an organization about which the activities, events, inner functioning, or membership are concealed. The society may or may not attempt to conceal its existence. The term usually excludes covert groups, such as intelligence ag ...
of the
Conservatoire National des Arts et Métiers The (; ; abbr. CNAM) is an AMBA-accredited French ''grande école'' and '' grand établissement''. It is a member of the '' Conférence des Grandes écoles'', which is an equivalent to the Ivy League schools in the United States, Oxbridge in th ...
.Vandermonde : secret society of the Conservatoire National des Arts et Métiers.
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See also

*
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 ...
*
Knot theory In topology, knot theory is the study of knot (mathematics), 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 be und ...
* Vandermonde's identity * Vandermonde polynomial * Vandermonde matrix


Notes


Further reading

* Gilbert Faccarello, ''Du Conservatoire à l'Ecole Normale'', Les cahiers d'histoire du CNAM, 2-3, 17–57, CNAM, Paris, 1993

* Jacqueline Hecht, ''Un exemple de multidisciplinarité : Alexandre Vandermonde (1735-1796)'', Population, 4, 641–676, INED, Paris, 197


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