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Cauchy was born in Paris in 1789 and recceived his early education from his
father. Later, at the Ecole Centrale du Pantheno. he excelled in ancient claassi
cal studies. In 1805. He entered the Ecole Polytechnique won the admire
tion of Lagrange and Laplace. Two years later, he enrolled at the Ecole ade
Ponts et Chaussees, where he prepared himself to be a civil engineer. Under
the persuasion of lagrange and Laplace, he decided to give up civil engineering
in favor of pure science and accepted a teaching post |
at the Ecole Ploytech
nique.
Cauchy wrote extensively and profoundly in both pure and applied mathe
matics, and he can probably be ranked next to Euler in volume of output. His
colected works contain,in addition to several books, 789 papers, some of
which are very extensive works, and fill twinty-four large quarto volumes. This
work is of uneven quality; consequently, Cauchy (quite unlike the case of
Gauss) has been criticized for overproduction and over-hasty composition. A
story is told in connection with Cauchy's prodigious productivity. In 1835, the
Academy of Sciences began publishing its Comptes rendus. So rapidly did
Cauchy supply this journal with articles that the Academy became alarmed
over the mounitng printing bill and accordingly passed a rule, still in force
today, hmiting all published papers to a maximum length of four pages. Cauchy
had to seek other outlets for his longer papers, some of which exceeded a
hundred pages.
Cauchy's numerous contributions to advanced mathematics include re
searches in convergence and divergence of infinite series, real and complex
function theory, differential equations, determinants, probability, and mathe
natical physics. His name is net by the student of calculus in the so-called
Cauchy root test and Cauchy ratio test for convergence or divergence of a
series of positive terms, and and in the Cauchy ratio test of two given series. Even in
a first course in comp;ex function theory, one encounters the Canchy inequao
ity, Cauchy's integral formula, Cauchy's integral theorem, and the basic
Cauchy-Riemann differential equations. Whereas during the eighteenth century integration
was generally teated as the inverse of differentiation, Cauchy preferred to
define the definite integral as the limit of the sum of an infinitely increasing set
of vanishingly small parts, much as se do today. The relation between an
integral and an antiderivative was then established by the theorem of mean
value. Cauchy's contributions to determinant theory, starting with a large eighty
four page menoir in 1812, mark him as the most prolific contributor in this field.
It was in his 1812 paper that Cauchy gave the first proof of the important and
useful theorem that if A and B are both ¥ç¡¿¥ç matrices, then AB = A B
Incidentally, it was Cauchy sho, in 1840, introduced the word "characteristic
into matrix theory, by calling the equation A - = 0 the characteristic
equation of matrix A.
Cauchy's work exhibits great attention to rigor, and as such was largely
reaponsible for inspiring other mathematicians to attempt the banishment of
blind formal manipulation and of intuitive proofs from analysis.
Cauchy died suddenly on May 23, 1857, when he was sixty-eingt years old.
He had gone to the country to rest and to cure a bronchial trouble. only to be
smitten by a fatal fever. Just before his death, he was talking with the Arch
bishop of Paris. His last words addressed to the Archbishop, were "Men pass
away, but their deeds abide."
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