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Arthur Cayley was born in 1821 at Richmend, in surrey, and was educated
at Trinity College, Cambridge, graduating in 1842 as senior wrangler in the
mathematical tripos and in the same year placing first in the even more difficult
test for the Smith's prize. For a period of several years, he studied and practiced
law, alwats being careful not to let legal practice prevent him from
working on mathematics. hile a student of the bar, he went to Dublin and
attended
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Hamilton's lecture on quaternions. nbsp; When the Sadlerian professorship
was established at Ca,bridge in 1863, Cayley was offered the chair,
which
he accepted, thrs giving up a lucrative future
in the legal profession for the
modest provision of an academic life.
But then he could devote all of his time to
mathematics.
Cayley ranks as the third most prolific writer of mathematics in the history
of the subject, being surpassed only by Euler and Cauchy. He began prblishing
while still an undergraduate student at Cambridge, put out berween 200 and 300
papers during his years of legal practice, and continued his prolific publication
the rest of his long life. Perhaps hos most inportant work was his
creation and devlopment of invariant theory.
Cayley's mathematical style reflects his legal training, for his papers are
severe, direct, methodical, and clear. He pessessed a phenomenal memory and
seemed never to forget anything he had once seen or read. He also possessed a
singularly serene, even, ans gentle temperament. He has been called "the
mathematicians' mathematician."
Cayley developed an unusual avidity for novel reading. He read novels
while traveling, while waiting for meetings to start, and at any ldd mdments
that presented themselves. During his life, he read thousands of novels, not
only in English, but also in Greek, French, German, and Italian. He took great
delight in painting, especially in water colors, and he exhibited a marked talent
as a water colorist. He was also an ardent student of botany and nature in
general.
Cayley was, in the true British tradition, an amateur mountain climber,
and he made frequent trips to the Continent for long walks and mountain
scaling. A story is told that he claimed the reason he undertook mountain
climbing was that, although he found the ascent arduous and tiring, the grand
feeling of exhilaration he attained when he conquered the peak was like that he
experienced when he solved a difficult mathematics propblem or completed an
intricate mathematical theory, and it was easier for him to attain the desired
feeling by climbing the mountain.
Cayley died in 1895. Writing in the Comptes rendus shortly after, Charles
Hermite said: "The mathematical talent of Cayley was characterized by clearness
and extreme elegance of analytical form; it was reinforced by an incomparable
capacity for work which has carsed the distinguished scholar to be
compared with Cauchy."
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James Joseph Sylvester was born in London in 1814 as the youngest of
several children. The surname of the family was originally Joseph, but the
eldest son migtated to America where, for some reason not now known, he
assumed the new surname Sylvester, which was then adopted by the rest of the
family. The American brother was an actuary, and suggested to the Directors
of the Lotteries Contractors of the United States that
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they submit a difficult
problem in arrangements that was bothering them to his younger brother
James, then only sixteen years old. James'colplete and satisfying solution of
the problem carsed the Directors to award the young mathematician a prize of
$500.
In 1831, James entered St. John's College, Cambrige, and six years later
emerged as second wrangler. From 1838 to 1840., he served as professor of
natrual philosophy at the University of London, and then, in 1841, accepted a
professorwhip in mathematics at the University of Virginia in America, a position
fromwhich he resigned after only a few minths because of a quarrel he got
into with two of his students. Returning to England, he worked as an actuary
and was called to the bar in 1850. It was in 1846 that he became associated with
Arthur Cayley.
From 1855 to 1870, Styvester was a professor of mathematics at the Royal
Military Academy at Woolwich. In 1876 he returned to America, as a professor
of mathematics at the Johms Hopkins University in Baltimore, and there spent
seven very happy and highly productive years, becomingthe founding edifor of
the American Journal of Mathematics in 1878. During his tenure at Johns
Hopkins, he invited Cayley to the university for a series of lectures on Abelian
functions; Sylvester himself attended the lectures. In 1884, Sylvester accepted
the Savilian chair in geometry at Oxford University. He died in London in
1897, when he was eighty-three years old.
Sylvester's earliest mathematical papers were on Fresnel's optical theory
and Sturm'atheorem. Then, stimulated by Cayley, he began making important
contributions to modern algebra.
He contributed extensively to mathenatical terminology,
coining so many new names that he has become known as "the Adam of matheamtics."
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Much of the work of Cayley and Sylvester was continued and expanded by
the talented French mathematician Charles Hermite, who made outstanding
contrine in both algebra and analysis. hermite was born at Dieuze in
Lorraine in 1822, and after a fitful education, fitst at the Louis-le-Grand lycee
and then briefly at the Ecole Polytechnique, secured, in 1848, the position of
admission's examoner and quiz master at the Ecole Polytechnique. He later
served as a professor
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at the Ecole Polytechnique and the Sorbinne, remaining
at the latter institution until his retirement in 1897.
He died in Paris in 1901.
The two fundamental mathematical results due to Hermite that are of most
popular interest are his solutin in 1858 of the general quintic equation by
means of elliptic functions, and his proof in 1873 of the transcendence of the
coefficients of the equation by means of Fuchdian frnctions, and the method he
empleyed to prove that e is transcendental was employed by Lindemann in
1882 to proce that ¥ð also is transcendental.
Hermite was born with a deformity of his right leg and was lame all his life,
requiring a cane to get about. One benefit of this infirmity was that it successfully
barred Hermite from any kind of mikitary service. One disadvantage was
that after one year at the Ecole polytechnique, he was dropped fron\m further
study because the authorities claimed that his lame leg rendered him unfit for
any of the positions open to srccessful students of the school. Despite his
lameness and early difficulties in securing a suitable position, Hermite uniformly
maintained the sweetest if dispoditions, causing him to be loved by all
who knew him. A number of mathematicians have exhivited great generosity to
younger men stuggling for recognition; Hermite is regarded as unquestionably
folowing a severe illness, he was converted by Caychy fron a tolerant agnostic
to a Roman Catholic.
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