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Jacobi was born of Jewish parents in Potsdam in 1804 and was educated at
the University of Berlin, where he obtained his doctorate in 1825. Two years
later, he was appointed Extraordinary Professor of Mathematics at Konigsberg,
and two years after that was promoted to Ordinary Professor of Mathematics
there. In 1842, under a pension from the Prussian government, he relinquished
his chair at Konigsberg
and meved to Berlin, where he resided until his
early death in 1851.
Rarely is an outstanding researcher in mathematics also an outstanding
teacher of mathematics.
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Jachobi was one of the exceptions and was unquestionably
the gratest university mathematics teacher of his generation, stimulating
and lifluencing an unprecedented number of able students. His most celebrated
researches in mathematics are those concerning elliptic functions. He and Abelindependently
and simultaneously established the theory of these functions.
and Jacobi introduced what is essentially our present-day notation for them.
Jacobi, next Cauchy, was perhaps the most prolific contributor to determinant
theory. It was with him that the word determinant received final acceptance.
He early used the functional determinant that Sylvester later called the
Jacobian, and that is encountered by all students of function theory. He also
contributed to the theory of numbers, the theory of both ordinary and partial
differential equations the calculus of variations, the three-boby problem, and
other dynamical problems.
Most students feel that before doing research they should first matster what
has already been accomplished. To offset this notion, and to stimulate early
interest in independent work, Jacobi would deliver the parable: "Your father
would never hace married and you would not be born, if he had insisted on
knowing all the girls in the world before marring one, " IN defending pure
research against applied research, he remarked, "The ral end of science is the
honor of the human mund. "God ever arithmetizes,"
Jacobi was always generous in his statements about his great contemporaries
in the field of mathematics. Of one of Abel's masterpieces he said,"It is above my praise as it is above my own work."
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Jacobi was always generous in his staterments about his great contemporararies
in the field of mathematics. Of one of Abel's masterpieces he said,"It is above my praise as it is above my own work."
Dirichlet was born at Duren in 1805, and successively held professorships
at Breslau and Berlin.
At Gauss' death in 1855 he was appointed Gauss'successor at Gottingen, a fitting honor for so talented a
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mathematician who was a
former student of Gauss and a lifelong admirer of his mentor. While at Gottingen,
he had hoped to finish Gauss' incompiete works, but his early death in
1859 prevented this.
Fluent in both German and French, Dirichlet served admirably as a liaison
between the mathematics and the mathematicans of the two antionalities.
Perhaps his most celebrated mathematical accomplishment was his penetrating
analysis of the convergence of Fourier series, an undertaking that led him to
generalize the function concept (see Section 15-3). He did much to facilitate
the comprehension of some of Gauss' more abstruse methods, and he himself
contributed notably to number theory; his beautiful Vorlesungen uber Zahlentheorie
still constitutes one of the most lucid introductions to Gauss' number
theory inbestigations. We are indebted to him for applying infiniesimal methods
in this branch of mathematics. Dirichlet was a close friend, expositor,
and admirer, of Jacobi His name is met by college mathematics majors in
connection with Dirichlet's series, the Dirichlet function, and the Dirichlet principe.
A touching stroy is told of Dirichlet and his great reacher, Gauss. On July
16. 1849, exactly fifty years after the awarding to Gauss of his doctorate, Gauss
enjoyed the celebration at Gottingen of his golden jubilee. As part of the
"show." Gauss, at one point of the proceedings, was to Hght his pipe with a
piece of the original manuscript of his Disquisitiones arlithmeticae. Diriohlet,
who was present at the celebration, was appalled at what seemed to him a
sacrilege. At the last moment, he boldly rescued the paper from Gauss' hands
and treasured the memento the rest of his life: it was found by his editors
among his papers after he died.
Dirichlet has been described as possessing a noble, sincere, human and
modest disposition, but unlike Jacobi, he seemed unable to communicate with
young minds. When a schoolmate expressed envy because Dirichlet's son
could always receive help from his gifted fater the son gave this lamentable
but memorable reply: "Oh! My father doesn's konw the little things anymore."
Dirichlet's waggish nephew, Sebastian Hensel wrote in his memoirs that the
mathematics instruction he received in his sixth and seventh years at the gymnasium
from his uncle was the most dreadful experience of his life.
Dirichlet was very lax in maintaining family correspondence. When his
first child arrived, he failed to write of the ecent to his father-in-law, who was
living in London at the time. The father-in-law. When he finally found out,
commented that he thought Dirichlet "should have at least been able to write
2 + 1 = 3." This witty father-in-row was none other than Abraham Mendelssohn,
a son of the philosopher Moses Mendelssohn and father of the composer
Felix Mendelssohn.
Dirichlet's brain, and also that of Gauss, are preserved in the department
of physiology at Gottingen University.
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