C. F. Gauss (1777 - 1855) |
Johann Carl Friedrich Gauss (Gauß) (30. April 1777 - 23. February 1855) was a legendary German
mathematician, astronomer and physicist with a very wide range of contributions. He is considered
to be one of the greatest mathematicians of all time.
Early years
Gauss was born in Braunschweig, Duchy of Brunswick-Lüneburg (now part of
Germany) as the only son of lower-class uneducated
parents. According to legend, his genius became apparent at the age of three, when he corrected,
in his head, an error his father had made on paper while calculating finances.
It is also said
that while in elementary school, his teacher tried to occupy pupils by making them add up the
(whole) numbers from 1 to 100. A few seconds later, to the astonishment of all, the young Gauss
produced the correct answer, having realized that pairwise addition of terms from opposite ends
of the list yielded identical intermediate sums.
Gauss earned a scholarship and in college, he independently rediscovered several important
theorems. His breakthrough occurred in 1796 when he was able to show that any regular polygon,
each of whose odd factors are distinct Fermat primes, can be constructed by ruler and compass
alone, thereby adding to work started by classical Greek mathematicians.
Gauss was so pleased by this result that he requested that a regular 17-gon be inscribed on his
tombstone.
Gauss was the first to prove the fundamental theorem of algebra; in fact, he produced four
entirely different proofs for this theorem over his lifetime, clarifying the concept of complex
number considerably along the way.
Middle years
Gauss also made important contributions to number theory with his 1801 book Disquisitiones
Arithmeticae, which contained a clean presentation of modular arithmetic and the first proof
of the law of quadratic reciprocity.
He had been supported by a stipend from the Duke of Brunswick, but he did not appreciate the
insecurity of this arrangement and also did not believe mathematics to be important enough to
deserve support; he therefore aimed for a position in astronomy, and in 1807 he was appointed
professor of astronomy and director of the astronomical observatory in Göttingen.
In 1809, Gauss published a major work about the motion of celestial bodies. Among other things,
he introduced the gaussian gravitational constant. It also contains an influential treatment of
the method of least squares, a procedure used in all sciences to this day to minimize the impact
of measurement error. He was able to prove the correctness of the method under the assumption of
normally distributed errors. The method had been described earlier by Adrien-Marie Legendre in
1805, but Gauss claimed that he had been using it since 1795.
Gauss discovered the possibility of non-Euclidean geometries but never published it. His friend
Farkos Wolfgang Bolyai had tried in vain for many years to prove the parallel postulate from
Euclid's other axioms of geometry and failed. Bolyai's son, János Bolyai, rediscovered non-Euclidean
geometry in the 1820s. His work was published in 1832.
In 1818, Gauss started a geodesic survey of the state of Hanover, work which later led to the
development of the normal distribution for describing measurement errors and an interest in
differential geometry and his theorema egregrium establishing an important property of the
notion of curvature.
Later years and death
In 1831, a fruitful collaboration with the physics professor Wilhelm Weber developed, leading
to results about magnetism, the discovery of Kirchhoff's laws in electricity and the construction
of a primitive telegraph.
He died in Göttingen, Hanover (now Germany) in 1855 and is interred in the cemetery Albanifriedhof
there.
Personal life
Although Gauss never worked as a professor of mathematics and disliked teaching, several of his
students turned out to be influential mathematicians, among them Richard Dedekind and Bernhard
Riemann.
Gauss was deeply religious and conservative. He supported monarchy and opposed Napoleon whom he
saw as an outgrowth of revolution. Gauss' personal life was overshadowed by the early death of
his beloved first wife, Johanna Osthoff, in 1809, soon followed by the death of one child, Louis.
Gauss plunged into a depression from which he never fully recovered.
He married again, to
Friederica Wilhelmine Waldeck (Minna), but the second marriage does not seem to have been very
happy. When his second wife died in 1831 after long illness, one of his daughters, Therese, took
over the household and cared for Gauss until the end of his life. His mother lived in his house
from 1812 until her death in 1839. He rarely if ever collaborated with other mathematicians and
was considered aloof and austere by many.
Gauss had six children, three by each wife. With Johanna (1780-1809), his children were
Joseph (1806-1873), Wilhelmina (1808-1846) and Louis (1809-1810). Of all of Gauss' children,
Wilhelmina was said to have come closest to his talent, but regrettably, she died young.
With Minna Waldeck, he had three children: Eugene (1811-1896), Wilhelm (1813-1879) and Therese
(1816-1864).
Eugene immigrated to the United States about 1832 after a falling out with his
father, eventually settling in St. Charles, Missouri, where he became a well respected member
of the community. Wilhelm came to settle in Missouri somewhat later, starting as a farmer and
later becoming wealthy in the shoe business in St. Louis. Therese kept house for Gauss until his
death, after which she married.
Banknote displaying Carl Friedrich Gauss
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