|
Johann Carl Friedrich Gauss (Gauß) (April 30, 1777 - February 23, 1855) was a legendary German mathematician, astronomer and physicist with a very wide range of contributions; he is considered to be one of the leading mathematicians
of all time. (His name rhymes with "house", and is sometimes spelled Gauß in German.)
Biography
Early years
Gauss was born in Braunschweig, Duchy of Brunswick-Lüneburg (now part of Germany) as only son of lower-class uneducated parents. According to legend, while in elementary school, his teacher tried to occupy pupils by making them add
up the (whole) numbers from 1 to 100. Shortly thereafter, 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:
1+100=101, 2+99=101, 3+98=101, etc., for a total sum of 50 × 101 = 5050. (see: summation)
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;
see Gauss-Markov theorem; see also Gaussian. 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. Later, Gauss tried to determine whether the physical world is in fact Euclidean by
measuring out huge triangles.
In 1818, Gauss started a geodesic survey of the state of Hanover, work which later lead
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, death, and afterwards
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.
From 1989 until the end of 2001, his portrait and
a normal distribution curve was featured on the German ten-mark banknote.
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 Johnanna (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 emigrated 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.
G. Waldo Dunnington was a life-long student of Gauss. He
wrote many articles, and a biography: Carl Frederick Gauss: Titan of Science. This book was re-issued in 2003, after
having been out of print for almost 50 years.
See also
Further reading
- Simmons, J, The giant book of scientists -- The 100 greatest minds of all time, Sydney: The Book Company,
(1996)
- Dunnington, G. Waldo, Carl Friedrich Gauss: Titan of Science, The Mathematical Association of America; (June
2003)
External links
|