Johann Carl Friedrich Gauss

**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 greatest mathematicians of all time.

## Biography

### 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: 1+100=101, 2+99=101, 3+98=101, etc., for a total sum of 50 × 101 = 5050. (see: summation)

The Duke of Brunswick awarded Gauss a scholarship to the Collegium Carolinum, which he attended from 1792 to 1795, and from there went on to the University of Göttingen from 1795 to 1798. While 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 his 1799 dissertation; 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. In that same year, Italian astronomer Giuseppe Piazzi discovered the planetoid Ceres, but could only watch it for a few days. Gauss predicted correctly the position at which it could be found again, and it was rediscovered by Franz Xaver von Zach on December 31, 1801 in Gotha, and one day later by Heinrich Olbers in Bremen. Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have found Ceres again." Though Gauss had up to this point been supported by the stipend from the Duke, he doubted the security of this arrangement, and also did not believe pure mathematics to be important enough to deserve support. Thus, following this path, he sought a position in astronomy, and in 1807 was appointed professor of astronomy and director of the astronomical observatory in Göttingen, which he held for the remainder of his life.

The discovery of Ceres and then of the planetoid Pallas by Olbers in 1802 led Gauss to his work on a theory of the motion of planetoids disturbed by large planets, published in 1809 under the name *Theoria motus corporum coelestium in sectionibus conicis solem ambientum* (theory of motion of the celestial bodies moving in conic sections around the sun). Among its contents were the introduction of the gaussian gravitational constant, and 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 also stated that he had discovered the possibility of non-Euclidean geometries before everybody else but that he never published it. His friend Farkos Wolfgang Bolyai (with whom Gauss had sworn "brotherhood and the banner of truth" as a student) 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, discovered non-Euclidean geometry in 1829; his work was published in 1832. After seeing it, Gauss wrote to Farkas Bolyai: *"To praise it would amount to praising myself. For the entire content of the work ... coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years ."* This unproved statement (that nonetheless nowadays is generally taken at face value) understandably put a strain on his relationship with János Bolyai (who thought that Gauss was "stealing" his idea).

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, death, and afterwards

In 1831, a fruitful collaboration with the physics professor Wilhelm Weber developed, leading to results about magnetism (including finding a representation for the unit of magnetism in terms of mass, length and time) and the discovery of Kirchhoff's laws in electricity. Gauss and Weber constructed the first electromagnetic telegraph in 1833, which connected the observatory with the institute for physics in Göttingen. Gauss ordered a magnetic observatory to be built in the garden of the observatory and with Weber founded the *magnetischer Verein* ("magnetic club"), which supported measurements of earth's magnetic field in many regions of the world.

He died in Göttingen, Hanover (now Germany) in 1855 and is interred in the cemetery *Albanifriedhof* there. His brain has been well-preserved to date.

From 1989 until the end of 2001, his portrait and a normal distribution curve were featured on the German ten-mark banknote.

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.

### Personal life

Although Gauss never worked as a professor of mathematics and disliked teaching (it is said that he only attended a single scientific conference, which was in Berlin in 1828), 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, a friend of Johanna's whom he married after her death, 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.

Gauss is said to have claimed, "There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein".

## 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)

## References and external links

### Obituaries