C F Gauss

                                                            Carl Friedrich Gauss

Carl Friedrich Gauss was a German mathematician who was born on 30 April 1777 in Braunschweig (Germany) as the son of poor working-class parents. His mother was illiterate, but Gauss was one of those child prodigies whose natural aptitude for mathematics soon became apparent.

As a child of three, according to a well-authenticated story, he corrected an error in his father’s payroll calculations. His arithmetical powers so overwhelmed his schoolmasters that, by the time Gauss was 10 years old, they admitted that there was nothing more they could teach the boy. It is said that in his first arithmetical class Gauss astonished his teacher Butner and his assistant Martin Bartels by instantly solving what was intended to be a busy work problem: - Find the sum of all the numbers from 1 to 100. The young Gauss later confessed to having recognized the pattern: 1 + 100 = 2 + 99 =.... 50 + 51 =101. Since, there are 50 pairs of numbers, each of which adds up to 101, the sum of all the numbers must be 50 x 101 = 5050.

In 1788 Gauss began his education at the Gymnasium with the help of Buttner and Bartels, where he learnt German and Latin. Gauss's intellectual abilities attracted the attention of the Duke of Braunschweig, who sent him to the Collegium Carolinum from 1792 to 1795, and to the University of Göttingen from 1795 to 1798.

While in university, Gauss independently rediscovered several important theorems. Gauss went on to a succession of triumphs, each new discovery following on the heels of a previous one. The problem of constructing regular polygons with only “Euclidean Tools”, that is to say with ruler and compass alone, had long been laid aside in the belief that the ancients had exhausted all the possible constructions. In 1796, Gauss showed that the 17- sided regular polygon is so constructable, the first advance in this area since Euclid’s time and the discovery ultimately led Gauss to choose mathematics instead of philology as a career. Gauss was so pleased by this result that he requested that a regular heptadecagon be inscribed on his tombstone. The year 1796 was most productive for both Gauss and number theory.

He discovered a construction of the heptadecagon on 30 March. He further advanced modular arithmetic, greatly simplifying manipulations in number theory. He became the first to prove the quadratic reciprocity law. This remarkably general law allows mathematicians to determine the solvability of any quadratic equation in modular arithmetic. Gauss returned to Brunswick where he received a degree in 1799.

After the Duke of Brunswick had agreed to continue Gauss's stipend, he requested that Gauss submit a doctoral dissertation to the University of Helmsted. Gauss's dissertation was a discussion of the Fundamental Theorem of Algebra, which has been stated first by Girard in 1629 and then proved imperfectly by d’Alembert in 1746 and later by Euler in 1749. The theorem states that an algebraic equation of degree n has exactly n complex roots. This theorem was always a favourite with Gauss, and he gave, in all, four distinct demonstration of it. He published the book Disquisitiones Arithmeticae in the summer of 1801. This book placed Gauss in the front rank of mathematician.

The most extraordinary achievement of Gauss was more in the realm of theoretical astronomy than of mathematics. On the opening night of the 19^th century, January 1,1801, the Italian astronomer Piazzi discovered the first of the so called minor planets Geres. But after the course of this newly found body, visible only by telescope, passed the sun, neither Piazzi nor any other astronomer could locate it again. Piazzi’s observations extended over a period of 41 days, during which the orbit swept out an angle of only 9 degrees of its orbit before it disappeared behind the Sun. Zach published several predictions of its position, including one by Gauss which differed greatly from the others. When Ceres was rediscovered by Zach on 7 December 1801 it was almost exactly where Gauss had predicted. 

Gauss married Johanna Ostoff on 9 October, 1805. Despite having a happy personal life for the first time, his benefactor, the Duke of Brunswick, was killed fighting for the Prussian army. In 1807 Gauss left Brunswick to take up the position of director of the Göttingen observatory.Gauss arrived in Göttingen in late 1807. In 1808 his father died, and a year later Gauss's wife Johanna died after giving birth to their second son. Gauss's work never seemed to suffer from his personal tragedy.

He published his second book, Theoria motus corporum coelestium in sectionibus conicis Solem ambientium, in 1809, a major two volume treatise on the motion of celestial bodies. In the first volume he discussed differential equations, conic sections and elliptic orbits, while in the second volume, the main part of the work, he showed how to estimate and then to refine the estimation of a planet's orbit. Gauss's contributions to theoretical astronomy stopped after 1817, although he went on making observations until the age of 70.

Gauss had been asked in 1818 to carry out a geodesic survey of the state of Hanover to link up with the existing Danish grid. Gauss was pleased to accept and took personal charge of the survey. Because of the survey, Gauss invented the heliotrope which worked by reflecting the Sun's rays using a design of mirrors and a small telescope. The survey of Hanover fueled Gauss's interest in differential geometry, a field of mathematics dealing with curves and surfaces.

Among other things he came up with the notion of Gaussian curvature. Gauss also claimed to have discovered the possibility of non-Euclidean geometries but never published it. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.

In 1831 Gauss developed a fruitful collaboration with the physics professor Wilhelm Weber, leading to new knowledge in magnetism and the discovery of Kirchhoff's circuit laws in electricity. His health deteriorated slowly, and Gauss died in his sleep early in the morning of 23 February, 1855.