Gauss delivered his first mathematical proof at the age of 19: The constructability of a regular polygon with 17 sides. Together with his work on number theory, this first new geometrical construction since antiquity belongs to his early work. This period also saw Carl Friedrich developing the “method of least squares”. This provided him with the basis on which he could, amongst other things, participate successfully in a worldwide scientific competition. In 1801, astronomers were universally occupied with attempting to locate the lost minor planet Ceres, by means of computation of its orbit. It was Gauss who succeeded in calculating the orbit correctly and thus it was possible to rediscover the asteroid in the sky. This event at once catapulted the 24-year-old Gauss into international fame.
Gauss also opened up a new era in the science of form and size determination of the earth, geodesy. Up to this point, maps were based on estimates of distance. In 1820, George IV gave Gauss the task of carrying out arc measurement for Hanover. For five years he was travelling almost perpetually in order to cover the whole country with a coarsely meshed triangulation network starting from Göttingen (point of zero being located in the Observatory). His work initiated the new age of classical cartography.
Subsequent to this came a period of work on physical subjects. Together with Wilhelm Weber, Gauss invented the electromagnetic telegraph in 1833 and embarked on significant research concerning terrestrial magnetism. A geomagnetic observatorium a building free of iron was built in the garden of the existing Observatory. Gauss invented a measuring device for small magnetic fields and set up the system of electric and magnetic units that bears his name.
At this stage the Observatory became a centre of international research. Involving 53 geomagnetic observatories throughout the world, on fixed dates measurements were carried out every five minutes for a period of 24 hours according to Göttingen time, in order to examine precisely time-dependant fluctuations of the magnetic field.
In 1851, four years before his death, Gauss established one last set of scientific principles, this time in the field of actuarial mathematics. In his report for the University’s pension fund for widows, he introduced for the first time a computation of pension scheme contributions based on mortality rates and probability calculations.