Skip to main content

The National MagLab is funded by the National Science Foundation and the State of Florida.

Carl Friedrich Gauss

Although he is best known as one of the greatest mathematicians of all time, Carl Friedrich Gauss was also a pioneer in the study of magnetism and electricity.

Carl Friedrich Gauss

For an extensive survey of terrestrial magnetism, he invented an early type of magnetometer, a device that measures the direction and strength of a magnetic field. Gauss also developed a consistent system of magnetic units, and with Wilhelm Weber built one of the first electromagnetic telegraphs. Gauss’ laws describing magnetic and electric fluxes served as part of the foundation on which James Clerk Maxwell developed his famous equations and electromagnetic theory.

Johann Friedrich Carl Gauss was born in 1777 to a poor family in Brunswick, Germany. The boy was found to be a mathematical prodigy. Gauss’ amazing calculating abilities aroused the interest of his teachers, and the child received a solid education despite lack of money. His teachers gave him advanced textbooks and introduced him to the work of prominent mathematicians of the day. Gauss’ skills in that field as well as his facility for languages eventually gained him the patronage of the Duke of Brunswick. Those funds allowed Gauss to study at Brunswick Collegium Carolinum, then at the University of Göttingen in 1795. There he continued his education in mathematics until 1798.

While still a student at Göttingen, Gauss made several important contributions to mathematics. In 1796, he demonstrated that the heptadecagon (a 17-sided polygon) is geometrically constructible. He considered his discovery, which had eluded scientists and mathematicians for thousands of years, of such significance that he requested a heptadecagon be inscribed on his headstone when he died. The task seemed too daunting to stonemasons at the time, however. Also in 1796, he advanced number theory through his development of modular arithmetic and the formulation of the law of quadratic reciprocity, demonstrated a theorem of prime numbers, and found that all integers can be represented as a sum of no more than three triangular numbers. Many other mathematical breakthroughs soon followed, although when Gauss left Göttingen, he had not yet received a degree. At the request of his patron, Gauss submitted thesis work for a doctorate to the University of Helmstedt, which granted him a degree for his initial proof of the fundamental theorem of algebra (he would improve on this proof throughout his life).

With his doctorate in hand, Gauss was assured of the continued patronage of the duke, allowing him to pursue his mathematical and scientific interests with little concern for money. In 1801, he published two notable works. One was Disquisitiones arithmeticae, a treatise he had begun several years before and which was a comprehensive treatment of number theory. In it Gauss recounted the work of his mathematical predecessors, but also corrected all errors and shortcomings he found and included his own new contributions to the subject. The treatise served as a foundational text in number theory throughout most of the 19th century.

Gauss’ second major publication, in 1801, reflected his developing interest in astronomy. In 1800, the asteroid Ceres had been discovered by Giuseppe Piazzi, an astronomer from Italy. The discovery sparked the interest of the scientific community, but Ceres moved behind the sun before anyone was able to calculate its orbit very accurately. As a result, no one knew where to look for the asteroid when it reemerged, though numerous scientists tried. Gauss was the first to succeed in the task, which required his use of the least squares method of approximation and an improved estimate of orbit shape. When Gauss published his finding, he gained wide recognition and became sought after for his skills in astronomy. He turned down several offers to direct foreign observatories due to his loyalty to his German patron. In 1807, Gauss did accept a post at the observatory in Göttingen, which he vastly improved over the years. His research there led to the writing of a number of other works relating to astronomy.

Gauss often directed his attention to projects he considered important for society, in addition to those that simply aroused his scientific interest. One such project was a thorough geodesic survey of the city of Hanover. The complex and tedious endeavor began in 1818 and was not completed until 1832. The difficulties it presented spurred Gauss to develop various surveying improvements. Most notably, he invented the heliotrope (a device that used a mirror to magnify the rays of the sun in order to send signals to distant observers), advanced the understanding of curved surfaces, and suggested improved cartography methods.

Toward the end of his surveying project, Gauss became acquainted with Wilhelm Weber, a physics professor at the University of Göttingen. The two scientists shared an interest in electricity and magnetism and quickly developed a friendship. Their association led to a number of advances in these fields. Soon after they met, Gauss and Weber began work relating to terrestrial magnetism, and later discovered Kirchhoff's laws of electrical circuits. In order to speed communication with one another, Gauss and Weber also constructed a telegraph system that linked Weber’s laboratory to the observatory nearly a mile away.

Both Gauss and Weber recognized that accurate measurements were critical to obtaining the consistent results necessary to develop and verify scientific laws. As a result, they developed new systems of units for electricity and magnetism. In the early 1830s, Gauss defined a system of magnetic units based on length, mass and time. Weber defined a number of electrical units several years later. These systems served as the basis of the first attempt at terminology and definition standardization carried out by the British Association’s Committee on Electrical Standards in the 1860s. Eventually gauss was adopted as the term used in the cgs (centimeter-gram-second) system of units to describe a unit of magnetic flux density or magnetic induction. Both men also developed more sensitive measuring instruments. In 1833, Gauss published his description of a device that he called a magnometer , more commonly known today as a magnetometer. Weber later developed the electrodynamometer, which used the interacting magnetic fields of two coils to measure electric current and voltage.

After Weber was dismissed from his position in 1837, Gauss’ research began to taper off. He did continue to correspond with other scientists for many years, however, often pointing out flaws in their work or intimating that he had made the same discovery earlier. A perfectionist at heart, Gauss’ hesitation to publish anything that was not above reproach prevented him from making many of his findings publicly known. Many of his views and calculations were not discovered until his notes and other unpublished writings were perused after his death.

In his personal life, Gauss faced problems less easily solved than his mathematical challenges. He outlived two wives and two of his six children, and was reportedly afflicted with depression at times. After the death of his second wife in 1832, his daughter by her took over the household duties. She lived with her father and looked after him until he passed away on February 23, 1855.