Johann Friedrich Carl Gauss, regarded as one of the greatest mathematicians of all time, was born on 30 April 1777 in Brunswick. A German mathematician; he worked in number theory, algebra, statistics, geodesy, planetology, function theory, and potential theory.

Childhood and Youth

Gauss was the only child of poor parents. He was born on 30 April 1777 in Brunswick, now part of Germany, to a laborer’s family. He impressed his elementary school teacher in a short time. The teacher convinced Gauss’s father that his son needed to be allowed to pursue an education to enter university. In middle school, after 1788, he quickly demonstrated exceptional talent in ancient languages and mathematics.

At the age of 14, Gauss was presented to the Duke of Brunswick, who allowed him to demonstrate his computational abilities. The duke was so impressed that he generously supported Gauss until his death in 1806.

Gauss designed nearly all of his fundamental mathematical discoveries between the ages of 14 and 17. In 1791 he began making entirely new and innovative contributions to mathematics. Between 1793 and 1794 he conducted intensive research in number theory, particularly on prime numbers. He was rare among mathematicians for his computational genius and retained throughout most of his life the ability to perform detailed calculations mentally.

Education, Career and Achievements

• Gauss studied at the University of Göttingen from 1795 to 1798. He soon decided to write a book on number theory. The book was published in 1801 under the title Disquisitiones Arithmeticae. This classic work is generally regarded as Gauss’s greatest achievement.
• On 30 March 1796, Gauss discovered that a regular 17-gon could be constructed inside a circle using only a compass and ruler; this was the first such discovery in Euclidean construction in over 2,000 years.
• In April 1799 his interest turned to astronomy, a field that occupied his attention for the rest of his life. He developed a rapid method to determine the orbital elements of a planet from only three observations. Another of Gauss’s scientific achievements was the rediscovery of the dwarf planet Ceres. The dwarf planet Ceres was originally discovered in 1800 by the Italian astronomer Piazzi but disappeared behind the sun before sufficient observations could be made. In response, Gauss worked on calculating orbits using the method of least squares.
• In 1807 he was appointed director of the Göttingen Observatory and professor of mathematics, a position he held for the rest of his life.
• After 1831 Gauss collaborated with Wilhelm Weber on research into electricity and magnetism. In 1833 they designed an electromagnetic telegraph. They encouraged others across many countries to conduct magnetic observations and in 1836 founded the Magnetic Union.
• He was well versed in Greek and Roman classics, studied Sanskrit, and read European literature extensively. In later years he received honorary awards from scientific institutions and governments around the world.

Death

Gauss died on 23 February 1855 in Göttingen, where he had lived for many years, at the age of 78. He was buried in the Albanifriedhof cemetery in that city. At his funeral, his son-in-law Heinrich Ewald and his friend and biographer Wolfgang Sartorius von Waltershausen delivered eulogies. His brain was preserved for study and is still kept in formalin at the medical faculty of the University of Göttingen.

Personal Life

Gauss was a perfectionist and a workaholic. According to one anecdote, when he was told his wife was dying while he was working on a problem, he replied, “Let her wait a moment, I am almost finished.”

After his death, his diaries were examined and revealed that he had made many important mathematical discoveries long before his contemporaries published them, but had chosen not to publish them. According to historian Eric Temple Bell, if Gauss had published all the mathematical ideas he recorded in his diaries during his lifetime, mathematics would have advanced by 50 years. Gauss never explained how he arrived at his proofs. Once he found a proof, it seemed to him as if it had come by divine revelation; he gave no clues about how he reached the conclusion.

Gauss did not believe in a personalized deity. For this reason he can be described as a deist. He was also a monarchist and disapproved of the 1848 revolutions that swept across Germany.

Gauss married Johanna Osthoff in 1805. From this marriage he had a son, Joseph (1806–1873), and a daughter, Wilhelmine (1808–1840). In 1809, Johanna died during the birth of their third child, whom they named Louis. Louis died less than a year after his mother. Gauss never fully recovered from the depression caused by these losses. Shortly after Louis’s death, in 1810, Gauss married Minna Waldeck, a friend of his first wife. This marriage produced three children: Eugen (1811–1896), Wilhelm (1813–1879), and Therese (1816–1864). After Minna died of illness in 1831, his daughter Therese cared for him until his death. Eugen and Wilhelm settled in the state of Missouri in the United States.

Gauss had a poor relationship with his father, who did not want him to study mathematics or science and wished for him to become a craftsman like himself. Gauss received the support he never got from his father during his education from his mother. Gauss also had difficulty getting along with his sons and encouraged Eugen and later Wilhelm to emigrate to the United States.

Legacy and Influence

Gauss’s recognition as a truly exceptional genius stems largely from two major publications in 1801. The most important was his publication of the first systematic treatise on algebraic number theory: Disquisitiones Arithmeticae. This book presents the first systematic treatment of modular arithmetic, a comprehensive analysis of solutions to two-variable quadratic polynomials over integers, and concludes with the theory of factorization. His choice of subject and natural generalizations set the agenda for number theory for much of the 19th century, and Gauss’s continued interest in the subject stimulated numerous investigations, especially at German universities. Gauss claimed to have discovered non-Euclidean geometries but withheld his ideas due to fear of criticism.

A visual illustrating Gauss’s Theorem.

Awards Received: Copley Medal (1838)

Inventions: Heliotrope, magnetometer.

Major Work: Disquisitiones Arithmeticae

Areas of Research: Ceres, asteroid, bell curve, complex number, computation, congruence, electromagnetism, elliptic function, fundamental theorem of algebra, hypergeometric series, orbit, polygon, quadratic reciprocity law, compass and straightedge construction, method of least small squares.