Riemann
Full Name: Georg Friedrich Bernhard Riemann
Achievements: Riemann posed one of the greatest mathematical puzzles of all time, the Riemann Hypothesis, which continues to confound mathematicians. His work to extend geometry beyond three dimensions helped lead to Einstein's Theories of Relativity.
Born: September 17, 1826; Breselenz, Germany
Died: July 20, 1866; Selasca, Italy
Field & Discipline: Mathematics; Natural Science
Language: German
Father: Riemann, Friedrich Bernhard Riemann
Mother: Charlotte Ebell
Siblings: Ida; 3 brothers; 3 other sisters
Spouse: Elise Koch
Children: Daughter: Ida
Education: University of Gottingen; University of Berlin
Major Work:
Developed work on geometry that helped lead to Einstein's theory of relativity.
DETAILS:
Riemann was named Friedrich Bernhard after his father, a Lutheran minister, and was first educated at home. Aged 14, he moved eighty miles to school in Hanover. To reduce expenses he boarded there with his grandmother. Shy and homesick, he found it difficult to make friends.
In 1842, his grandmother died and Riemann moved to another school, in Luneburg. In 1846 he entered Gottingen University to study theology, but dropped the subject when he became a student of the great mathematician Carl Friedrich [studied under] Gauss*.
Gauss had studied prime numbers and saw, for example, that 25 of the first 100 counting numbers were prime (divisible only by 1 and itself), but only 168 of the first 1,000. In other words, the primes appeared to thin out as you went higher. So did they eventually stop altogether? Gauss developed a way to calculate approximately how many primes exist and suggested that there would be 664,579 primes in the first ten million numbers (this is just 339 higher than the correct answer).
Although this might appear to be an esoteric issue, prime numbers, the 'atoms' of the mathematical world, lie behind much of the security in modern-day e-commerce and cryptography, and remain a very hot topic today. Riemann found his own, more accurate, method of estimating how many primes there are.
In 1847 he moved to the University of Berlin, where he came under the influence of the mathematician [studied under] Dirichlet* and in 1849 followed him back to Gottingen to begin work on his Ph. D.
Riemann studied work that Gauss had done on a simple but intriguing mathematical formula called the zeta function. During his graphing work with the function Riemann produced waves in his graph. Riemann recognized a link between prime numbers and the waves of the zeta function. The French mathematician [influenced by work of] Fourier*, had conducted groundbreaking work on wave analysis, and Riemann consulted [studied] Poisson's* writings on the Fourier series.
Riemann also attended the lectures of physicist [student of]Wilhelm Weber*. The two men became friends, and Riemann was attracted to Weber's daughter, though she did not reciprocate.
In May, 1859 Dirichlet died. Riemann was made a full professor and elected to the Berlin Academy. French mathematician Gaspard [developed work of] Monge* had already developed ways to map three dimensions to two and his techniques gave birth to a new field known as 'descriptive geometry.' Riemann studied the topic extensively.
He saw that geometry, which involves the study of elements such as lines and angles, could be separated from topology, which concerns itself with the study of the underlying space. An example of how different is topology from geometry lies in the way the internal angles of a triangle (which in 2D geometry add up to 180) on the surface of a balloon (an example of curved space) can add up to more than 180, depending on how much the balloon is inflated.
Riemann's work was taken up by [influenced] Henri Poincare*, widely considered to be one of the first mathematicians to investigate the field of topology. [influenced] Einstein* discovered Riemann's work in 1912 and used it as part of the foundation of his General Theory of Relativity (which involved the gravitational curvature of space by massive objects such as stars).
In 1860 Riemann worked on the theory of sound waves. These studies eventually led to the discovery of shock waves. The German physicist Ludwig [his work used by] Prandtl* studied shock waves using the schlieren imaging equipment conceived by Ernst [his work related to that of] Mach* to produce the first explanation of the behavior of supersonic nozzle efflux.
In 1862 Riemann married Elise Koch, a friend of his sisters. About a month later, his health, which had never been very robust, began to deteriorate, and he moved to Italy in search of a better climate. In 1863 his only child, Ida, was born in Pisa.
By 1866 he was back in Gottingen until war broke out between Hanover and Prussia. To escape the conflict, Riemann fled to Italy and died the same year, from consumption, in the town of Selasca, on Lake Como.
Extra Connections: He influenced French poet [influenced] Paul Valery*
He taught Norwegian Carl Anton [taught] Bjerknes*
He was influenced by the philosopher Johann Friederich [influenced by] Herbart*
Assessment: A brilliant mathematician who made significant contributions to analysis and geometry, providing a key element of Einstein's General Theory of Relativity.
Oneliner: Bernhard Riemann, great mathematician
Bibliography:
" The Music of the Primes by Marcus du Sautoy.
" Prime Obsession by John Derbyshire.
" Wikipedia, http://www.americanscientist.org/template/BookReviewTypeDetail/assetid/55514;jsessionid=baah_jm3UVAHaT.