Bernhard Riemann: A Short Life in Mathematics

I wrote this piece for school, and I deem it blogworthy. I would like to write upon the history of mathematics, and this is a start on my favourite mathematician Bernhard Riemann.

In the nineteenth century, Germany produced the foremost mathematicians in the world. One of the most famous of these was Bernhard Riemann. He was born on September 17, 1826 in Germany. Riemann would go on to produce the greatest unsolved problem in mathematics (since Fermat’s Last Theorem fell to Andrew Wiles in 1994), the Riemann Hypothesis.
Riemann’s father was a pastor and hoped for his son to continue in his footsteps. So, when Riemann enrolled at the University of Göttingen he set out to study philology and theology. Yet once he attended lecture of the immensely influential Carl Friedrich Gauss, his interest shifted to mathematics. He wanted to switch his major, but feared his father would not support him. Yet he finally did ask him, and while his father was slightly disappointed he embraced his decision. Now Riemann could finally embrace mathematics. He also studied with the famous mathematicians Lejeune Dirichlet, Jakob Steiner and Ferdinand Eisenstein.
In 1854, Riemann developed the field of non-Euclidian geometry known as Riemannian Geometry. This is the field that in differential geometry (essentially geometry using calculus) that basically deals with curved surfaces and differential equations. It also is applicable in hyperbolic geometry, which is the field of geometry where the parallel postulate fails to hold true.
Riemann’s greatest contribution (in the opinion of many including myself) to mathematics was his 1859 paper “On the number of primes less than a given magnitude.”
In this he detailed the holy grail of mathematics, the Riemann Hypothesis:
Hitherto no mathematician has been able to write a proof if, when graphed, there is or a 0 on a real or imaginary axis that crosses the x-axis. The Zeta Function deals with the spacing of the prime integers.
The problem was brought to the forefront of the mathematical community by German mathematician David Hilbert in 1900, along with a list of 23 other problems. At the close of the twentieth century it was still unsolved and another committee of mathematical elite developed seven problems with a million dollar reward for solving them. So far no one has been able to solve anyone, and judging by the Gödel Theorem it is possible that no one will ever solve it. The practical ramifications of this is that if it is solved it may be the end of e-Commerce because people could potentially crack the codes that keep anonymity in fiscal transactions of the world wide web.
Riemann’s life was cut short in 1862 by tuberculosis. He had a wife and child at this time, and he was on his way to Italy. Throughout his mathematical career Riemann remained at Göttingen except for two years spent at the slightly more prestigious University of Berlin from 1847-1849. However, Göttingen will always be remembered for being home to two titans of mathematics: Carl Friedrich Gauss and Bernard Riemann. Riemann’s contributions to mathematics are wide ranging and everlasting, and it is remarkable all he contributed in his short life as a mathematician.