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An Image of en:Georg Friedrich Bernhard Riemann taken in 1863,Public Domain,

Top 10 Astonishing Facts about Bernhard Riemann

 Bernhard Riemann was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on the Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in the natural, geometric treatment of complex analysis. His 1859 paper on the prime-counting function, containing the original statement of the Riemann hypothesis, is regarded as a foundational paper of analytic number theory. Through his pioneering contributions to differential geometry, Riemann laid the foundations of the mathematics of general relativity. He is considered by many to be one of the greatest mathematicians of all time. He was born on September 17 Breselenz, Hanover [Germany] and died  on July 20, 1866, Selasca, Italy.

Here are the top 10 astonishing facts about Bernhard Riemann that you should consider knowing;

1. He is considered by many to be one of the greatest mathematicians of all time

Riemann exhibited exceptional mathematical talent, such as calculation abilities, from an early age but suffered from timidity and a fear of speaking in public.

He was considered the greatest mathematician because he made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on the Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in the natural, geometric treatment of complex analysis.

2. He made some famous contributions to modern analytic number theory

His lone published work on the Riemann zeta function formed the basis for understanding prime number distribution, and the Riemann hypothesis investigates the properties of this same zeta function and that now bears his name, establishing its importance for understanding the distribution of prime numbers. The Riemann hypothesis was one of a series of conjectures he made about the function’s properties.

3. He discovered the Riemann integral in his habilitation

An Image of en:Georg Friedrich Bernhard Riemann taken in 1863,Public Domain,

In the field of real analysis, he discovered the Riemann integral in his habilitation. Among other things, he showed that every piecewise continuous function is integrable. Similarly, the Stieltjes integral goes back to the Göttinger mathematician, and so they are named together the Riemann–Stieltjes integral.

He also made important advancements in real analysis and established both Riemann integral and Riemann sums, along with the later Riemann-Liouville differ integral.

4. His father was a Lutheran pastor

Riemann was born in Germany to a poor Lutheran pastor; his mother died before he grew up. While he showed almost prodigious talent in math and calculation, his shyness kept him from speaking openly about his findings. He was a dedicated Christian, the son of a Protestant minister, and he saw his life as a mathematician as another way to serve God. During his life, he held close to his Christian faith and considered it to be the most important aspect of his life. At the time of his death, he was reciting the Lord’s Prayer with his wife and died before they finished saying the prayer.

5. He founded Riemannian geometry

The first published works on non-Euclidean geometries appeared about 1830. Such publications were unknown to the German mathematician Bernhard Riemann. In 1866 Riemann found the correct way to extend into n dimensions the differential geometry of surfaces, which Gauss himself proved in his theorem premium. The fundamental objects are called the Riemannian metric and the Riemann curvature tensor.

6. His father fought in the Napoleonic wars

An Image of en:Georg Friedrich Bernhard Riemann taken in 1863,Public Domain,

  The Napoleonic wars were a series of major global conflicts pitting the French Empire and its allies, led by Napoleon I, against a fluctuating array of European states formed into various coalitions. It produced a period of French domination over most of continental Europe. The wars stemmed from the unresolved disputes associated with the French Revolution and the French Revolutionary Wars consisting of the War of the First Coalition (1792–1797) and the War of the Second Coalition (1798–1802). The Napoleonic wars are often described as five conflicts, each termed after the coalition that fought Napoleon: the Third Coalition (1803–1806), the Fourth (1806–07), the Fifth (1809), the Sixth (1813–14), and the Seventh (1815) plus the Peninsular War (1807–1814) and the French invasion of Russia (1812).

7. He was honored by the Royal Society of London and the French Academy of Sciences

On a visit to Berlin Borchardt, Kummer, Kronecker, and Weierstraß, all very famous mathematicians showered him with praise. He went to Â鶹APP where he met Hermite who greatly admired him.

8. Riemann was a pure genius

An Image of en:Georg Friedrich Bernhard Riemann taken in 1863,Public Domain,

His phenomenal contributions to the mathematical world are proof of his creativity and depth of knowledge. Despite his ailing health, he was one of the greatest mathematicians of all time. He had an extraordinary command over complex analysis which he interconnected with topology and number theory. He was therefore considered to be a pure genius.

9. He was a lecturer

Riemann became a lecturer on the recommendation of his teacher Gauss at the University of Göttingen. Seeing the brilliance of Reimann, efforts were made to promote him to a position of an extraordinary Professor. This, however, could not be done and he was paid like any other professor at the University of Göttingen. He was later made the head of the Mathematics Department.

10. He died of Tuberculosis

the Riemann’s tombstone in Biganzolo Cemetery, Italy (where he was buried in 1866), By g.rondena – personal photo,

It is said that Riemann caught a cold which worsened to become tuberculosis. Although he made several efforts to get better all in vain. He spent the final days of his life in Italy in the village of Selasca with his wife and daughter. Riemann died on 20th July 1866.