The Tale Of Riemann: Many Acclaimed Mathematicians ✓ Solved

The Tale of Riemann Many acclaimed mathematicians and

Many acclaimed mathematicians and scientists, Georg Friedrich Bernhard Riemann and Albert Einstein among many others, have come from humble and trying backgrounds. Riemann provided society with the Riemann Hypothesis, a problem that continues to vex mathematicians over a century and a half later. This paper will explore how Riemann overcame his hard beginnings to become one of the greatest mathematicians of all time.

Riemann was born on September 17, 1826 in Breselenz, a village near Dannenberg in the Kingdom of Hanover. His father, Friedrich Bernhard Riemann, was a Lutheran minister and a veteran of the Napoleonic Wars. As an impoverished family with a menial income, the children often suffered from malnutrition. Riemann also suffered from anxiety and depression. Despite all these hardships, the Riemann family was a close-knit and loving family.

Riemann was homeschooled by his father until he was 14 years old. When his father had saved enough money, Riemann moved to Hanover to live with his grandmother and finally attend formal school. He was very shy and extremely homesick while he was there. After his grandmother died, he attended school closer to home. He was not a good scholar, only doing well in mathematics, which he found interesting. The school director arranged for Riemann to board with a Hebrew teacher named Seffer, under whose direction he improved drastically academically.

In 1846, Riemann was admitted into the University of Göttingen as a student of theology. It was at Göttingen that Riemann attended lectures on linear algebra by Carl Friedrich Gauss and theory of equations lectures by Moritz Stern. Riemann and his father decided it was better for him to pursue a career in mathematics. Riemann received his doctorate in 1851, at age 25, with a dissertation on complex function theory.

Riemann’s work led him to be appointed a corresponding member of the Berlin Academy at the age of 32. He submitted a notable paper, “Uber die Anzahl der Primzahlen unter einer gegebenen Größe,” which had significant implications for mathematics. The Riemann Hypothesis, a fundamental mathematical conjecture, states that the non-trivial zeros of the Riemann Zeta Function all lie on a critical line. This hypothesis has profound implications in number theory.

The Riemann Zeta Function inputs and outputs complex number values. The hypothesis asserts that the real part of any non-trivial zero is one-half. The distribution of prime numbers is believed to be linked to the non-trivial zeros of the zeta function. Many mathematicians have attempted to prove the Riemann Hypothesis, with some approaches suggesting that it may be unprovable under the current foundations of mathematics.

Polya’s theorem suggested that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen Polynomials related to the Riemann Zeta Function. Most recently, Ken Ono of Emory University made progress on the hyperbolicity of Jensen polynomials, with findings suggesting that in many cases, the zeros of the Jensen Polynomials are only real. However, complete proof remains elusive.

Riemann is a fascinating figure whose perceived sadness and withdrawal contrasted sharply with his brilliance in mathematics. His inner genius shone brightly through his remarkable contributions to the field, much like characters in literature who exhibit profound talents despite their grim circumstances. In conclusion, Riemann’s life and work serve as an inspiration for those who persevere through hardships to realize their potential.

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