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Bernhard Riemann and the Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics

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Published in Prime Obsession: Bernhard Riemann And The Greatest Unsolved Problem In Mathematics

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Bernhard Riemann was a brilliant German mathematician who lived in the 19th century. He made significant contributions to number theory, complex analysis, and differential geometry. One of his most famous conjectures, known as the Riemann Hypothesis, is considered to be one of the greatest unsolved problems in mathematics.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

by John Derbyshire

4.7 out of 5

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Riemann's Life and Work

Bernhard Riemann was born on September 17, 1826, in Breselenz, Hanover, Germany. He showed an early aptitude for mathematics, and in 1846 he entered the University of Göttingen. There he studied under the famous mathematician Carl Friedrich Gauss. Gauss quickly recognized Riemann's talent, and he became one of Gauss's favorite students.

In 1851, Riemann submitted his doctoral dissertation on the theory of functions of a complex variable. This dissertation contained many new and important ideas, and it established Riemann as one of the leading mathematicians of his time. After graduating from Göttingen, Riemann taught at the universities of Göttingen, Berlin, and Freiburg. He died on July 20, 1866, at the age of 39.

Riemann made significant contributions to a wide range of mathematical fields. In number theory, he developed the theory of Dirichlet series and the Riemann zeta function. In complex analysis, he introduced the concept of the Riemann surface, which is a fundamental tool for studying the behavior of complex functions. In differential geometry, he developed the theory of Riemannian manifolds, which are now used in many areas of mathematics and physics.

The Riemann Hypothesis

The Riemann Hypothesis is one of the most famous unsolved problems in mathematics. It was first proposed by Bernhard Riemann in 1859, in a paper on the distribution of prime numbers. The hypothesis states that the Riemann zeta function has its zeros only at the negative even integers and at complex numbers with real part 1/2.

The Riemann Hypothesis has been studied extensively by mathematicians over the past 150 years, but it has not yet been proven or disproven. It is considered to be one of the most important unsolved problems in mathematics, and its solution would have major implications for number theory and other areas of mathematics.

The Legacy of Bernhard Riemann

Bernhard Riemann was one of the most brilliant mathematicians of the 19th century. His work had a profound impact on many areas of mathematics, and he is considered to be one of the founders of modern mathematics. The Riemann Hypothesis is just one of the many unsolved problems that Riemann left behind, and it is a testament to his genius that this problem continues to challenge mathematicians to this day.

Bernhard Riemann was a brilliant mathematician who made significant contributions to number theory, complex analysis, and differential geometry. The Riemann Hypothesis is one of his most famous conjectures, and it is considered to be one of the greatest unsolved problems in mathematics. Riemann's work continues to inspire mathematicians to this day, and his legacy as one of the greatest mathematicians of all time is secure.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

by John Derbyshire

4.7 out of 5