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What made bernhard riemann a great mathematician?

Updated: 8/19/2019
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11y ago

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The almost unparalleled depth and impact of the concepts introduced by Riemann.

His investigations in geometry led to Riemannian geometry.

His investigations in trigonometric series gave us the modern definition of function and a first notion of the integral (Riemannian integral).

His 9-page investigation into number theory founded the field of analytic number theory.

Riemann was so ahead of his time that the "approximate functional equation" that he

devised during the time of publication of his paper on number theory, was only rediscovered 40 years later after that Siegel investigated his notes.

He is known for the Riemann Hypothesis, the biggest currently open problem in mathematics.

He is also known for the development of variational methods and the application of the Dirichlet principle.

An mathematician of such a caliber ... is very rare. I think that Riemann is in the same league as Grothendieck.

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