7 votes
Accepted

Did Riemann invent the Riemann curvature tensor?

A short answer: yes, he did. Riemann's habilitation lecture was aimed at a broad non-mathematical audience, so he did not use formulas in it, trying to explain everything in words. The curvature ...
Alexandre Eremenko's user avatar
6 votes
Accepted

How did Gauss determine the number of primes?

For what it's worth: As Goldshtein writes, “Evidently Gauss considered the tabulation of primes as some sort of pastime and amused himself by compiling extensive tables on how the primes distribute ...
akhmeteli's user avatar
  • 961
6 votes

Origin of Riemann-Stieltjes Integral

The Riemann-Stieljes was introduced by Thomas Stieltjes in his long paper (or book) on continued fractions, Recherches sur les fractions continues, Mém. Sav. étr. 32, Nr. 2, 197 S. (1904). The purpose ...
Alexandre Eremenko's user avatar
5 votes

How much ground was prepared for Riemann so that he could conjecture Riemann hypothesis?

Riemann wrote his paper on the zeta-function in 1859. He was the first person to consider the zeta-function in the complex plane, first for ${\rm Re}(s) > 1$ and then he worked out an analytic ...
KCd's user avatar
  • 5,597
4 votes

Origin of Riemann-Stieltjes Integral

An important use of the Stieltjes integral, after its creation by Stieltjes, was its use by Riesz in $1909$ to describe the continuous dual space of $C([0,1])$, the space of real-valued continuous ...
KCd's user avatar
  • 5,597
2 votes

To what extent were Riemann surfaces a precursor to algebraic geometry?

Hermann Weyl's book on Riemann surfaces was instrumental in the development of the Riemann-Roch theorem and its generalisations. The relevant chapter in Weyl's book is chapter 17: The single-valued ...
Mikhail Katz's user avatar
  • 5,772
2 votes

What is Metric tensor's origin?

The metric tensor was introduced by Riemann in his lecture: 1854 – Über die Hypothesen, welche der Geometrie zugrunde liegen. There are several English translations, and a comprehensive commentary in ...
Alexandre Eremenko's user avatar
1 vote

To what extent were Riemann surfaces a precursor to algebraic geometry?

Algebraic geometry is much older than Riemann surfaces. Algebraic curves (of second degree, over the field of real numbers) where studied in great detail by Apollonius in 2 BC, and algebraic varieties ...
Alexandre Eremenko's user avatar
1 vote

How much ground was prepared for Riemann so that he could conjecture Riemann hypothesis?

As a further data point, you might want to look at André Weil's article "On Eisenstein's Copy of Disquisitiones" (Advanced Studies in Pure Mathematics 17, 1989, pp. 463-469), where he ...
Frunobulax's user avatar

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