Riemann hypothesis and number theory

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Discussion Overview

The discussion revolves around the implications of proving the Riemann Hypothesis on the field of number theory. Participants explore whether such a proof would lead to a collapse or a flourishing of the discipline, considering the dependence of certain theorems on the hypothesis.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • Some participants question whether number theory would collapse or flourish if the Riemann Hypothesis is proved true.
  • Others note that there are theorems that rely on the Riemann Hypothesis being true.
  • A participant speculates that revealing the properties of prime numbers might affect the usefulness of number theory.
  • Another participant argues that number theory would still be useful, although certain assumptions might no longer hold, citing that the Fundamental Theorem of Arithmetic would still be valid.

Areas of Agreement / Disagreement

Participants express differing views on the impact of proving the Riemann Hypothesis on number theory, indicating that multiple competing perspectives remain without a consensus.

l-1j-cho
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Would the field of the number theory collapse or flourish if the Riemann Hypothesis is proved as true?
 
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l-1j-cho said:
Would the field of the number theory collapse or flourish if the Riemann Hypothesis is proved as true?

There are theorems that depend on it being true.
 
Mensanator said:
There are theorems that depend on it being true.

Oh I mean if the property of prime numbers is revealed, would the number theory no longer useful or something?
 
l-1j-cho said:
Oh I mean if the property of prime numbers is revealed, would the number theory no longer useful or something?
Number theory would still be useful, it's just that you might not be able to make certain assumptions. Things like The Fundamental Theorem of Arithmetic would still hold.
 

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