Would Number Theory Collapse if Riemann's Hypothesis is Proven True?

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Discussion Overview

The discussion revolves around the implications of proving the Riemann Hypothesis on the field of number theory, particularly whether such a proof would lead to a collapse of number theory or open new avenues of inquiry.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions whether number theory would collapse if the Riemann Hypothesis is proven true.
  • Another participant expresses confusion about the Riemann Hypothesis but suggests that proving it could allow for predicting the pattern of prime numbers, which are central to number theory.
  • A different viewpoint argues that proving the Riemann Hypothesis would not lead to a collapse but rather generate numerous new questions and areas of exploration in mathematics, similar to historical developments in physics.
  • This participant also notes that if the hypothesis were refuted, it would present significant challenges for mathematicians.

Areas of Agreement / Disagreement

Participants express differing views on the consequences of proving the Riemann Hypothesis, with no consensus on whether it would lead to a collapse of number theory or instead stimulate further inquiry.

Contextual Notes

Some assumptions about the implications of the Riemann Hypothesis and its relationship to prime numbers remain unresolved, and the discussion does not clarify the specific nature of these implications.

l-1j-cho
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If Riemann's Hypothesis is proved as true, would number theory collapse?
 
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No. Why would you think that?
 
well, I have absolutely no idea what Riemann hypothesis is, but apparently, if it is proved as true, then we can predict the pattern of prime numbers, of which number theory mostly consists of prime numbers
 
In science, when you get an answer, you get also several new questions.
At the end of 19th century, physicists thought that Physics was nearly terminated.
All the relevant questions had been yet studied and understood.
It only left some "secondary" aspects that would be quickly dispatched...
These secondary points gave birth to both Quantum and Relativistic Physics..

If Riemann's Hypothesis is confirmed, thousands of more interesting questions will arise.
(And if it is refuted, then mathematicians will have a lot of work to do !)

That's why science is so wonderful...
 

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