Riemann hypothesis and number theory

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SUMMARY

The discussion centers on the implications of proving the Riemann Hypothesis for the field of number theory. It is established that if the Riemann Hypothesis is proven true, number theory will not collapse but rather continue to be relevant, as foundational theorems like the Fundamental Theorem of Arithmetic will remain valid. The conversation highlights the dependency of certain theorems on the truth of the Riemann Hypothesis while affirming the ongoing utility of number theory regardless of its proof status.

PREREQUISITES
  • Understanding of the Riemann Hypothesis
  • Familiarity with number theory concepts
  • Knowledge of the Fundamental Theorem of Arithmetic
  • Basic comprehension of prime number properties
NEXT STEPS
  • Research the implications of the Riemann Hypothesis on prime number distribution
  • Study the Fundamental Theorem of Arithmetic in detail
  • Explore theorems that are contingent on the Riemann Hypothesis
  • Investigate current research and debates surrounding the Riemann Hypothesis
USEFUL FOR

Mathematicians, number theorists, and students interested in the foundational aspects of number theory and the implications of the Riemann Hypothesis.

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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