What would be the impact of solving the Riemann hypothesis?

In summary, the Riemann hypothesis has been a perplexing unsolved theorem in mathematics for 153 years, with a $1,000,000 prize for its solution. No mathematician, including Bernhard Riemann himself, has been able to solve it. If it were to be solved, it would require a complete re-thinking of mathematics and could potentially have impacts in various fields such as economics, finance, computer programming, and cyber security. However, the practical applications of its solution are uncertain and it is possible that new mathematics may be discovered during the process of solving it. The popular press should not be used as evidence for scientific positions.
  • #1
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The Riemann hypothesis is arguably the most difficult and perplexing unsolved theorems in all of mathematics. There is currently a $1,000,000 prize for it's solution. It's been 153 years since it's inception in 1859 and no mathematician has ever been able to solve it, not even Bernhard Riemann himself.

What would happen if it actually did get solved? I read that it's solution would require a complete re-thinking of mathematics itself and could have a major impact in economics, finance, computer programming, cyber security, etc...
 
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  • #2
Kutt said:
The Riemann hypothesis is arguably the most difficult and perplexing unsolved theorems in all of mathematics. There is currently a $1,000,000 prize for it's solution. It's been 153 years since it's inception in 1859 and no mathematician has ever been able to solve it, not even Bernhard Riemann himself.

What would happen if it actually did get solved? I read that it's solution would require a complete re-thinking of mathematics itself and could have a major impact in economics, finance, computer programming, cyber security, etc...

I suspect that the implications as described in your second paragraph are overstated.
 
  • #4
Kutt said:
The Riemann hypothesis is arguably the most difficult and perplexing unsolved theorems in all of mathematics. There is currently a $1,000,000 prize for it's solution. It's been 153 years since it's inception in 1859 and no mathematician has ever been able to solve it, not even Bernhard Riemann himself.

What would happen if it actually did get solved? I read that it's solution would require a complete re-thinking of mathematics itself and could have a major impact in economics, finance, computer programming, cyber security, etc...

Proving RH is true is not, in itself, likely to have major practical applications. For instance, in cryptography, instead of "waiting" for RH to be proven, one could easily assume its truth and see whether more efficient decryption algorithms can be constructed on that basis.

It is, however, possible that "new" mathematics may be discovered with its potential applications, during the process of solving RH.
 
  • #5
Kutt said:

Well if The Times says it...

To my knowledge, the truth of the Riemann hypothesis would not immediately impact modern cryptography in any substantial way, or provide any new, more efficient factorization schemes. The article even goes on to say...
There is no simple way to tell if a number is prime, and that is the basis for most modern encryption schemes.

...which is just bizarre. The difficulty of decomposition a number into its prime factorization is the basis for many public key encryption schemes, which is perhaps what they meant. Either way, the article is poorly written. Please don't cite the popular press as evidence for scientific positions.
 

1. What is the Riemann hypothesis?

The Riemann hypothesis is a mathematical conjecture proposed by mathematician Bernhard Riemann in 1859. It states that all nontrivial zeros of the Riemann zeta function lie on the critical line of 1/2.

2. Why is the Riemann hypothesis important?

The Riemann hypothesis is considered to be one of the most important unsolved problems in mathematics. Its resolution would have significant implications in many areas of mathematics, including number theory, analysis, and geometry.

3. How does the Riemann hypothesis relate to prime numbers?

The Riemann hypothesis provides a connection between the distribution of prime numbers and the behavior of the Riemann zeta function. If proven true, it would give a better understanding of the patterns and distribution of prime numbers.

4. Has the Riemann hypothesis been proven?

No, the Riemann hypothesis has not been proven yet. It remains one of the most famous unsolved problems in mathematics, and many mathematicians have attempted to prove or disprove it over the years.

5. What are the potential consequences if the Riemann hypothesis is proven false?

If the Riemann hypothesis is proven false, it would have a significant impact on the field of mathematics. It could lead to the development of new techniques and theories to understand the distribution of prime numbers and other mathematical phenomena.

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