What would be the impact of solving the Riemann hypothesis?

[Kutt]

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...

 

[mathman]

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.

 

[Kutt]

I suspect that the implications as described in your second paragraph are overstated.

http://www.nytimes.com/2002/07/02/s...maticians-guessing.html?pagewanted=all&src=pm

 

[Curious3141]

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.

 

[Number Nine]

http://www.nytimes.com/2002/07/02/s...maticians-guessing.html?pagewanted=all&src=pm

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.