5 ms·

> if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in

by badosu 9y ago

> if the riemann conjecture is proven, precisely nothing happens. its not even possible that something happens in the tangible world, because of some result in mathematics. Unless I'm mistaken, if proved the Riemann Conjecture could provide insights on the distribution of prime numbers or a polynomial-time algorithm for prime factorization, which would enable attacks on ciphers that rely on the difficulty of this problem (e.g. RSA). This is not assured by the yes/no answer of the conjecture, but the underlying work to reach that.

wayn3 9y ago
im not saying that proving the riemann conjecture doesnt do anything for mathematics. it does a whole lot. but the world itself isnt going to change. i mean the 5 pm news world. heres the thing. we already kind of assume the riemann conjecture to be true. you can do a lot of things with it. its not PROVEN, and mathematicians will tell you that its not proven, but if it was such a big massive RSA attacks deal, hackers would just "assume" its proven and then calculate those primes. they would very quickly figure out whether the conjecture holds or not, in a practical sense. i think what you misunderstand is that the riemann conjecture already exists. you can already use the result of the conjecture. the missing link is the proof. but you dont need the proof to apply the result. you can just apply it. maybe some mathematician comes along and disproves it. but the result is very accessible. so the result cant be what would enable you to perform polynomial time attacks. it must be the proof. but since you dont know what the proof would look like (because it doesnt exist), it cant be in the proof. therefore, i kinda doubt what youre saying. a conjecture is just a statement by a smart person that lacks the proof. from a mathematical point of view, its not a result. but for everyone else, including serious physicists, conjectures can be used as is to make progress. if the riemann conjecture allowed for primes to be calculated so fast that modern cryptography would suffer, then that would already be happening. but thats just a tangent. my initial point was that the riemann conjecture isnt going to say anything about the world that a journalist will find interesting enough to construct something reportable out of.
- drdeca 9y ago
  I think they meant that finding a proof could involve discoveries leading up to that proof which could lead to <blah>, not that, once we have a proof, we know it, and then we can deriving things using it as an assumption and be more confident in our conclusions, which could lead to <blah>.
  - wayn3 9y ago
    sure, but proofs can involve all kinds of things. remember that millenium problem solved by perelman? its a problem in topology, but the proof is expressed in terms of elliptic curves which lives in the number theory space, and so far, we havent found a way to express it in terms of topology. this is pissing topologists off a good bit. that a number theory guy solved their problem. similar things could happen to the riemann conjecture. proven in unforeseen ways without revealing prime number stuffs. betting on how a particular conjecture is GOING TO be proven sounds far fetched at best.
    - pathsjs 9y ago
      How does Perelman proof involve elliptic curves? I thought it was about properties of the solutions to the Ricci flow equation, hence more of a difficult problem in PDE. I have no clue where elliptic curves would arise
      - wayn3 9y ago
        "Hamilton created a list of possible singularities that could form but he was concerned that some singularities might lead to difficulties. He wanted to cut the manifold at the singularities and paste in caps, and then run the Ricci flow again, so he needed to understand the singularities and show that certain kinds of singularities do not occur. Perelman discovered the singularities were all very simple: essentially three-dimensional cylinders made out of spheres stretched out along a line. An ordinary cylinder is made by taking circles stretched along a line. Perelman proved this using something called the "Reduced Volume" which is closely related to an eigenvalue of a certain elliptic equation." "an eigenvalue of a certain elliptic equation" is probably an elliptic curve. I know very little about number theory. There are many techniques involved. What I know about the Poincare Conjecture comes from a story a professor told during one of his classes.
gjem97 9y ago
> which would enable attacks on ciphers that rely on the difficulty of this problem I don't get this. If such attacks are possible, wouldn't assuming the truth (without proof) of the Riemann Conjecture allow you to develop such attacks?
- wayn3 9y ago
  that is correct

by badosu 9y ago

wayn3 9y ago

im not saying that proving the riemann conjecture doesnt do anything for mathematics. it does a whole lot. but the world itself isnt going to change. i mean the 5 pm news world. heres the thing. we already kind of assume the riemann conjecture to be true. you can do a lot of things with it. its not PROVEN, and mathematicians will tell you that its not proven, but if it was such a big massive RSA attacks deal, hackers would just "assume" its proven and then calculate those primes. they would very quickly figure out whether the conjecture holds or not, in a practical sense. i think what you misunderstand is that the riemann conjecture already exists. you can already use the result of the conjecture. the missing link is the proof. but you dont need the proof to apply the result. you can just apply it. maybe some mathematician comes along and disproves it. but the result is very accessible. so the result cant be what would enable you to perform polynomial time attacks. it must be the proof. but since you dont know what the proof would look like (because it doesnt exist), it cant be in the proof. therefore, i kinda doubt what youre saying. a conjecture is just a statement by a smart person that lacks the proof. from a mathematical point of view, its not a result. but for everyone else, including serious physicists, conjectures can be used as is to make progress. if the riemann conjecture allowed for primes to be calculated so fast that modern cryptography would suffer, then that would already be happening. but thats just a tangent. my initial point was that the riemann conjecture isnt going to say anything about the world that a journalist will find interesting enough to construct something reportable out of.

drdeca 9y ago
I think they meant that finding a proof could involve discoveries leading up to that proof which could lead to <blah>, not that, once we have a proof, we know it, and then we can deriving things using it as an assumption and be more confident in our conclusions, which could lead to <blah>.
- wayn3 9y ago
  sure, but proofs can involve all kinds of things. remember that millenium problem solved by perelman? its a problem in topology, but the proof is expressed in terms of elliptic curves which lives in the number theory space, and so far, we havent found a way to express it in terms of topology. this is pissing topologists off a good bit. that a number theory guy solved their problem. similar things could happen to the riemann conjecture. proven in unforeseen ways without revealing prime number stuffs. betting on how a particular conjecture is GOING TO be proven sounds far fetched at best.
  - pathsjs 9y ago
    How does Perelman proof involve elliptic curves? I thought it was about properties of the solutions to the Ricci flow equation, hence more of a difficult problem in PDE. I have no clue where elliptic curves would arise
    - wayn3 9y ago
      "Hamilton created a list of possible singularities that could form but he was concerned that some singularities might lead to difficulties. He wanted to cut the manifold at the singularities and paste in caps, and then run the Ricci flow again, so he needed to understand the singularities and show that certain kinds of singularities do not occur. Perelman discovered the singularities were all very simple: essentially three-dimensional cylinders made out of spheres stretched out along a line. An ordinary cylinder is made by taking circles stretched along a line. Perelman proved this using something called the "Reduced Volume" which is closely related to an eigenvalue of a certain elliptic equation." "an eigenvalue of a certain elliptic equation" is probably an elliptic curve. I know very little about number theory. There are many techniques involved. What I know about the Poincare Conjecture comes from a story a professor told during one of his classes.

gjem97 9y ago

> which would enable attacks on ciphers that rely on the difficulty of this problem I don't get this. If such attacks are possible, wouldn't assuming the truth (without proof) of the Riemann Conjecture allow you to develop such attacks?

wayn3 9y ago
that is correct