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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 th
by 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 agoI 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 agosure, 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 agoHow 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.
- pathsjs 9y agoI think it is an elliptic equation as in elliptic partial differential equation https://en.wikipedia.org/wiki/Elliptic_partial_differential_equation https://en.wikipedia.org/wiki/Elliptic_partial_differential_... (the simplest one being the Laplace equation, which is satisfied by harmonic functions). As far as I know, there is no direct link between elliptic PDEs and elliptic curves. Elliptic PDEs are called like that because the coefficient in the second order term look like those of the equation of an ellipse (as opposed to parabolic or hyperbolic PDEs) Elliptic curves take their name because they were first studied in the context of elliptic functions, which are certain integrals that arise in computing the arc length of an ellipse. Even then, the kind of elliptic curves used by number theorists are generalizations where the algebraic form of the curve is the same, but the field of coefficients is a finite extension of the rationals (while the first appearance was with complex numbers). There is a relation between the two, but in general the study of the curve over the complex field only tells part of the story. I am not aware of any more direct relations, but it would be fascinating to learn that there is something that relates them!