A Step Towards Proving the Riemann Hypothesis

arbitraryaardvark writes "A new mathematical object has been discovered by Bristol University student Ce Bian. The Riemann hypothesis, unproven since 1859, has to do with the distribution of primes and something called L-functions. Bian has demonstrated the first known third-degree transcendental L-function. This apparently opens up a new way to go about looking for proofs of the Riemann hypothesis. There is an unclaimed $1 million prize for a valid proof. We've discussed a couple of earlier attempts to claim the prize."

Comments

Re:Proof of Hypnosis?

[pilgrim23]

Regardless of the money,
Ce Bian and Andrew Booker (and their computer) should at least win SOME prize and may need to practice their Sweedish.....

Re:wow...

[Stormy Dragon]

A proof of the Riemann Hypothesis itself won't have any effect on the security of encryption (if it did, you could compromise the encryption by just assuming the hypothesis is true and your exploit would work in nearly all cases). The only concern is if the process of developing the proof leads to an insight about the nature of prime numbers that weakens encryption in some other manner, but this wouldn't be the result of the Riemann Hypothesis itself.

Re:What's really going on here

[ediron2]

In short, this is an important advance in automorphic forms, but it is so technical that it doesn't belong on SlashDot.

You do not really understand something unless you can explain it to your grandmother. -- A. Einstein.

Lucky for us, my grandma doesn't read slashdot. But in a long-ago life, I earned a minor degree in math and took much more math en route to a degree in physics (undergrad and grad... but nowhere near this Riemann space stuff). So, I am both curious and competent. And I regret to say you didn't do the best job explaining the topic.

Rather than just bitch... here's where I wish you'd explain more:

• give (my grandma) an analogy for a membrane,
  
• What are subtle number-theoretic symmetries? Again, handwavy analogies (for me and my grandma) are fine.
  
• Is there a linkage or relationship between modes and frequencies, akin to physics standing wave equations?
  
• Any pictures you can link to that visualize these in 2-space or 3-space in a way that makes us get a hint of a grasp of 5-space?
  
• Ditto for the symmetries of 2-dim membranes: pics, examples, analogies?
  
• What's this something and why did Gelbart-Jacquet lift it?
  
• What's a native mode?... oh, wait, you did this one: a native mode is one that doesn't look like it merely adds a dimension (of complexity?) by doing something minor to alter a 2d or 3d or 4d case. What exactly would that something be? Is an ok analogy taking a bessel function in 2 or 3d, then adding a 1-d unrelated critter in to the 4th dimension that doesn't add any value that affects the other 3?
  
• So, once I have this 5-d rippling thing that isn't some lazy mashup of a 2d and a 3d or any other easy simplification, are we ready to take on 'to each such mode of vibration there is an associated L-function?
  
• What's automorphic? Messes with itself, literally, but... ?
  
• If it is numerically computed, WHY? Why can't it be solved symbolically? Is this like PDE's or n-body problems, where the problem isn't mathematically solvable but we can get close to the answer via discarding nth terms in series, perturbations, approximations, or the likes?
  
• While I agree that numerical solutions aren't purely 'right' like symbolic proofs, one can use them to do disproofs: if one shows that the error is less than E(x), and that numerical plus error's limit won't ever reach some condition, or that E(x) diverges, or whatever... that's useful and may be a step toward proving the Riemann Hypothesis. Granted, any time a tech journalist (including the slashdot editors) writes a headline, the baby jesus stabs a scientist's voodoo-doll with a long needle...
  
• And what the hell is GRH? General/global/great/ Riemann Hypothesis?
  

Thanks. Deconstructing this, I now have a (probably WRONG) sense for what you tried to say:

These guys did some computational/numerical work that doesn't really go THAT far to proving the Riemann Hypothesis. They found some 5-d examples that were really 5-d complex (not just stunts to extend 2d, 3d or 4d without the additional dimension of complexity), they did numerical work to find some 'native' 5d modes (insert a better definition of mode than 'a solution set that is like a stable solution or a standing wave or whatever'). So, we now have computationally-done 5d hints, but we're no closer to symbolically solving 5d equations. It's a bit of computational insight, but it isn't a pure proof.

Um, how did I do?