Claimed Proof of Riemann Hypothesis 345
An anonymous reader writes "Xian-Jin Li claims to have proven the Riemann hypothesis in this preprint on the arXiv." We've mentioned recent advances in the search for a proof but if true, I'm told this is important stuff. Me, I use math to write dirty words on my calculator.
So what? (Score:3, Insightful)
Re:$1,000,000 prize to be collected then if true (Score:4, Insightful)
The Riemann hypothesis is considered the most important unsolved problem in math. But, considering the source here (random paper on ArXiv by complete unknown), there's no real reason to believe this paper is correct. The number of incorrect proofs to major mathematics problems every year is staggering.
Re:The continuum hypothesis will be next... (Score:4, Insightful)
First Fermat, now this. Is nothing sacred?!
Money. Not much else these days.
Re:Coulda told us more... (Score:3, Insightful)
Re:The continuum hypothesis will be next... (Score:5, Insightful)
The Continuum Hypothesis is known to be neither provable nor disprovable in the standard axiomatic set theory ZF, enriched with the axiom of choice (ZFC). So I wouldn't really count on someone settling that one either way any time soon. Of course one could come up with a new set of axioms for the set theory and *then* prove or disprove CH but you would be hardpressed to find anyone showing interest in that result. After all, I could just add CH or not(CH) to ZFC and trivially prove or disprove it. So anything in that line first needs to even define what a sensible problem is.
For those who have no clue what I said above:
Continuum hypothesis: There is no set strictly larger than the set of natural numbers and at the same time strictly smaller than the set of real numbers. The size of a set in relation to other is defined in terms of mapping. Positive integers are the same number as even numbers because you can define a bijection between the two. Reals are strictly more than naturals.
ZF: Set theory made axiomatic. Few axioms (like empty set exists, supersets are larger than original sets etc) that you need to believe and most of the set theory believed to follow.
Axiom of Choice: Given a set of sets, one can make a set containing one element from each set. Looks obviously true but in some equivalent but different sounding formulations looks obviously false. Known to be independent to ZF.
Y Independent to axioms X: Believing that Y is true does not yield contradiction together with X unless X itself yield contradictions. Same holds for believing that Y is false.
PS: Apologies for not including links. I am feeling lazy. Wikipedia has nice articles about all of the above. Articles on ZF, CH or Axiom of Choice are the place to start for a fun reading.
Re:Tried to RTFA (Score:1, Insightful)
Th thing is - how does the riemann hypothesis help with that? You could just _assume_ it before it was proved ?!
I've never worked out how to make breaking crypto easier with a proved riemann hypothesis. That's not to say it isn't relevant. But does the riemann hypothesis speed up factorisation? Certainly not directly, though techniques used in its proofs and attempted proofs have been relevant (number fields, duh).
Re:So what? (Score:3, Insightful)
Just look at the above threads.