Mathematician Claims Proof of Riemann Hypothesis 561
TheSync points to this press release about a Purdue University mathematician, Louis de Branges de Bourcia, who claims to have "proven the Riemann hypothesis, considered to be the greatest unsolved problem in mathematics. It states that all non-trivial zeros of the zeta function lie on the line 1/2 + it as t ranges over the real numbers. You can read his proof here. The Clay Mathematics Institute offers a $1 million prize to the first prover."
If there's one thing I know (Score:5, Funny)
homer simpson (Score:5, Funny)
Infinite, or really infinite?? (Score:3, Funny)
Q.
Re:If there's one thing I know (Score:5, Interesting)
De branges is a bit of a crank on the Riemann hypothesis. No-one believes his approach(s) will work. This is well documented in the book "Riemann's Zeros". When some of the leading mathematians were asked about his approach they said it was "full of errors" and "unlikely to work". The only reason he is given the light of day is because he managed to prove to the Bieberbach conjecture. That was a difficult problem, hats off to him for getting it aswell, but it's no Riemann hypothesis!
Rest assured, we'll all be dead and burried when it actually gets solved.
Simon
Re:If there's one thing I know (Score:5, Informative)
----------------
Riemann Hypothesis "Proof" Much Ado About Noithing
A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.
Re:If there's one thing I know (Score:5, Informative)
Not to spoil your joke or anything, but actually, AFAIK, NP-complete problems are perfectly solvable. The problem is how long it takes to solve them in general (a certain instance of a problem could prove easy). They cannot be solved deterministically in polynomial time (i.e., quickly).
Re:If there's one thing I know (Score:4, Informative)
NP problems are problems that can be solved by a Nondeterministic Turing machine in Polynomial time. NP-Complete problems are the class of "hardest" problems in NP. All the usual suspects (Traveling Salesman, 3-SAT, SAT, ...) are proven
to be in NPC.
We know that we can solve NPC problems in exponential time (as we can simulate a non-deterministic Turing maschine on deterministic hardware with exponential overhead). What we do not know is if there is any smarter way. That is the P=?=NP question.
Re:If there's one thing I know (Score:4, Informative)
No, you're wrong. NP problems are, by definition, problems that can be solved in polynomial time by a nondeterministic Turing machine
Essentially this means that a Turing machine could solve the problem in polynomial time, if it had some magic 'oracle' which instructed it on the right computational path to follow for a given input.
Obviously there are problems out there that would require exponential time for even a nondeterministic Turing machine to solve. An example from the Wikipedia link I provided is finding the best move in a chess or Go game.
Such problems are not in NP, and proving P=NP would not suddenly give us algorithms for solving these problems deterministically in polynomial time.
However, most problems that are considered NP-Complete are not mathematically proven to be so.
What? Sorry, if there ain't a proof, it ain't NP-complete. There are a lot of problems that are described as "believed to be NP-complete", but that's different.
Re:If there's one thing I know (Score:4, Informative)
Not quite correct, because:
The set NP is defined as all problems whose solutions can be verified in polynomial time
"Set of all problems which can be solved in polynomial time by a nondeterministic Turing Machine."
So the question "Does P equal NP?" is also the question "Does an NTM have the same computional power(in time) as a TM, or does it have more?" (It is already known that as far as decidiblity is concerned, TMs and NTM are equivalent.)
Because of the way the proofs have been constructed, if you can solve any of the NP-Complete problems in polynomial time, you can solve all of them in polynomial time.
Some more detail here:
An NP-hard problem is a problem to which any problem in NP can be reduced in polynomial time.
(Essentially, it can be used as a subroutine for any NP problem, with only a polynomial number of calls. Thus a solution to it is a solution to any problem in NP.)
An NP-complete problem is one that is:
1. NP-hard
2. In the set NP.
Thus if a polynomial-time solution exists to an NP-complete problem, then P=NP, because a polynomial number of calls to a function that terminates in polynomial time is O({polynomial}*{polynomial}) = O({polynomial}) .
Please note, however, that not all NP-hard problems are NP-complete.
Apology (Score:5, Funny)
"We humbly apologize for the complete illegibility of this proof. The mathematician responsible has been sacked."
Googlized HTML version (Score:3, Informative)
Re:Apology (Score:5, Funny)
"A Slashdotter has discovered a truly wonderful proof of the sacking of the mathematician responsible, but his bandwidth is too narrow to host it!"
WTF? Mods? (Score:5, Informative)
Apology - 2: a formal written defense of something you believe in strongly
This should at most have earned a "Funny", or is there something I'm missing here?
Re:WTF? Mods? (Score:5, Funny)
Yeah, I think you missed:
Equivocation - \E*quiv`o*ca"tion\, n. The use of expressions susceptible of a double signification, with a purpose to mislead boneheaded moderators, especially when you are just making a joke.
Re:Apology (Score:4, Insightful)
Re:Apology (Score:4, Informative)
Re:Apology (Score:5, Interesting)
As it is, it looks like he proposed this solution over a year ago and has been getting it vetted in a tightly controlled community. Now that the cat is out of the bag he will have to get it into a peer reviewed journal (takes 6 months or so) and wait 2 years to see how it is bashed...
Yeah - that is about the time it would take for me to UTFA, except I am not a Mathemetician, so add in another 6-8 years to get that training as well. So I will get back to you sometime around 2120 with an insightful comment after UTFA
Re:Apology (Score:5, Interesting)
Re:Apology (Score:4, Funny)
-B
Re:Apology (Score:5, Interesting)
My favorite selection:
Hilarious stuff. He apologizes to the people who will now feel the need to go over his proof with a fine toother comb, looking for mistakes...and also explains (three pages in) why he's chosen to start his proof with a history of the golden age of mathematics, stretching back to Newton. Basically, he's saying "oh hey, thanks for joining me. I was just explaining ALL OF MATHEMATICS for those playing at home. Bear with me, this one's worth it, and I promise you can get back to your euclidian algorithms and Ving diagrams in short time."
Ever read "The Life and Opinions of Tristram Shandy?" It's an amazing book from the 18th century, which attempts to tell a simple narrative but due to the extremely schizophrenic style of the narrator, it keeps breaking down into tangential pockets of narrative self awareness. Basically, the author wrote from the perception of a disturbed dandy who couldn't keep his mind on the task at hand, an author who keeps apologizing to his readers for the inconvenience of his own poor editing.
This mathematical proof reminds me a lot of this book...the text of the proof doesn't act as though the proof isn't something interesting or ground breaking, nor does it make a big deal of this. It just ambles on in all directions until the Riemann hypothesis is well and truly proven, but with no real hurry to illustrate the proof until the outlines have been inked. Not that I know for sure that Riemann is proven or isn't...my brain was full when I got to differentials. But if it is, this paper will stand out not only as a great work of mathematics, but a great work of WRITING about mathematics.
I'm going to read it again. Maybe I'll understand it this time!
Well, not exactly (Score:4, Informative)
It is not proved; he is not at the top of his field; this "paper" will be quickly forgotten among professional mathematicians; and I doubt any professional mathematician is going over the proof with any sort of comb.
L. de Branges first achieved fame for proving the Bieberbach conjecture [wikipedia.org]. His proof went through strange and abstract methods. He went on the road to present his proof at various seminars in France, Russia, etc; IIRC a bunch of Russian students got very excited and basically rewrote his proof. Their new proof was much shorter and avoided the use of strange methods. Nowadays, their proof is remembered and his is not, but the proof still bears his name, since after all he was the first to come up with *some* kind of proof, and their proof did more or less come out of his.
So he deserves credit for that, and it was quite an achievement to prove the Bieberbach conjecture. But even then he was using unwieldy proofs with unnecessarily abstract methods.
For many years he has been claiming to have a proof of the Riemann Hypothesis. Professional mathematicians stopped listening a long time ago.
This guy is washed-up.
I whole-heartedly agree that this short article is hilarious, but I would like to add the adjective condescending. What kind of asshole apologizes for solving a problem? Does he think he lives on some higher plane, and therefore must take direct, personal responsibility for every aspect of our lives?
Look at how G. Perelman submitted his ideas on proving the Poincare conjecture [wikipedia.org] just a little while ago. He didn't waste anyone's time by rehashing the already-available history of the problem or its wider context in mathematics. Nor did he apologize for having an idea. Rather, he submitted his ideas for consideration, with the full awareness that there may have been a mistake.
de Branges is so full of crap, it makes me sick.
zach
Re:Apology (Score:3, Funny)
Good job (Score:5, Funny)
Re:Good job (Score:3, Funny)
Re:Good job (Score:5, Insightful)
Gotta prove 'em all (Score:5, Funny)
Riemann-chu, I prove you! Then bust out the paper.
Re:Gotta prove 'em all (Score:5, Funny)
Yeah but then a few years later Yu-Physics-Oh comes along and replaces it in popularity. Then before you know it that two is gone replaced by annother populare science.
Plus it would replace Arceology the gathering.
Magic The Gathering, Pokemon and yugioh are in the 15 minuts of fame catagory. Populare today gone tomarow.
I don't want Math to be gone tomarow. I'm counting on it to stay for a while.
Now english I wouldn't mind if it's own end was spelled out. You can see the proof reading this very post.
Nope! Nice try (Score:5, Funny)
For some suggested approaches, see (Score:5, Interesting)
Re:Nope! Nice try (Score:3, Funny)
Failed proof (Score:5, Informative)
Ha! They've already found an error in the proof! All that he posted was his apology! [purdue.edu] :-)
Yes, I was actually confused at first. For the non-math geeks like myself, who are feeling stupid, look at definition 2a of apology [reference.com].Usage of "apology" (Score:3, Informative)
Uh-oh! There's a mistake! (Score:5, Funny)
Hilbert Turns in his Grave? (Score:5, Interesting)
"If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?"
David Hilbert
Re:Hilbert Turns in his Grave? (Score:5, Interesting)
Really, folks, this is a big deal if it's true. It just doesn't get the attention Fermat's Last Theorem did because it's harder to understand what it means and why it's important.
After all, most people don't even know what complex numbers are, much less complex functions. The zeta function, then, is already beyond the understanding of most people, not because they're incapable, but because they're not interested. But the implications of the Riemann Conjecture are far-reaching indeed, affecting things like quantum mechanics and statistical physics.
--Mark
Re:Hilbert Turns in his Grave? (Score:3, Interesting)
The significance may be more in the mathematical machinery required to prove it than in the result itself.
Re:Hilbert Turns in his Grave? (Score:5, Funny)
Oh yeah? Mine would be "Is Doom 3 out yet?"
Honestly, which is more likely?
I'm in trouble (Score:5, Funny)
The question, explained (Score:5, Informative)
First: complex numbers [wolfram.com], explained. You may have heard the question asked, "what is the square root of minus one?" Well, maths has an answer and we call it i [wolfram.com]. i*i = -1. If the real number line ...-4, -3, -2, -1, 0, 1, 2, 3, 4... is represented as a horizontal line, then the numbers ...-4i, -3i, -2i, -i, 0, i, 2i, 3i, 4i... can be thought of as the *vertical* axis on this diagram. The whole plane taken together is then called the complex plane [wolfram.com]. This is a two-dimensional set of numbers. Every number can be represented in the form a+bi. For real numbers, b=0.
Right. Now the Riemann Zeta Function [wolfram.com] is a function/map (like f(x)=x^2 is a function) on the complex plane. For any number a+bi, zeta(a+bi)will be another complex number, c+di.
Now, a zero [wolfram.com] of a function is (pretty obviously) a point a+bi where f(a+bi)=0. If f(x)=x^2 then the only zero is obviously at 0, where f(0)=0. For the Riemann Zeta Function this is more complicated. It basically has two types of zeros: the "trivial" zeroes, that occur at all negative even integers, that is, -2, -4, -6, -8... and the "nontrivial" zeroes, which are all the OTHER ones.
As far as we know, *all* the nontrivial zeroes occur at 1/2 + bi for some b. No others have been found in a lot of looking... but are they ALL like that? The Riemann Hypothesis [wolfram.com] suggests that they are... but until today nobody has been able to prove it.
Oh Hocky Sticks!!!! (Score:5, Insightful)
Thanks!
Re:The question, explained (Score:5, Informative)
Great Cthulhu help me, but I'm going to try and answer this for you.
We have natural numbers - 1,2,3,
And then we have Zero and once upon a time this disturbed people. You grew up with it, you're happy with it; but we can see that it was less intuitive than 1,2,3,
And yet, the discovery (or creation
Now perhaps at this point, you're nodding and saying 'yes, yes, I know that already.' If so, then good, because you've just understood the principle of a complex number. It's another abstraction that can't easily be represented in the real world (nuclear physicists shut up, please). And yet, it has very real use in making calculations.
If you're a programmer, think about how much code there is behind the scenes of a program to produce the result you want from it. Suppose that your program counts how many oranges people have given you. Maybe it has the line
for (i=0; i < oranges_owed; i++) {}
Well i isn't physically real, it doesn't represent a physical aspect of what you are modelling (the oranges) but it's useful. And in the same way, i is also useful, even if it's just part of a intellectual model.
For a mathematician: I think therefore i is.
The only thing remaining is to give you an example of how it is useful. Easily done - Quantum Physics. All of it.
Hope this helps, IASNAM (I Am Surprisingly Not...)
* Proof that 0x0=0:
Re:But you're interested, right? (Score:3, Funny)
Now it's back to work, or my job will be in the past.
Is it... (Score:5, Funny)
Impact on crypto? (Score:4, Interesting)
There is no impact on crypto (Score:4, Informative)
Re:Impact on crypto? (Score:3, Informative)
So, in short, no, no help for cracking crypto based on primes...though the article does mention possible crypto applications down the line. I'm not sure what, exactly, those would be.
Re:Impact on crypto? (Score:5, Informative)
It's actually a little more complex than that.
Riemann was investigating the distribution of prime numbers. Along the way he devised (discovered?) the Zeta Function, which describes with considerable accuracy the distribution of prime numbers. While working with the Zeta Function, he discovered an interesting property: It appeared that all the non-trivial zeroes of the function had a real part of one-half. However, since this property of the function was not related to the prime-distribution work he was doing, he did not bother to prove this apparent property, which came to be known as the "Riemann Hypothesis" (presumably, once it is proven it will be known as the Riemann Theorem, or some such).
Thus, the Riemann Hypothesis is in fact tangential to (and possibly unrelated to) the distribution of prime numbers. Riemann's notes on the Zeta Function, regarding his work on prime distribution, are pretty explicit about this.
Re:Impact on crypto? (Score:4, Funny)
*smack!*
Re:Impact on crypto? (Score:5, Informative)
Actually, as with most things Euler was the first to study it. The zeta function is also the simplest of a class of functions that Dirichlet studied Dirichlet L-series. There is also a Generalized Riemann Hypothesis that states that no Dirichlet L-series has zero with real part greater than 1/2.
The Riemann Hypothesis is more than tangential to the study of the distribution of primes. There is a function derived from the distribution of the primes that can be expressed in terms of the non-trivial zeros of the zeta function. The Prime Number Theorem is also equivalent to the statement that the zeta function has no zeros with real part 1. The Generalized Riemann Hypothesis implies the weak form of Goldbach's conjecture (i.e. that any odd number greater than 7 can be expressed as the sum of three odd primes).
Re:Impact on crypto? (Score:5, Informative)
No. Almost all mathematicians have assumed for years that GRH is true anyway; proving it would mean that all those footnotes ([1] Under the assumption of the Riemann Hypothesis) could be removed, but that's the only practical effect it would have.
Re:Impact on crypto? (Score:4, Informative)
Prime numbers are easy to multiply together. Little CPU needed.
But it's hard to do the reverse: Factor a big number into two separate prime numbers. Lots of CPU needed.
It's based on that principle.
Re:Impact on crypto? (Score:3, Informative)
Not the best explanation, I prefer this [amazon.com]
Re:Impact on crypto? (Score:4, Informative)
No. GRH implies that isprime() is in P (by bounding the cost of a strong pseudoprime test); but we already knew that, thanks to AKS.
What are the consequences for cryptography? (Score:4, Interesting)
Does this affect prime based public key schemes at all? How does it affect them?
Re:What are the consequences for cryptography? (Score:5, Informative)
Most mathematicians felt that the Riemann Hypothesis was true so that this view has been taken into consideration into mathematics for a long time. Perhaps if he developed some new methods for playing with numbers in the proof, but it doesn't seem like it to me.
There's a ton of math papers that begin with "Assume the extended riemann hypothesis...".
At least that's my guess.
Apologies to the proof? (Score:4, Funny)
The media never learn? (Score:3, Insightful)
Will the media keep publishing claims of extraordinary mathematical findings without checking the facts forever?
Just like this one over again:
Swedish Student Partly Solves 16th Hilbert Problem [slashdot.org]
That's what I like about /. If the article is wrong, there is always the comments there to solve it.
Re:The media never learn? (Score:3, Insightful)
de Branges' reputation with other mathematicians (Score:4, Interesting)
Re:de Branges' reputation with other mathematician (Score:5, Funny)
He appears to be 72.
A Proof .... Maybe (Score:4, Interesting)
quick google search (Score:3, Interesting)
Re:quick google search (Score:5, Insightful)
Hm (Score:5, Funny)
what?
Seems not-unlikely to be wrong (Score:5, Informative)
The same guy claimed [google.com] to have solved the same problem at least 4 years ago.
The guy has a reputation [google.com] for sometimes getting it wrong.
(Probably because he has published flawed proofs [google.com] of other well-known problems.)
He could be right, but I wouldn't get my hopes up.
Re:Seems not-unlikely to be wrong (Score:5, Informative)
Re:Seems not-unlikely to be wrong (Score:5, Informative)
However, a quick scan suggests that if his proof is indeed verified, it won't do what a lot of people want it to do: Quote from the article: "The proof of the Riemann hypothesis verifies a positivity condition only for those Dirichlet zeta functions which are associated with nonprincipal real characters. The classical zeta function does not satisfy a positivity condition since the condition is not compatible with the singularity of the function. But a weaker condition is satisfied which has the desired implication for zeros."
So I may be wrong, but it looks like he may have found ground on a restricted interpretation of the GRH (or Generalized Riemann Hypothesis), -ie concerning Dirichlet zeta functions which are associated with nonprincipal real characters only.
As for consequences, If GRH is indeed true, then e.g. the Miller-Rabin primality test is guaranteed to run in polynomial time.
The Problem (Score:5, Informative)
Most of you have who have taken basic calculus courses have probably seen a simplified definition of the zeta function for real intergers greater than 1. when z=n, a natural number, the zeta function reduces to the infinite series Zeta(n)= SUM (k=1-->inf) 1/k^n
Died before he could prove it (Score:4, Funny)
I think I might as well write my epitaph now:
Re:Died before he could prove it (Score:3, Insightful)
Re:Died before he could prove it (Score:3, Insightful)
Re:Died before he could prove it (Score:3, Insightful)
You need to read this a bit more carefully. It does not say "died before he proved it." It says "died before he could conclusively prove it," as in before he was able to do so.
Re:Died before he could prove it (Score:4)
Re:Died before he could prove it (Score:5, Funny)
Re:Died before he could prove it (Score:4, Funny)
actual paper (Score:5, Informative)
So if his "proof" isn't obviously wrong, it'll likely take quite a while for the experts to verify.
Much ado about nothing? (Score:5, Informative)
Here is the general outline:
1) At the end of page 19 he mentions that "The positivity condition which is introduced implies the Riemann hypothesis if it applies to Dirichlet zeta functions."
2) After some introduction of the quantum gamma functions that lasts two pages, the actual proof starts at the end of page 21 with the phrase "A quantum gamma function is obtained when is nonnegative. A proof of positivity is given from properties of the Laplace transformation."
3) The proof ends in the middle of page 23 with the a verification that W(z) is a quantum gamma function with quantum q = exp(-2*pi), obtained from a spectral theory of the shift operator.
Overall this is just a very brief sketch of the whole proof.
BTW, to add gas on fire, here is an exceprt from mathworld.com, which surprisingly was missed by
http://mathworld.wolfram.com
Riemann Hypothesis "Proof" Much Ado About Noithing (sic)
A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing.
The counterexample to Brangles approach can be reached here: http://arxiv.org/abs/math.NT/9812166
Maybe (Score:3, Interesting)
Even though he is a kook, I root for him; no one believed him when he claimed he had proven the Bieberbach conjecture. I believe, however, that he has claimed to have proven the Riemann hypothesis previously. One should check carefully before trusting his claim.
It's already been solved... (Score:4, Funny)
Besides, I think he forgot to carry the one.
"Apology" an old paper? (Score:4, Informative)
Another Proof (Score:3, Funny)
Cool background material (Score:5, Informative)
If nothing else check out the animation [ex.ac.uk].
mind-boggling
Good Book about the Hypothesis (Score:3, Interesting)
This is a very informative book about Riemann's work on the hypothesis, as well as the work of many other mathematicians. You probably need a solid college-level understanding of math to follow most of the technical explanations, but the historical parts of the book are very interesting.
Why people haven't believed him so far (Score:5, Informative)
The reasons why most specialists doubt that his approach can ever yield the result are well described in this paper [arxiv.org] from 1998:
(i.e., despite the name, the "generalized RH" proved by de Branges actually did not include the standard RH as a special case.)Riemann Hypothesis Interview (Score:3, Informative)
Probably a hoax: (Score:4, Informative)
Riemann Hypothesis "Proof" Much Ado About Noithing A June 8 Purdue University news release reports a proof of the Riemann Hypothesis by L. de Branges. However, both the 23-page preprint cited in the release (which is actually from 2003) and a longer preprint from 2004 on de Branges's home page seem to lack an actual proof. Furthermore, a counterexample to de Branges's approach due to Conrey and Li has been known since 1998. The media coverage therefore appears to be much ado about nothing
Overview of proof? (Score:3, Interesting)
I found a wonderful proof for this theorem (Score:3, Funny)
Re:Proof of theory (Score:5, Insightful)
Bull. There are thousands of mathematical researchers. Most don't have hefty salaries, and most aren't working on money-prize problems.
Mathematicians are never in it for the money.
Wonder what he'll do with the money?
Seems like he wants to restore the old family castle:
I must say that at he seems a bit full of himself, or at least, getting a bit ahead of himself. Given how many have tried and failed witht his problem.
Re:Proof of theory (Score:3, Funny)
You got it! They are in it for the chicks!
Re:Proof of theory (Score:3, Insightful)
Mathematicians have been working on this for a long time. it is not like one day this guy woke up and said "oh, 1 million dollars for it eh, well I better get to work."
Re:Proof of theory (Score:3, Informative)
Mathematicians tackle difficult problems all of the time, regardless of the (lack of) money involved.
I don't know why you say that interest in "theoretical" mathematical proof is waning. It certainly isn't where I come from. (And what is ultra-math??!)
Re:Proof of theory (Score:5, Funny)
Then the IRS will send de Branges a huge bill for the 45% tax rate on "winnings."
Then his ex-wife will sue for 50% of the million dollars because "he used to moan 'oh, Riemann' while we were doing it."
Then de Branges will spend 25 years opening letters from the poor and destitute who desparately deserve a chunk of his newfound yet nonexistent wealth.
Then eventually he will take his place in an unmarked mass grave reserved for all the great mathematicians who died peniless and unloved.
Well, that's my guess anyways.
Re:Already failed once! (Score:5, Insightful)
It took Einstein many tries to arrive at the correct fomulation for general relativity. I guess according to you, he should have just given up after his first failure?
re:Already failed once (Score:5, Insightful)
Most reseachers I know produce one magnificent failure after another on the quest for a new piece of knowledge. Everything that is easy to find has probably already been discovered, and mathematics is no different. So the guy made a few failed attempts at solving the puzzle, this doesn't make each sucessor to the first attempt a garaunteed failure.
Re:Already failed once (Score:4, Funny)
And so it came to pass, Gentle Reader, that some of the Finders did find their fruit, and these were known as Keepers. But a few still lost their newfound fruit on the way home, and these poor souls were thenceforth known as Losers, unless they wept, in which case they were also known as Weepers.
Re:Already failed once! (Score:3, Insightful)
Re:The Reimann Hypothesis (Score:3, Informative)
Re:Riemann hypothesis proof is useless (Score:3, Funny)
I stopped reading here, because you are an idiot.
Re:Riemann hypothesis proof is useless (Score:4, Insightful)
Your comment explains why discovering a proof for the Riemann Hypothesis is such a monumental event. Mathematicians have assumed it to be true for some time now, and there exists a massive amount of mathematical theory which rests upon its validity. Proving the hypothesis ensures that their reasoning is on solid ground. Without one, there's no way to know for sure whether or not their conjectures are true.