# Riemann Hypothesis Proved?

#### Hemos posted more than 11 years ago | from the cracking-the-problems dept.

454
Theodore Logan writes *"Has the Riemann Hypothesis finally been proved? The proof is a couple of months old, and to the best of my knowledge a Swedish newspaper is the only one to take up the story yet, so there is certainly a possibility that this is a hoax, or a less than watertight proof. But if it turns out to be the real thing, it will, apart from winning the authors eternal fame and glory for finding the holy Grail of modern math, provide them with a cool $1 million as they claim the first Millennium Prize."* We had a story a while back about this as well.

## Aww Yeah (-1, Offtopic)

## DJ FirBee (611681) | more than 11 years ago | (#5424063)

## Re:Aww Yeah (-1)

## Anonymous Coward | more than 11 years ago | (#5424068)

## It's "Millennium"!! (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5424066)

## yeah... (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5424120)

prove Learn to grammar...## Re:yeah... (-1)

## Anonymous Coward | more than 11 years ago | (#5424141)

## Riemann hypothesis (5, Funny)

## YellowSnow (569705) | more than 11 years ago | (#5424070)

## First post hypothesis (-1)

## Anonymous Coward | more than 11 years ago | (#5424077)

## in related news (-1)

## Anonymous Coward | more than 11 years ago | (#5424079)

## um... (4, Funny)

## Anonymous Coward | more than 11 years ago | (#5424086)

"A proof of the Riemann's hypothesis (RH) about the non-trivial zeros of the Riemann zeta-function is presented. It is based on the construction of an infinite family of operators D^{(k,l)} in one dimension, and their respective eigenfunctions \psi_s (t), parameterized by continuous real indexes k and l. Orthogonality of the eigenfunctions is connected to the zeros of the Riemann zeta-function. Due to the fundamental Gauss-Jacobi relation and the Riemann fundamental relation Z (s') = Z (1-s'), one can show that there is a direct concatenation among the following symmetries, t goes to 1/t, s goes to \beta - s (\beta a real), and s' goes to 1 - s', which establishes a one-to-one correspondence between the label s of one orthogonal state to a unique vacuum state, and a zero s' of the \zeta. It is shown that the RH is a direct consequence of these symmetries, by arguing in particular that an exclusion of a continuum of the zeros of the Riemann zeta function results in the discrete set of the zeros located at the points s_n = 1/2 + i \lambda_n in the complex plane."What the fuck?

## Re: um... (0)

## sfraggle (212671) | more than 11 years ago | (#5424100)

Duh.

## Re:um... (0)

## Anonymous Coward | more than 11 years ago | (#5424102)

yeah so what...what is this good for?

## Re:um... (0)

## Anonymous Coward | more than 11 years ago | (#5424374)

## Re:um... (1)

## agentZ (210674) | more than 11 years ago | (#5424181)

## Re:um... (5, Informative)

## shayborg (650364) | more than 11 years ago | (#5424213)

-- shayborg

## Attempt at putting it in more layman's terms. (4, Informative)

## MarvinMouse (323641) | more than 11 years ago | (#5424227)

A proof of the Riemann's hypothesis (RH) about the non-trivial zeros of the Riemann zeta-function is presented.We are going to show you beyond a shadow of a doubt that the non-trivial zeros of the zeta-function are of the form 1/2 +- i*theta_n.

It is based on the construction of an infinite family of operators D^{(k,l)} in one dimension, and their respective eigenfunctions \psi_s (t), parameterized by continuous real indexes k and l.To do this, we are going to use the operators D^{(k,1)} and their respective vectors \psi_s (t), such that using D^{(k,1)} on \psi_s (t) will produce k*(\psi_s (t)), where k is some non-zero constant. Unfortunately though, we have to show a way to product all of these operators. So the "construction of" the operators will be contained within the proof.

Orthogonality of the eigenfunctions is connected to the zeros of the Riemann zeta-function.These \psi_s (t) vectors are also all at "right-angles" to eachother. So their cross products = 0.

Due to the fundamental Gauss-Jacobi relation and the Riemann fundamental relation Z (s') = Z (1-s'), one can show that there is a direct concatenation among the following symmetries, t goes to 1/t, s goes to \beta - s (\beta a real), and s' goes to 1 - s', which establishes a one-to-one correspondence between the label s of one orthogonal state to a unique vacuum state, and a zero s' of the \zeta.Z(s') = Z(1-s') is true. Thus, we can show that there is a connection between the follwing symmetries:

t goes to 1/t,

s goes to \beta -s (where beta is a real number),

and s' goes to 1 - s'

In Q.M. we can show then a correspondence between one of these orthogonal states to a unique vacuum state (from Quantum Mechanics), and thus a solution of the zeta function.

It is shown that the RH is a direct consequence of these symmetries, by arguing in particular that an exclusion of a continuum of the zeros of the Riemann zeta function results in the discrete set of the zeros located at the points s_n = 1/2 + i \lambda_n in the complex plane.From these neat little tricks, we can show that the Riemann Hypothesis must be true, because these things are true.

## Re:Attempt at putting it in more layman's terms. (1)

## will592 (551704) | more than 11 years ago | (#5424331)

Orthogonality of the eigenfunctionsis connected to the zeros of the Riemann zeta-function. These \psi_s (t) vectors are also all at "right-angles" to eachother. So theircross products = 0.You sure about this? You might mean do product, no?

Chris

## Re:Attempt at putting it in more layman's terms. (2, Informative)

## MarvinMouse (323641) | more than 11 years ago | (#5424360)

I mean dot product... Sorry about that.

(for those of the unitiatied)

dot product means

A . B = sum(a_n*b_n), for all n.

cross product is something completely different.

## Re:Attempt at putting it in more layman's terms. (3, Funny)

## tomzyk (158497) | more than 11 years ago | (#5424358)

Honestly, you basically just translated that gobbledeegook from Latin to French for me. I still don't really understand what it all means, but I shall now do what I have done in the past for articles related to extremely complex mathematical hypothesis (hypothesese?)... I'll just nod my head, tell myself "Sure! But of course!" and move on to look for more "+5 Funny" comments.

Then maybe get back to work too.

## Re:Attempt at putting it in more layman's terms. (1)

## petronivs (633683) | more than 11 years ago | (#5424367)

understandthis, so we might as well just leave it at:This is WAY cool, man!## Re:Attempt at putting it in more layman's terms. (0)

## Anonymous Coward | more than 11 years ago | (#5424381)

Pretend we are REALLY dumb.

## Re:um... (0)

## Eu4ria (110578) | more than 11 years ago | (#5424269)

A proof of the Riemann's hypothesis...Eu4ria## News for Nerds (0)

## barnaclebarnes (85340) | more than 11 years ago | (#5424345)

*Except really, really nerdy people.

## So does anyone want to explain what this means? (0, Redundant)

## nick255 (139962) | more than 11 years ago | (#5424107)

## Re:So does anyone want to explain what this means? (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5424128)

## Okay, assuming this proof to be correct... (1, Informative)

## Spyral999 (546020) | more than 11 years ago | (#5424109)

## Re:Okay, assuming this proof to be correct... (0)

## Anonymous Coward | more than 11 years ago | (#5424146)

## Re:Okay, assuming this proof to be correct... (0, Insightful)

## Kevin Stevens (227724) | more than 11 years ago | (#5424160)

## Re:Okay, assuming this proof to be correct... (5, Informative)

## epong (561351) | more than 11 years ago | (#5424275)

## Re:Okay, assuming this proof to be correct... (5, Interesting)

## MarvinMouse (323641) | more than 11 years ago | (#5424281)

The coolest thing that ever happened to me in University (not involving social life), was when we started to prove things that I just took for granted as true.

Suddenly an order and majesty came out of all of it, and it was the more invigorating feeling I've had. There's something to be said about being good at math and able to memorize all of those formulae and how they work, etc. But there is something completely different about proving those formulae and knowing for a fact (beyond any doubt) that they are absolutely true.

Everyone generally assumed RH was true, this is exciting because if it is valid (I don't have the time to validate the proof, albeit I will read it over), than RH is absolutely true beyond any shadow of a doubt.

Now if RH were proven to not be true, that would be even more exciting, but this is just as good. ^_^

## Re:Okay, assuming this proof to be correct... (4, Interesting)

## exp(pi*sqrt(163)) (613870) | more than 11 years ago | (#5424300)

This is not a "most fundamental theor[y]" on which calculus is based. Calculus is not based on it at all. Ostensibly it has nothing to do with calculus at all although any proof will almost certainly use calculus.

You're also confused about the words "theory" and "theorem". We're talking about the latter here. A theorem is a proposition that has been rigorously proved by deriving it from axioms. A theory is something quite different: loosely is means something like a "systematic body of knowledge". Like the theory of evolution or group theory. Or it can be used to mean a tentative hypothesis as in "I have a theory that this doesn't work because you forgot to ...". (That's two distinct meanings by the way - I might as well clear up some Creationist FUD while I'm at it.)

And what are you talking about when you say "proofs are rarely meant to be practical". The truth or falsity of Rimemann's Hypothesis affects things like the theoretical expected time for things like factoring algorithms to run. Maybe /. readers can.

youcan't see the consequences of that but I'm sure most## Re:Okay, assuming this proof to be correct... (1)

## Eccles (932) | more than 11 years ago | (#5424332)

Proofs are rarely meant to be practical, unless they prove that there is the possibility that something can happenyes, but ITInfo says "The math whiz who solves the Riemann hypothesis problem stands to not only earn a million dollars and global acclaim, but also to stand the information security industry on its ear." A question is why? If it's assumed to be true, how is finding that assumption is actually correct going to have as dramatic an effect as suggested here?

## Re:Okay, assuming this proof to be correct... (1)

## laughing_badger (628416) | more than 11 years ago | (#5424164)

Of what practical use is it again?? Anyone?Um, well if I managed to do this and won 1M, I'd practically never have to work again. Or, more correctly, I'd never have to practically work again...

## Re:Okay, assuming this proof to be correct... (3, Insightful)

## Oopsey (638667) | more than 11 years ago | (#5424180)

Who knows what use someone may derive from the proof of the RH?

## Re:Okay, assuming this proof to be correct... (3, Insightful)

## Anonymous Coward | more than 11 years ago | (#5424189)

Scanning Tunnelling microscopes are just one example. Based on the pure science of quantum mechanics, which was very easy to dismaiss as "of no practical use" for a good thirty years.

## Re:Okay, assuming this proof to be correct... (5, Insightful)

## monadicIO (602882) | more than 11 years ago | (#5424190)

16-year-old John Quincy Adams and 77-year-old Ben Franklin had watched as Alexandre Charles tested an unmanned hydrogen balloon in Paris. That was where someone asked Franklin what use this all could be, and he gave his much-quoted answer, "What good is a new-born baby?"Not everything need have immediate application.

## Re:Okay, assuming this proof to be correct... (-1, Troll)

## popeyethesailor (325796) | more than 11 years ago | (#5424191)

## Re:Okay, assuming this proof to be correct... (0)

## Anonymous Coward | more than 11 years ago | (#5424206)

proving the re. hy. will not have any practical value for the present, but will have strong value for the future. If you dont understand this, then your a moron.

## Of course (5, Funny)

## Pac (9516) | more than 11 years ago | (#5424237)

It also proves that all non-trivial zeros are in the line Re(s) = 1/2. This is important because it humbles people without a very wierd Mathematical background, by informing them thre is such a this as trivial and non-trivial zeros. It may also get the Math guys some more girls.

## Re:Of course (1)

## syle (638903) | more than 11 years ago | (#5424364)

## Re:Okay, assuming this proof to be correct... (2, Insightful)

## patrixx (30389) | more than 11 years ago | (#5424259)

So mr Pytagoras you say that if one multiply the radius of a circle with two and then by approxymatley 3.14 one gets the size of that circle. Of what practical use is it again?? Anyone?

## Re:Okay, assuming this proof to be correct... (0)

## Anonymous Coward | more than 11 years ago | (#5424264)

and may very well hold one of the keys to defining the states of symmetry in a vacuum and also providing reasons for the zero point of that vacuum. I think that is the coorect interpretation of the data someone correct me if I'm wrong.

## Re:Okay, assuming this proof to be correct... (0)

## Anonymous Coward | more than 11 years ago | (#5424270)

ST is a broadsword of mathematics, it sounds very obscure when you read it but it is profoundly powerful. Read aboud the Riemann's Zeta function some time and tell me you're not fascinated. For starters, it provides a way to estimate a value of the totient function of Euler. If I'm not mistaken there are attacks on RSA that stem from RH also.

## Re:Okay, assuming this proof to be correct... (2, Interesting)

## Qzukk (229616) | more than 11 years ago | (#5424290)

Is it getting more practical now? No?

Modern electronic encryption uses prime numbers to work. Large prime numbers. Prime numbers that are currently "unguessable" without lots of brute force.

And if the function is truly solved, now they're all in a straight line.

## Re:Okay, assuming this proof to be correct... (2, Insightful)

## Anonymous Coward | more than 11 years ago | (#5424293)

provingthe Riemann Hypothesis and thus putting it beyond any doubt (which experimental verification never can). It's applications are immense, but already exist.## Re:Okay, assuming this proof to be correct... (4, Interesting)

## arvindn (542080) | more than 11 years ago | (#5424310)

However, what is discovered today may find application 50 or 100 years or even centuries later. As an example, consider Hardy's quote in the "Mathematician's Apology":It is undeniable that a good deal of elementary mathematics-- and I use the word 'elementary' in the sense in which professional mathematicians use it, in which it includes, for example, a fair working knowledge of the differential and integral calculus) has considerable practical utility. These parts of mathematics are, on the whole, rather dull; they are the parts which have the least aesthetic value. The 'real' mathematics of the 'real' mathematicians, the mathematics of Fermat and Euler and Gauss and Abel and Riemann, is almost wholly 'useless'(and this is as true of 'applied' as of 'pure' mathematics. It is not possible to justify the life of any genuine professional mathematician on the ground of the 'utility' of his work.Hardy says that pure mathematics is completely useless. The sweet irony is this: Hardy was a number theorist. In his time, no one could ever conceive that there would ever be any application of that field of mathematics. However, public key cryptography, which was born in 1976, is built on number theory, and is the foundation of modern information privacy and computer security. Immensely practical.

See how it works?

So no, no practical applications for you, but this would still (if correct) be a result of enormous impact.

## Re:Okay, assuming this proof to be correct... (0)

## Glytch (4881) | more than 11 years ago | (#5424356)

Of what practical use is it again?? Anyone?In plain, crude english, it means that public-key encryption is in

deepshit if it's solved.## oook (-1, Troll)

## Anonymous Coward | more than 11 years ago | (#5424124)

## Sooo... what is it exactly? (1, Insightful)

## Max Romantschuk (132276) | more than 11 years ago | (#5424134)

The URL to the hypothesis is: http://www.utm.edu/research/primes/notes/rh.html

The URL contains the word "primes".

Primes are essential to much of todays cryptography, like public key encryption.

But what does the hypothesis say, in laymans terms?

What are the practical implications?

Anyone?

## Re:Sooo... what is it exactly? (1)

## ShortSpecialBus (236232) | more than 11 years ago | (#5424151)

## Re:Sooo... what is it exactly? (0)

## Anonymous Coward | more than 11 years ago | (#5424174)

But what does the hypothesis say, in laymans terms?Nothing. I'm going to just assume that whatever the fuck this shit is talking about is way beyond explaination to the layman, even in laymen's terms.

On the other hand, next month is April. I wonder if this will be the cover story of next month's scientific journals. Heh heh

## Re:Sooo... what is it exactly? (2)

## kormoc (122955) | more than 11 years ago | (#5424316)

## Re:Sooo... what is it exactly? (1)

## glMatrixMode (631669) | more than 11 years ago | (#5424375)

## Well cool (0, Offtopic)

## Knightfall (558914) | more than 11 years ago | (#5424142)

Nothing useful to say, just wanted to mention that.

## Re:Well cool (1)

## Knightfall (558914) | more than 11 years ago | (#5424165)

## GREAT SCOTT!!! (5, Funny)

## siliconwafer (446697) | more than 11 years ago | (#5424154)

## Wow ... (3, Informative)

## shayborg (650364) | more than 11 years ago | (#5424156)

-- shayborg

## Not more attacks! (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5424158)

## On a related note.... (1, Funny)

## Boss, Pointy Haired (537010) | more than 11 years ago | (#5424161)

Point to a random cell, and shout "That should be a 3". Then turn and walk away just as quickly.

Really pisses them off.

## Re:On a related note.... (0, Offtopic)

## GlassUser (190787) | more than 11 years ago | (#5424323)

## No one noticed this? (5, Interesting)

## epong (561351) | more than 11 years ago | (#5424167)

The arXiv will post nearly anything that resembles a mathematical paper-they don't do any refereeing. However, they apparently use the "general mathematics" section for papers that seem crankish like this one. And the fact that it took more than six months for this proof to make the news is proof that absolutely no one reads that section.

I haven't looked at the proof yet, but I'm worried that it will be at best a "physicist's proof"-a series of claims deduced by using some sort of physical reasoning that is not mathematically rigorous, since it seems to have been written by physicists, and is in the physics section.

## Svedish Noospapers (1)

## ackthpt (218170) | more than 11 years ago | (#5424172)

Swedish newspaper is the only one to take up the story yetDoes any US paper have a decent Science section? There's a Technology section in the SJ Murky News, but it seems more a mouthpiece for pushing the latest technotoys.

## Sciencemag.org (1)

## NoCoward (648971) | more than 11 years ago | (#5424272)

You will want to subscribe to this: www.sciencemag.org

Newspapers are there to report on news relevant to the average person...

## Translation (4, Funny)

## Quixote (154172) | more than 11 years ago | (#5424176)

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He am declaring that certainof Hilberts problem rather is problemområden than separate problem. A bit had also word if under these term as gone. If now Riemannhypotesen is absolved so is tens of they 23 problems absolved, seven is olösta, five is part absolved and one is nots inferior current.Under Andes Karlqvist each Hilbert really grand within sits precinct, with him was concluding a epok. He each the lastly as had survey over heal the mathematical science.

Mathematics have the latestdecade deployed very quickly, and the cheers article one aid as it olds 1900- digits mathematics nots be able anticipate datorn. Day all prompt and major datorer able manipulate huge amount speech and on short term make computations as formerly each impossible for a mans although he/ she was working a good deal currency with sina figure.With datorernas helphad certain problem absolved, as fyrfärgsproblemet. The says that the nots ring up to more than four various colours for that färglägga a maps so that nots area with a common limit had same colour. One datorprogram had systematic gone through all conceivable alternative.Andes Karlqvist deem yetthat the find one philosophy dilemma with this: inquiring is if husband bark accept evidence in form of one datorprogram. He am believing that wes now am standing before one kulturskifte within mathematics. Wonder the next decade am arriving the that evolve radically, and the because they all efficient datorerna.Bengal Jonsson

## Re:Translation (1)

## forgoil (104808) | more than 11 years ago | (#5424204)

For everybody else, I speak Swedish as well, and it so sounds like a Swede who can't speak proper English, and adding Swedish words in the middle of everything.

No offense to the original poster, and bork bork bork everyone.

## Re:Translation - FAKE (-1, Offtopic)

## Anonymous Coward | more than 11 years ago | (#5424226)

There isn't a single "bork" here.

## From a Swede (4, Informative)

## Anonymous Coward | more than 11 years ago | (#5424233)

Slashdot them to hell. It's my university, they can take it.

## real translation - mod parent up (0)

## Anonymous Coward | more than 11 years ago | (#5424274)

## Re:Translation (1, Funny)

## Anonymous Coward | more than 11 years ago | (#5424342)

## One explanation (1)

## Hao Wu (652581) | more than 11 years ago | (#5424177)

It's not a proof exactly, but it should be convincing if you follow the method visually. Draw a graph on paper and practice yourself, you will see.

## Re:One explanation (0)

## Anonymous Coward | more than 11 years ago | (#5424377)

## New Businessplan?! (-1, Funny)

## zensonic (82242) | more than 11 years ago | (#5424185)

Q.E.D!

## Re:New Businessplan?! (-1)

## Anonymous Coward | more than 11 years ago | (#5424246)

## Re:New Businessplan?! (0)

## agilen (410830) | more than 11 years ago | (#5424250)

1. Write complex math that nobody understands.

2. Say it solves complex problem that everyone assumes is true but nobody could prove before.

3. Get it verified by the mathematics community.

4. Win $1 million.

5. Profit....see step 4.

## New karma plan? (-1)

## Anonymous Coward | more than 11 years ago | (#5424268)

2.

3. Karma!

## You can help (4, Interesting)

## Slightly Askew (638918) | more than 11 years ago | (#5424187)

## Re:You can help (2, Insightful)

## turgid (580780) | more than 11 years ago | (#5424247)

## Re:You can help (2, Insightful)

## Alranor (472986) | more than 11 years ago | (#5424335)

You might want to mention that to the people who finally proved the 4 colour conjecture a few years back then.

And anyway, even if you couldn't find a proof of this theorem through pure number crunching, you may be able to find a counter-example, which would be equally interesting.

## Re:You can help (1)

## stixman (119688) | more than 11 years ago | (#5424353)

In case you're tired of looking for UFOs with SETI, you can use your spare CPU cycles to help prove/disprove this hypothesis here## The proof is... (5, Funny)

## Anonymous Coward | more than 11 years ago | (#5424196)

## Don't get too excited yet... (5, Informative)

## kip3f (1210) | more than 11 years ago | (#5424202)

## point from the swedish article (1, Interesting)

## Anonymous Coward | more than 11 years ago | (#5424211)

Andwers Karlqvist believes that there's a philosophical dilemma; the question is whether one should accept proof in the form of a computer program.Aren't computer programs as fundamentally mathematical as "classic" mathematics? If the computer program yields a correct result (or conclusion, rather), why should it not be regarded as correct? It'll require human analysis to make sure that the result is correct, so I think his question is redundant; if it is a valid proof then it really shouldn't matter in what flavor it comes.

## Why not a computer program (1)

## sckienle (588934) | more than 11 years ago | (#5424319)

First, and probably the main reason, is that pure mathematicians do not think computers are mathematics. This is probably doubly so in the number theory area; where the people sometimes act like algebra isn't real mathematics....

Second, most computer programming languages cannot be "proven" themselves. This means, from a purely theoretical standpoint, that even if they produce the results desired, there is no way to "prove" that they really did what they were supposed to do. Or put another way, how can these author's prove that the "proof" isn't really the result of a programming error. Obviously, in the normal world, no one cares about this; if the program displays the correct graph, who cares whether it is really proven or not. But in the world of mathematical proofs, that sort of "slip-shod" work is really frowned upon. On the other hand, there are computer languages which are formally provable, so this may not matter depending on what the proof program was written in.

Finally, it looks much cooler to have a bunch of greek characters up on a white board then a computer monitor saying "Yup, it works."

## Not first millenium prize? (3, Interesting)

## levell (538346) | more than 11 years ago | (#5424215)

## Conjecture then, True now... (0)

## Anonymous Coward | more than 11 years ago | (#5424222)

What does showing that it's true actually get us? It's prime number theory, does it suddenly mean that we can crack asymetric cyphers based upon factoring primes?

Does it really give the real world any useful benefits, or is it just a "I can piss higher up the wall" competition for mathmaticians?

If it does have meaningful consequences: great, please tell us what they are.

otherwise: who really cares?

## Statement of the hypothesis (5, Informative)

## arvindn (542080) | more than 11 years ago | (#5424230)

Definition of the zeta function:There is something called Riemann's zeta function: it is a function of a single complex variable. It is defined as zeta(z) = 1^(-z)+2^(-z)+3^(-z)+... (ad infinitum) You can easily see that zeta(z), as defined, converges if and only if Re(z)>1 (real part of z). However, the function is defined for all complex z using something called the analytic continuation: basically there is a unique way to extend zeta(z) for re(z) < 1 in such a way that derivatives of all orders exist at all points.The hypothesis states that all (nontrivial) zeroes of the zeta function occur on the line Re(z) = 1/2.

If proved, it has immense implications in many areas of pure and applied mathematics. For instance, in number theory: it would say a lot about the distribution of prime numbers.

The stature of the problem can be seen from the fact that it was one of the 23 problems which would shape the mathematical progress of the 20th century that David Hilbert drew up in his lecture at the 1900 Paris congress of mathematicians.

## HINT: Go read the comments on the previous article (5, Informative)

## siliconwafer (446697) | more than 11 years ago | (#5424236)

by njj (133128) on Tuesday July 02, @12:05PM (#3808279)

(http://www.csv.warwick.ac.uk/~marem/

If you can't explain something in ordinary words to a layman, then you really don't understand it.

I'm about halfway through writing up my PhD thesis on some applications of homological algebra to knot theory and low-dimensional geometric topology (provisional title liber rerum dementiae, but it'll probably end up being called something more mathematically appropriate).

In principle, yes, I could explain the details of my research to a suitably motivated layman. But I suspect it would take rather a long time.

You see, and this really isn't meant to sound arrogant, supercilious, or dismissive, university-level mathematics is pretty damned difficult, and the details of most cutting-edge research really doesn't make sense until you've spent several years learning the background (the mindset, the language, the fundamental concepts).

My current area of research is essentially the applications of homological algebra to knot theory and low-dimensional geometric topology. To explain this to a non-mathematician, I'd first have to teach them a lot of background stuff (group theory, a bit of stuff about rings and modules, point set topology, basic algebraic topology (the fundamental group, (co)homology theory), some geometric topology (basic course in knot theory, some stuff about 3-manifolds), a bit of category theory, and some homological algebra (broad overview of the (co)homology theory of groups and algebras)).

It's taken me nearly nine years (3-year BA, 1-year MSc specialising in topology and knot theory, plus nearly five years doing a (part-time) PhD) to get to this point myself. If I were a bit cleverer (or didn't have a `proper' job as well) I might have been able to shave a couple of years off that.

My friend Steve has a physics degree. I managed, in ten minutes one evening, with much handwaving, to give him some idea of what my thesis is all about. It helped that he knew what a group was already though. But for me to explain it fully to him would probably necessitate him doing at least one mathematics degree first. And that's not really something I'd wish on one of my friends

Now this really isn't meant in an arrogant way, and I hope you won't read it like that, but Euclid was right: There is no royal road to geometry.

I can have a go at explaining the Riemann hypothesis, though. To fully understand what it's about and why it's so damned difficult you'll need to do an advanced course in complex analysis (which isn't my field either).

A complex number is a sort of two-dimensional number, which you can regard as a point in a plane (the `complex plane' or `argand diagram'). You add them together coordinate-wise, and you multiply them together in a weird manner which involves something which behaves like a `square root of -1' (engineers also like to think of it as a sort of 90-degree phase-shift operator, I'm told).

There's a particular function (`Riemann's zeta function') defined on the complex plane (it takes one complex number as input and returns one complex number). For some complex numbers (`the zeros of the function'), the value of this function is zero.

The `trivial' zeros occur at the points -2, -4, -6,

The `non-trivial' zeros (that is, all the other points for which zeta is zero) all seem to occur on the line parallel to the vertical axis that intersects the horizontal axis at +0.5. Indeed, nobody's ever found one which doesn't.

The Riemann Hypothesis is that *all* the non-trivial zeros lie on this line. It's known to be true for the first (large number which temporarily escapes me), but it turns out to be phenomenally difficult to prove that it's true in every case.

Now that's the basic idea, but it doesn't (and I can't - it's not my field) explain *why* it's so difficult that some of the greatest minds (Hardy, Littlewood, Ramanujan, etc) of the past 150 years have failed to prove it, and why the Clay institute are willing to pay a million dollars to someone who can.

- nicholas (we don't just sit around doing big sums, you know

## Grammer different? (1)

## KFury (19522) | more than 11 years ago | (#5424241)

## Re:Grammer different? (2, Informative)

## kfg (145172) | more than 11 years ago | (#5424339)

"Usage Note: Prove has two past participles: proved and proven. Proved is the older form. Proven is a variant. The Middle English spellings of prove included preven, a form that died out in England but survived in Scotland, and the past participle proven, a form that probably rose by analogy with verbs like weave, woven and cleave, cloven. Proven was originally used in Scottish legal contexts, such as The jury ruled that the charges were not proven. In the 20th century, proven has made inroads into the territory once dominated by proved, so that now the two forms compete on equal footing as participles. However, when used as an adjective before a noun, proven is now the more common word: a proven talent."

Go figure.

KFG

## Heh (3, Interesting)

## pclminion (145572) | more than 11 years ago | (#5424249)

The Riemann hypothesis isn't exactly the most practical of problems, but many people have spent decades working on it (and some have gone insane). It's good that it is finally put to rest.

## Re:Heh (0)

## Anonymous Coward | more than 11 years ago | (#5424324)

## Sadly... (0)

## Anonymous Coward | more than 11 years ago | (#5424284)

## Got Math? (0)

## Anonymous Coward | more than 11 years ago | (#5424294)

I may have flunked math, but I know a hottie if I see one [pajonet.com] .

News, all the friggin time [pajonet.com]

## This proof has already gone down in flames (5, Informative)

## King Babar (19862) | more than 11 years ago | (#5424299)

I know the editors of this site mean well, but what we have here is a link to a site that defines the Riemann Hypothesis in very abstract terms, a link to a LANL preprint from two completely unknown researchers

deposited there in November 2002, and a link to an obscure Swedish newspaper from almost two weeks ago, and no other supporting material. So my BS meter is running at 5.The odds that "this is the one!" given that pedigree would seem to be really tiny. But the clincher for me is the following web page dedicated to would-be proofs of the Riemnann Hypothesis [ex.ac.uk] whose important text is (and I quote):

And the Castro and Mahecha preprint (and another grandiosely titled preprint by Mahecha) is linked to from there. Now my BS meter is running at about 9. So now I check for messages abou this at deja.com in the sci.math group. [google.com] Read the thread yourself; it's pretty entertaining.

So, with my BS meter running at 11, the work having been submitted for coming up on 6 months, and no indication whatsoever that this is real, I suggest it is false.

And I also suggest that Slashdot might wish to consider contacting a real mathematician to filter their potential stories on mathematics, since I can't tell you the last time one of these "is X finally proven?" stories has panned out.

## An Explaination of what this means (5, Informative)

## MjDascombe (549226) | more than 11 years ago | (#5424306)

## I have proven the Sagat hypothesis (0)

## Anonymous Coward | more than 11 years ago | (#5424313)

Answer: "FUNK THAT!"

QED.

## Will some mathematician... (2, Interesting)

## stevens (84346) | more than 11 years ago | (#5424327)

## the real reason (0, Offtopic)

## digitalsushi (137809) | more than 11 years ago | (#5424344)

## sci.math, High Energy Physics? (2, Interesting)

## ariels (6608) | more than 11 years ago | (#5424347)

Note that the paper was submitted to the "High Energy Physics" archive, not the "Mathematics" archive. The abstract has some physics jargon, too. What this means for the proof I cannot say.

## Breaking Encryption? (1, Interesting)

## phorm (591458) | more than 11 years ago | (#5424350)

If it becomes simple to factor the product of prime numbers, current digital encryption software will be worthless.How does this make encryption software worthless? Being able to unfactor the primes wouldn't seem to me like it would automagically be the solution to cracking an encryption key, etc. Even a program could unencrypt a document by guessing various keys etc through prime factorization (I'm assuming that is what this is about), how would it know which solution is right?

## What is it good for? (3, Insightful)

## Anonymous Coward | more than 11 years ago | (#5424373)

How many prime numbers are there less than a given number.

It doesn't take much thought to work out why that would be handy in say cryptography.

But most complex maths starts for it's own sake. You build the tools in the knowledge that eventually someone is going to use them, and inevitably they always do.

I read about advances in nano-technology all the time. What's the point, no-one's using them? But without them now we wouldn't have cool stuff in 20 years. Same goes for maths. I would have thought nerds of all people would get that point.