Text 497, 173 rader
Skriven 2004-09-08 10:27:44 av Adam Flinton (1:379/45)
    Kommentar till text 489 av Rich Gauszka (1:379/45)
Ärende: Re: Math hypothesis solution = internet disaster?
=========================================================
From: Adam Flinton <adam_NO_@_SPAM_softfab.com>

I saw this. We "lost" someone over this. We had a very bright
mathematician/software writer from the Russian equiv of NASA come to us with a
program which could solve NP complete problems in a quite startling way.
Normally the result is what's called a "strawberry field" i.e. there are many
"most possibles" (the strawberries) each of which must be picked & examined.
His s/w / maths didn't do this.

The problem was that as noted the obvious NP complete problem is the encrypted
message/password. Suddenly a lot of people with leather jackets took a great
deal of interest in him as did the FSB. However he didn't want to work for the
mafia or state security but the FSB said they'd only protect him if he worked
for them.

So we shipped him in secret to Sweden. However.....3 weeks after he got there
everything went quiet & neither I nor his family have ever heard from him
again.

The whole thing completely put me off serious maths as there is a large
personal safety factor which must be bourne in mind.

Adam


Rich Gauszka wrote:
> http://www.guardian.co.uk/uk_news/story/0,3604,1298728,00.html
>
> Maths holy grail could bring disaster for internet
>
> Two of the seven million dollar challenges that have baffled for more than a
> century may be close to being solved
>
> Mathematicians could be on the verge of solving two separate million dollar
> problems. If they are right - still a big if - and somebody really has
> cracked the so-called Riemann hypothesis, financial disaster might follow.
> Suddenly all cryptic codes could be breakable. No internet transaction would
> be safe.
> On the other hand, if somebody has already sorted out the so-called Poincaré
> conjecture, then scientists will understand something profound about the
> nature of spacetime, experts told the British Association science festival
> in Exeter yesterday.
>
> Both problems have stood for a century or more. Each is almost dizzyingly
> arcane: the problems themselves are beyond simple explanation, and the
> candidate answers published on the internet are so intractable that they
> could baffle the biggest brains in the business for many months.
>
> They are two of the seven "millennium problems" and four years ago the Clay
> Mathematics Institute in the US offered $1m (œ563,000) to anyone who could
> solve even one of these seven. The hypothesis formulated by Georg Friedrich
> Bernhard Riemann in 1859, according to Marcus du Sautoy of Oxford
> University, is the holy grail of mathematics. "Most mathematicians would
> trade their soul with Mephistopheles for a proof," he said.
>
> The Riemann hypothesis would explain the apparently random pattern of prime
> numbers - numbers such as 3, 17 and 31, for instance, are all prime numbers:
> they are divisible only by themselves and one. Prime numbers are the atoms
> of arithmetic. They are also the key to internet cryptography: in effect
> they keep banks safe and credit cards secure.
>
> This year Louis de Branges, a French-born mathematician now at Purdue
> University in the US, claimed a proof of the Riemann hypothesis. So far, his
> colleagues are not convinced. They were not convinced, years ago, when de
> Branges produced an answer to another famous mathematical challenge, but in
> time they accepted his reasoning. This time, the mathematical community
> remains even more sceptical.
>
> "The proof he has announced is rather incomprehensible. Now mathematicians
> are less sure that the million has been won," Prof du Sautoy said.
>
> "The whole of e-commerce depends on prime numbers. I have described the
> primes as atoms: what mathematicians are missing is a kind of mathematical
> prime spectrometer. Chemists have a machine that, if you give it a molecule,
> will tell you the atoms that it is built from. Mathematicians haven't
> invented a mathematical version of this. That is what we are after. If the
> Riemann hypothesis is true, it won't produce a prime number spectrometer.
> But the proof should give us more understanding of how the primes work, and
> therefore the proof might be translated into something that might produce
> this prime spectrometer. If it does, it will bring the whole of e-commerce
> to its knees, overnight. So there are very big implications."
>
> The Poincaré conjecture depends on the almost mind-numbing problem of
> understanding the shapes of spaces: mathematicians call it topology.
> Bernhard Riemann and other 19th century scholars wrapped up the mathematical
> problems of two-dimensional surfaces of three dimensional objects - the
> leather around a football, for instance, or the distortions of a rubber
> sheet. But Henri Poincaré raised the awkward question of objects with three
> dimensions, existing in the fourth dimension of time. He had already done
> groundbreaking work in optics, thermodynamics, celestial mechanics, quantum
> theory and even special relativity and he almost anticipated Einstein. And
> then in 1904 he asked the most fundamental question of all: what is the
> shape of the space in which we live? It turned out to be possible to prove
> the Poincaré conjecture in unimaginable worlds, where objects have four or
> five or more dimensions, but not with three.
>
> "The one case that is really of interest because it connects with physics,
> is the one case where the Poincaré conjecture hasn't been solved," said
> Keith Devlin, of Stanford University in California.
>
> In 2002 a Russian mathematician called Grigori Perelman posted the first of
> a series of internet papers. He had worked in the US, and was known to
> American mathematicians before he returned to St Petersburg. His proof - he
> called it only a sketch of a proof - was very similar in some ways to that
> of Fermat's last theorem, cracked by the Briton Andrew Wiles in the last
> decade.
>
> Like Wiles, Perelman is claiming to have proved a much more complicated
> general problem and in the course of it may have solved a special one that
> has tantalised mathematicians for a century. But his papers made not a
> single reference to Poincaré or his conjecture. Even so, mathematicians the
> world over understood that he tackled the essential challenge. Once again
> the jury is still out: this time, however, his fellow mathematicians believe
> he may be onto something big.
>
> The plus: the multidimensional topology of space in three dimensions will
> seem simple at last and a million dollar reward will be there for the
> asking. The minus: the solver does not claim to have found a solution, he
> doesn't want the reward, and he certainly doesn't want to talk to the media.
>
> "There is good reason to think the kind of approach Perelman is taking is
> correct. However there are some problems. He is very reclusive, won't talk
> to the press, has shown no indication of publishing this as a paper, which
> you would have to do if you wanted to get the prize from the Clay Institute,
> and has shown no interest in the prize whatsoever," Dr Devlin said.
>
> "Has it been proved? We don't know. We have good reason to assume it has
> been and within the next 12 months, in the inner core of experts in
> differential geometry, which is the field we are speaking about, people will
> start to say, yes, OK, this looks right. But there is not going to be a
> golden moment."
>
> The implications of a proof of the Poincaré conjecture would be enormous,
> but like the problem itself, very difficult to explain, he said. "It can't
> fail to have huge ramifications: not only the result, but the methods as
> well. At that level of abstraction, that level of connection, so much can
> follow. Differential geometry is the subject that is really underneath
> understanding everything about space and spacetime."
>
> Seven baffling pillars of wisdom
>
> 1 Birch and Swinnerton-Dyer conjecture Euclid geometry for the 21st century,
> involving things called abelian points and zeta functions and both finite
> and infinite answers to algebraic equations
>
> 2 Poincaré conjecture The surface of an apple is simply connected. But the
> surface of a doughnut is not. How do you start from the idea of simple
> connectivity and then characterise space in three dimensions?
>
> 3 Navier-Stokes equation The answers to wave and breeze turbulence lie
> somewhere in the solutions to these equations
>
> 4 P vs NP problem Some problems are just too big: you can quickly check if
> an answer is right, but it might take the lifetime of a universe to solve it
> from scratch. Can you prove which questions are truly hard, which not?
>
> 5 Riemann hypothesis Involving zeta functions, and an assertion that all
> "interesting" solutions to an equation lie on a straight line. It seems to
> be true for the first 1,500 million solutions, but does that mean it is true
> for them all?
>
> 6 Hodge conjecture At the frontier of algebra and geometry, involving the
> technical problems of building shapes by "gluing" geometric blocks together
>
> 7 Yang-Mills and Mass gap A problem that involves quantum mechanics and
> elementary particles. Physicists know it, computers have simulated it but
> nobody has found a theory to explain it
>
>
>

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