Tuesday, September 07, 2004

Million dollars

Two of the seven million dollar challenges that have baffled Mathematicians for more than a century *may be* close to being solved.

First. The hypothesis formulated by Georg Friedrich Bernhard Riemann in 1859 is one of them. Marcus du Sautoy of Oxford University, said "Most mathematicians would trade their soul with Mephistopheles for a proof". The Riemann hypothesis would explain the apparently random pattern of prime numbers. He observed that the frequency of prime numbers is very closely related to the behavior of an elaborate function “z(s)” called the Riemann Zeta function. The Riemann hypothesis asserts that all interesting solutions of the equation

z(s) = 0

lie on a straight line. This has been checked for the first 1,500,000,000 solutions.

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.

Second. Poincare conjecture. If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two dimensional sphere is essentially characterized by this property of simple connectivity, and asked the corresponding question for the three dimensional sphere (the set of points in four dimensional space at unit distance from the origin). This question turned out to be extraordinarily difficult, and mathematicians have been struggling with it ever since.

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.

If you want 7 million dollars :
Visit : http://www.claymath.org/millennium
and of course forward this to 10 more of your friends to show how much you care for them.

Sardarji's are smarter nowadays. Atleast in jokes.

"Help.... the Titanic is sinking ...."

Everybody in the ship is shouting, crying, running or praying to God... Just then an Italian asks a Sardarji in the ship

Italian : How far is land, from here?

Sardarji : Two miles .

Italian : Only two miles, Then why are these fools making so much noise ?
Anyways, i am a professional swimmer..

The Italian jumps off the ship into the sea and comes up to the surface
to ask something again.

Italian : Just tell me which side, is land two miles from here ?

Sardarji : Downwards ...

--------------------------------

A Sardar died and went to heaven. When he got to the pearly gate Saint
Peter told him that new rules were in effect due to the advances in
education on earth. In order to gain admittance a prospective heavenly
soul must answer two questions:

1. Name two days of the week that begin with "T".
2. How many seconds are there in a year?

The Sardar thought for a few minutes and answered...

1. The two days of the week that begin with "T" are Today and
Tomorrow.

2. There are 12 seconds in a year.

Saint Peter said, "OK, I'll buy the Today and Tomorrow,
even though it's not the answer I expected.
But how did you get only 12 seconds in a year?"

The Sardar replied, "Well, January 2nd, February 2nd, March 2nd,
etc...." Saint Peter lets him in without another word


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