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| Riemann hypothesis solve |
We have always listened that nothing impossible in this
world. It also proved in practical by Sir Michael Atiyah. One of the world's
most renowned mathematicians showed how he solved the 160-year-old Riemann
hypothesis at a lecture on Monday - and he will be awarded $1 million if his
solution is confirmed.
Sir Michael Atiyah, who has won the two biggest prizes in
mathematics - the Fields Medal and Abel Prize - took the stage at the
Heidelberg Laureate Forum in Germany on Monday to present his work.
To solve the hypothesis you need to find a way to predict
the occurrence of every prime number, even though primes have historically been
regarded as randomly distributed.
Aityah's solution will need to be checked by other
mathematicians and then published before it is fully accepted and he can claim
the prize from the Clay Mathematics Institute of Cambridge.
The Riemann hypothesis is one of seven unsolved
"Millennium Prizes" from CMI, each worth $1 million to the person who
solves it.
What is the Riemann hypothesis, and how did Atiyah solve it?
The Riemann hypothesis was first posited by Bernhard Riemann
in 1859.
It attempts to answer an old question about prime numbers
(numbers that divide only by themselves and 1.) The hypothesis states that the
distribution of primes is not random, but might follow a pattern described by
an equation called the Riemann zeta function. 10,000,000,000,000 prime numbers
have been checked and are consistent with the equation, but there is no proof
that all primes follow the pattern.
So, the $1 million prize goes to someone who can prove that
the equation applies to all prime numbers. And Atiyah, using a "radically
new approach" to the hypothesis, according to his explanation of his
solution, thinks he has done it.
Markus Pössel, an astrophysicist in Heidelberg, Germany,
live-tweeted Atiyah's lecture and helped clarify the mathematician's process:
Atiyah said in the lecture that he used work from John von
Neumann and Friedrich Hirzebruch to help him on his way to solving the problem.
Mathematician Keith Devlin wrote in 1998: "Ask any
professional mathematician what the single most important open problem in the
entire field is, and you are almost certain to receive the answer 'the Riemann
hypothesis."
Atiyah has also served as president of the London
Mathematical Society, the Royal Society, and the Royal Society of Edinburgh.
Riemann hypothesis
First published in Riemann's groundbreaking 1859 paper
(Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which
states that the nontrivial Riemann zeta function zeros, i.e., the values of s
other than -2, -4, -6, ... such that zeta(s)=0 (where zeta(s) is the Riemann
zeta function) all lie on the "critical line" sigma=R[s]=1/2 (where
R[s] denotes the real part of s).
A more general statement known as the generalized Riemann
hypothesis conjectures that neither the Riemann zeta function nor any Dirichlet
L-series has a zero with real part larger than 1/2.
In 2000, the Clay Mathematics Institute
(http://www.claymath.org/) offered a $1 million prize
(http://www.claymath.org/millennium/Rules_etc/) for proof of the Riemann
hypothesis. Interestingly, disproof of the Riemann hypothesis (e.g., by using a
computer to actually find a zero off the critical line), does not earn the $1 million
award.
In 1914, Hardy proved that an infinite number of values for
s can be found for which zeta(s)=0 and R[s]=1/2 (Havil 2003, p. 213). However,
it is not known if all nontrivial roots s satisfy R[s]=1/2. Selberg (1942)
showed that a positive proportion of the nontrivial zeros lie on the critical
line, and Conrey (1989) proved the fraction to be at least 40% (Havil 2003, p.
213).
Now it is completely solved by Sir Michael Atiyah, 160-year-old
Riemann hypothesis & Sir Michael proved that nothing impossible in this
world.
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