Sir Michael Francis Atiyah has provided proof of the Riemann hypothesis and is now claiming the million dollar prize.
Sir Michael Francis Atiyah, the 89-year-old patriarch of British mathematics, an expert in topology and algebraic geometry, who has won many mathematical awards, including the Abel Prize and the Fields Medal, claims to have proven the famous Riemann hypothesis. The proof, which became known on September 24, 2018 at the Heidelberg Laureate Forum (HLF) in Germany, has already been published. It takes only 5 pages, of which the arguments relating directly to Sir Atiyah laid down in no more than 20 lines.
Here's the million dollar proof. For those who are able to understand it.
German mathematician Georg Friedrich Bernhard Riemann Bernhard Riemann formulated his hypothesis almost 160 years ago - in 1859. He believed that there is a certain pattern in the distribution of primes - those that are divisible by one and by themselves. Sir Atiyah seems to have found it - this very pattern. This greatly confused my colleagues, who were very skeptical about his proof. For example, all the more or less famous mathematicians who were contacted by the journalists of the popular magazine New Scientist declined to comment.
Bernhard Riemann, who puzzled mathematicians for almost 160 years in advance.
Atiyah himself expressed one more - no longer mathematical - hypothesis about the skeptics. Like, he guessed why they don't believe him. Because it is believed that mathematicians are productive at the age of 40. And he is already 89 years old.
Sir assures that he does not suffer from dementia. And the recognition that his proof is true is just around the corner. Together with a million dollars that are due for it.
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What else does a million dollars "shine" for?
In 1998, with funds from the billionaire Landon T. Clay, the Clay Mathematics Institute was founded in Cambridge (USA) to popularize mathematics. On May 24, 2000, the institute's experts chose seven of the most puzzling problems, in their opinion. And they assigned a million dollars each. The list was named Millennium Prize Problems - "Millennium Problems". The Riemann hypothesis is one of them.
The mathematicians now have the opportunity to make good money.
Of the seven "problems," if Sir Atiyah ultimately does not screw up because of his old age, five will remain:
1. Cook's problem
It is necessary to determine: whether the verification of the correctness of the solution of any problem can be more time-consuming than obtaining the solution itself. This logical task is important for specialists in cryptography - data encryption.
2. Birch and Swinnerton-Dyer hypothesis
The problem is related to solving equations with three unknowns raised to a power. You need to figure out how to solve them, regardless of the complexity.
3. Hodge hypothesis
In the twentieth century, mathematicians came up with a method to study the shapes of complex objects. Its essence is to use its simple "bricks" instead of the object itself. You need to prove that this is always permissible. And “the bricks assembled into a single whole represent a semblance of an object.
4. Navier - Stokes equations
The equations describe the air currents that keep objects in the air. For example, airplanes. Now the equations are solved approximately, according to approximate formulas. We need to find exact ones and prove that in three-dimensional space there is a solution of equations, which is always true.
5. Yang - Mills equations
There is a hypothesis in the world of physics: if an elementary particle has mass, then there is also its lower limit. But no one knows which one yet. It’s also necessary to get to him. It is possible that in order to solve such a complex problem, it will be necessary to create a "theory of everything" - equations that unite all forces and interactions in nature. Anyone who can do this will certainly receive the Nobel Prize.
The sixth problem was the Riemann hypothesis, and the seventh was the Poincaré conjecture. It was proved in 2003 by the Russian mathematician Grigory Perelman. For this, in 2006, he was awarded the International Fields Medal, which the mathematician refused. In March 2010, the Clay Mathematical Institute awarded Perelman a $ 1 million prize - all for the same proof. But he ignored her too.
According to Poincaré's hypothesis, a three-dimensional sphere is the only three-dimensional gizmo, the surface of which can be pulled into one point by some hypothetical "hypercord".
Jules Henri Poincaré suggested this in 1904. Perelman convinced everyone that the French topologist was right. And turned his hypothesis into a theorem.
The prime numbers continue to puzzle.
AT THIS TIME
Mathematicians have discovered mysterious complexity in prime numbers
Prime numbers - 2, 3, 5, 7, and so on, divisible by one and themselves without remainder, are the basis of arithmetic and all natural numbers. That is, those that arise naturally when counting objects, such as apples.
Any natural number is the product of some prime numbers. And those and others - an infinite number.
Prime numbers other than 2 and 5 end in 1, 3, 7, or 9. They were believed to be randomly distributed. And a prime number ending in, for example, 1 can with equal probability - 25 percent - be followed by a prime number that ends in 1, 3, 7, 9.
It suddenly occurred to two American mathematicians, Kannan Soundararajan and Robert Lemke Oliver of Stanford University in California, to check this out. They went over several hundred million primes. And it turned out that there is still a certain pattern in their following - some appear more often, while others less often.
The calculations showed that two primes that end in 1 follow each other 18.5 percent of the time. 30 percent of the time, after a prime number ending in 3, there is a prime number ending in 7. And after 22 percent of primes ending in 1, there are numbers ending in 9.
Cannan and Robert do not yet understand the meaning of the phenomenon they identified, but they consider it very strange.
- This should not be, - scientists are surprised. And they believe that it is worth taking a closer look at other mathematical concepts that seem to be unshakable.
VLADIMIR LAGOVSKY
