# Kazakhstan citizen claims solving Riemann hypothesis

23 september 2013, 16:04
Yessenbek Ushtenov, a mechanical engineer from Saryagash town, Kazakhstan, claims to to have solved one of the seven problems of the millennium, the Riemann hypothesis, Alau-Kazakhstan public-political magazine writes.

The zeta function was proposed by Bernhard Riemann who extended Euler's function based on the harmonic sequence. One of the shortest way to formulate the hypothesis is: "The real part of every non-trivial zero of the Riemann zeta function is 1/2. Thus the non-trivial zeros should lie on the critical line consisting of the complex numbers 1/2 + i t, where t is a real number and i is the imaginary unit. The function has no other zeros." It took Ushtenov three years to prove this statement.

The magazine writes that the secret of the amateur mathematician's success is that he did not go along the beaten path and found his own way that had never been used in the numbers theory before.

Ushtenov has frequently published his works in European scientific magazines before. So he is expecting the global scientific community to take his work that he plans to finish by 2018 seriously, the magazine writes.

The mechanical engineer was born in Uzbekistan. He spent most of his childhood in hospitals as he had to undergo over a dozen of surgeries because of his health problems. Later he graduated from Tashkent Polytechnical Institute. He then worked as a design engineer at the tractor plant. In 2000 he moved to Kazakhstan. In 2010 he and his daughter tried to get into the Guinness World Book of Records by finding and calculating the largest Mersenne prime number containing 100,021,321 digits, but Kazakhstan professors did not support this initiative.

Speaking about his current project he said: "I should be able to finish it by 2018,but if I got some grant and conditions to work on it, I could do the job earlier. I am sure about my algorithm of solving of the Riemann's hypothesis: this is a new direction in the numbers theory."

The magazine explained that in case any inaccuracy is discovered in Ushtenov's work, other scientists of the global community will be able to correct the mistake and assign authorship of the solution of the Riemann's hypothesis to themselves, as it has been done several times before in the international practice. That is why the mathematician is not rushing to bring his work for his colleague's review. He is now getting help from a senior professor of South Kazakhstan oblast's Kaplanbek Humanitarian Agroeconomic College Ablakhat Khamitov.

"Imagine that the Riemann's hypothesis is the hexagonal cube with every side of it being a certain sum of general knowledge in a specific possible approach to solving this problem. Whichever side of this cube the scientists approached from, they could only see three of its adjacent sides, while the three other sides remained on the invisible side. Solving this hypothesis requires an algorithm that allows to see the whole cube at the same time. In the other words, it can be solved not through the sum of the general knowledge accumulated over the years but through an ability to develop the right algorithm," Ushtenov said.

"Would it be wise to make a wheel wrench and a tire jack that weigh 80kg to replace the wheel of a sedan car? Certainly not. This is a crude example, but this is basically how most of the scientists approach the solution of the problem. Riemann's zeta function establishes a relation between its zeros and the distribution of prime numbers. My method simplifies the traditional approach to solving of the problem by dozens of times," the mathematician said.

In 1900 German mathematician David Hilbert presented a 23 problems that set the course for much of the mathematical research of the 20th century at the Paris conference of the International Congress of Mathematicians. 16 of these problems were solved by the end of the century. 2 of them were taken off the list for being too vague to be stated resolved or not. The other 5 problems remain unsolved.

The zeta function was proposed by Bernhard Riemann who extended Euler's function based on the harmonic sequence. One of the shortest way to formulate the hypothesis is: "The real part of every non-trivial zero of the Riemann zeta function is 1/2. Thus the non-trivial zeros should lie on the critical line consisting of the complex numbers 1/2 + i t, where t is a real number and i is the imaginary unit. The function has no other zeros." It took Ushtenov three years to prove this statement.

The magazine writes that the secret of the amateur mathematician's success is that he did not go along the beaten path and found his own way that had never been used in the numbers theory before.

Ushtenov has frequently published his works in European scientific magazines before. So he is expecting the global scientific community to take his work that he plans to finish by 2018 seriously, the magazine writes.

The mechanical engineer was born in Uzbekistan. He spent most of his childhood in hospitals as he had to undergo over a dozen of surgeries because of his health problems. Later he graduated from Tashkent Polytechnical Institute. He then worked as a design engineer at the tractor plant. In 2000 he moved to Kazakhstan. In 2010 he and his daughter tried to get into the Guinness World Book of Records by finding and calculating the largest Mersenne prime number containing 100,021,321 digits, but Kazakhstan professors did not support this initiative.

Speaking about his current project he said: "I should be able to finish it by 2018,but if I got some grant and conditions to work on it, I could do the job earlier. I am sure about my algorithm of solving of the Riemann's hypothesis: this is a new direction in the numbers theory."

The magazine explained that in case any inaccuracy is discovered in Ushtenov's work, other scientists of the global community will be able to correct the mistake and assign authorship of the solution of the Riemann's hypothesis to themselves, as it has been done several times before in the international practice. That is why the mathematician is not rushing to bring his work for his colleague's review. He is now getting help from a senior professor of South Kazakhstan oblast's Kaplanbek Humanitarian Agroeconomic College Ablakhat Khamitov.

"Imagine that the Riemann's hypothesis is the hexagonal cube with every side of it being a certain sum of general knowledge in a specific possible approach to solving this problem. Whichever side of this cube the scientists approached from, they could only see three of its adjacent sides, while the three other sides remained on the invisible side. Solving this hypothesis requires an algorithm that allows to see the whole cube at the same time. In the other words, it can be solved not through the sum of the general knowledge accumulated over the years but through an ability to develop the right algorithm," Ushtenov said.

"Would it be wise to make a wheel wrench and a tire jack that weigh 80kg to replace the wheel of a sedan car? Certainly not. This is a crude example, but this is basically how most of the scientists approach the solution of the problem. Riemann's zeta function establishes a relation between its zeros and the distribution of prime numbers. My method simplifies the traditional approach to solving of the problem by dozens of times," the mathematician said.

In 1900 German mathematician David Hilbert presented a 23 problems that set the course for much of the mathematical research of the 20th century at the Paris conference of the International Congress of Mathematicians. 16 of these problems were solved by the end of the century. 2 of them were taken off the list for being too vague to be stated resolved or not. The other 5 problems remain unsolved.

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