In a statement released by the Federal University, Oye Ekiti (FUOYE), Nigerian lecturer Dr Enoch Opeyemi, who has previously worked on mathematical models for generating electricity from sound, thunder and Oceanic bodies, has become the fourth person in the world to resolve the Mathematics problem called the Riemann Hypothesis.
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The real part (red) and imaginary part (blue) of the Riemann zeta function along the critical line Re(s) = 1/2. The first non-trivial zeros can be seen at Im(s) = ±14.135, ±21.022 and ±25.011.
In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.
The Riemann hypothesis implies results about the distribution of prime numbers. Along with suitable generalizations, some mathematicians consider it the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis, along with Goldbach's conjecture, is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems; it is also one of the Clay Mathematics Institute's Millennium Prize Problems.
The Riemann zeta function ζ(s) is a function whose argument s may be any complex number other than 1, and whose values are also complex. It has zeros at the negative even integers; that is, ζ(s) = 0 when s is one of −2, −4, −6, .... These are called its trivial zeros. However, the negative even integers are not the only values for which the zeta function is zero. The other ones are called non-trivial zeros. The Riemann hypothesis is concerned with the locations of these non-trivial zeros, and states that:
The real part of every non-trivial zero of the Riemann zeta function is 1/2.
Thus, if the hypothesis is correct, all the non-trivial zeros 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.
This hypothesis is one of the seven Millennium Problems in Mathematics presented to the public by the Clay Mathematics Institute and provision of a solution comes with a $1million prize.
Dr Enoch presented the proof on November 11, 2015 at the International Conference on Mathematics and Computer Science held in Vienna, Austria, the same day which marked 156 years since the problem was presented by a German Mathematician in 1859.
“Dr Enoch first investigated and then established the claims of Riemann,” the school’s statement read. “He went on to consider and to correct the misconceptions that were communicated by Mathematicians in the past generations, thus paving way for his solutions and proofs to be established.”
“He also showed how other problems of this kind can be formulated and obtained the matrix that Hilbert and Poly predicted will give these undiscovered solutions. He revealed how these solutions are applicable in cryptography, quantum information science and in quantum computers.”
Only three people have been able to solve three out of the seven millennium problems in the past 16 years. Dr Enoch is the fourth.
Some of Dr Enoch’s work includes designing a prototype of a silo for farmers, discovering scientific ways of detecting and tracking people, and inventing methods by which oil pipelines can be protected from vandalism.
He is currently working on mathematical approaches to climate change.
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