Rutu Ladage
An adventure lover and philosopher, her affair with words began at a young age. You can find her scribbling away at all odd hours of the day (and night) and if not with her head buried deep inside a b ... Read More
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This is absolutely amazing! The Riemann Zeta Hypothesis, a puzzle which was set by a mathematician in a classroom 156 years back had remained unsolved till now. Multiple mathematicians and those interested in the subject tried solving it with many theories put forth. However, the puzzle remained unsolved. However, a Nigerian professor, Dr. Opeyemi Enoch has finally provided a solution to the puzzle ending the century and half long debate. The Riemann Zeta Hypothesis is one of the 7 Millenium Problems as decided by the Clay Institute. Dr. Opeyemi Enoch became the fourth mathematician to solve one of the 7 Millenium Problems, earning him a reward of a million dollars.
Riemann Hypothesis Image Credit: State and University Library Gottigen
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The Riemann Zeta Hypothesis had been proposed in 1859, by Bernhard Riemann. It was considered to be one of the most important unsolved puzzles of pure mathematics by mathematicians and many theories had been put forward to solve the puzzle. Dr. Opeyemi presented his solution at the International Conference on Mathematics and Computer Science in Vienna, Austria. It was quite symbolic as the solution he provided was exactly 156 years (on the same day and month) after the puzzle was first put forth. Dr. Opeyemi Enoch is a professor at Federal University, Oye Ekiti, Ekiti State. Talking of his achievement, the University issued a statement saying:
“Dr. Enoch first investigated and established the claims by Riemann. He went on to consider and correct the misconceptions that were communicated by mathematicians in past generations, thus paving the way for his solution and proof 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.”
Bernhard Riemann
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The 7 Millennium Problems were put forth by the Clay Institute in 2000 as they are some of the most difficult mathematical problems scientists have been grappling with since centuries. The 7 problem, of which 5 remain unsolved are:
Yang–Mills and Mass Gap
Experiment and computer simulations suggest the existence of a “mass gap” in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.
Riemann Hypothesis
The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann’s 1859 paper, it asserts that all the ‘non-obvious’ zeros of the zeta function are complex numbers with real part 1/2.
P vs NP Problem
If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.
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Navier–Stokes Equation
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
Hodge Conjecture
The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.
Poincaré Conjecture
In 1904 the French mathematician Henri Poincaré asked if the three dimensional sphere is characterized as the unique simply connected three manifold. This question, the Poincaré conjecture, was a special case of Thurston’s geometrization conjecture. Perelman’s proof tells us that every three manifold is built from a set of standard pieces, each with one of eight well-understood geometries.
Birch and Swinnerton-Dyer Conjecture
Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles’ proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.
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