Michael Atovigba, a Mathematics lecturer at the Benue State University recently proved the elusive Riemanns Theory in Mathematics, a puzzle that has remained unresolved in 262 years. In this interview with SIMEON NWAKAUDU, Atovigba who has been acclaimed internationally speaks about himself, his motivations, the use of the theory and his frustrations.
WHAT is the detailed background of the Riemann Hypothesis mathematical puzzle?
The Riemann Hypothesis is a statement about the Riemann zeta function where for i imaginary and real numbers. Here, s is the set of analytic zeros or continuations of the zeta function. According to Riemann, the behaviour of prime numbers resembles the values of this zeta function. From the zeta function, Riemann stated his hypothesis that and that all = 0 must fall on this line: The interpretation of the hypothesis is that all the analytic zeros up to the largest number which is infinity must be tested to fall on this critical line . What happened was that many mathematicians and scientists developed computer programmes that tested the hypothesis with several analytic zeros up to tens of billions and they were found to fall on the critical line. However, the computer was unable to test the hypothesis up to infinity. I therefore manually tested the hypothesis at infinity using a simplistic approach, which worked and gave zero, thus concluding the search for the resolution of the hypothesis, thus the hypothesis can now be called the Riemann Theory, or even the Riemann-Atovigba Theory since I am the one who has proved it.
What triggered your interest in trying to resolve the said hypothesis?
As graduate assistant I was asked to assist Mr. Avar Tsue who was indisposed at that moment and he gave me Mathematics Methods to teach. The course involves mathematics history from which the structure and process and products of mathematics have emanated to the present standard. I preferred good research and teaching to enable my students to have a good perspective of mathematics education, so I indulged in browsing since the library is inadequate. It was then that I stumbled over the century old mathematics conjectures that have defied resolution all this while from which seven were penciled down as Millennium Open Prize problems in 2000 attracting $1million each to their solvers. I downloaded them so that I might attempt them after semester examinations. What triggered me into resolving the Riemann Hypothesis was that, the analytic zeros were the form I obtained in my masters dissertation which was keenly supervised by Dr. Emmanuel O’Kwu of Benue State University and externally examined by Dr Usman from University of Nigeria Nsukka, in which I demonstrated a simplistic approach of calculating quadratic zeros from the data analysis tools of mean and mean deviation. The Riemann Hypothesis further intrigued me from the fact that I had earlier on the Epistemology Google Group tried resolving the two frames of reference of quarks and electrons into a single second order homogeneous ordinary differential linear energy equation, and I used my dissertation with the mean and mean deviation approach to obtain its auxiliary equation, an exercise that my former lecturer Dr Moses Chiawa joined me to research into and which we jointly presented before the Mathematical Association of Nigeria MAN national conference at Lafia in 2010. The energy equation proved to be a launching pad for explaining the source of the Riemannian analytic zeros containing. This realization spurred me into working toward further resolving the Riemann Hypothesis.
How were you able to resolve the hypothesis and what methods did you adopt?
I was stuck after being able to appreciate the possible origin of the Rieman Hypothesis’ analytic zeros. I say possible origin, because the energy equation has to do with quarks and electrons’ speeds and energies generated, and when infused into the Riemann Hypothesis, the hypothesis turns a tool of thermodynamic analysis and of electrodynamism. However, the analytic zeros as stated by Riemann could apply in other situations like the social sciences and the general real life phenomena. The origin could be from somewhere else! and not from electrons and quarks. But the origin is immaterial in the proof of the hypothesis. I only tried to go the extra mile in order to help the scientific community to further examine the Riemannian thought so that much progress might be made on scientific works hanging because of non-resolution of the hypohtesis.
When I was stuck at this stage, I asked the Holy Spirit to help me. Even Riemann was close to God, from the history I read of him, and this hypothesis must have been given to him to immortalize his name owing to his devotion to God. The help came to me while at an all night service close to 11pm at Living Faith Church Makurdi Benue State. God led me into fraction simplification, which I learnt at Primary 4-7 long ago. Once I simplified the general term of the Riemann zeta function, it became glaring that my 200 Level elementary mathematics involving series convergence was handy. My former lecturer Mr. Peter Ugbem had taught us exhaustively on convergence and absolute convergence of series, and with that I found out that the Riemann Hypothesis had to converge absolutely using the ratio test. I further remembered lectures by my former lecturer Dr. Msugh Kembe on functions of functions f(g(x))} and realized that for the ratio test on Riemann Hypothesis would be a test on functions of functions of the type Un(t) since the hypothesis ultimately depends on t and not n. On the surface, it depends on increasing n, an issue which has deceived many great mathematicians into being unable to resolve it. In a deeper sense, the zeta function ultimately depends on t, and it is t that tends to infinity to cause the zeta function to converge to zero, which is the proof of the Riemann Hypothesis.
What challenges did you face while working on the hypothesis?
The challenge of resolving the Riemann Hypothesis was more intellectual than financial. First, I was surprised that the hypothesis had been there since my undergraduate days but none of my lecturers ever mentioned it to our hearing, and I neither stumbled over it until I started researching and teaching at the university. This is work that I should have solved in 2003 when I first appeared at the Mathematical Association of Nigeria MAN conference and presented 23 theorems. It is one of those theorems that I later used to develop into my dissertation at the masters which provided insight into the analytic zeros of the Reimann zeta function. On stumbling into the hypothesis, I faced the challenge of accessing related literature, which was lacking locally and I had to browse extensively to see what attempts were made to resolve it. It was most discouraging when great mathematicians like Professors Gauss, Minkowski, Hilbert, Polya and Selberg were unable to resolve the conjecture and when most concluded that it was impossible to prove the hypothesis. If you are not hardened of heart you might say goodbye to the research, which looked like chasing a wild goose. But on critical examination, using Polya’s problem solving approach of trying to understand the problem, I found out it was a series of a function of a function. After that stage, again I was stuck and went into the Polyan incubation period, to allow ideas to roam in my brain. I prayed to God to help me, and behold, Daniel 11.32 is right, that they that know their God shall be strong and do great exploits! God spoke to me to go to primary school arithmetic of fraction simplification. I did not really face financial challenges.
Governor Gabriel Suswam had earlier on donated to me a laptop computer while I was his SSA, which I used in my browsing and research work – and it is in this regard that I acknowledged him in the work. The Clay Mathematics Institute which instituted the Millennium Prizes in mathematics require that any claimed resolution of any of the conjectures must first be published in a reputable international journal, and when I proved the hypothesis I sent it to the Maxwell Science Organization based in Pakistan and UK and it was peer reviewed and published in the Research Journal of Mathematics and Statistics (www.maxwellsci.com). I was asked to pay $150 only after it was accepted for publishing, which I paid from my monthly salary. .
Why do you think the other mathematicians and scientists found it difficult to resolve the Riemann Hypothesis after 262 years?
In my opinion, past mathematicians and scientists failed to prove the hypothesis because they did not seek God’s face and God closed their minds and they got using advanced approaches, which could not help matters. I also opine that they did not solve it because as I saw their attempts they did not simplify the zeta function into a proper fraction. I also noticed that they never treated the Riemannian zeta function as a series of the Un(t) type and wasted energies on n, rather than t which makes the function to decay faster. I feel also, that they failed to resolve it out of spinelessness, because they probably felt it was impossible to resolve the hypothesis since big goons like George Boole, Hermann Minkowski, David Hilbert, Polya, Selberg and even Gauss who was Riemann’s teacher and who is tagged till date as the prince of mathematics were unable to solve it. They did not persevere.
What are the implications of your success in resolving this hypothesis for the international community and Nigeria?
The implications of resolving the Riemann Hypothesis were long anticipated and can be obtained on browsing. However, I can say confidently that the Riemann Hypothesis or theory has application throughout science, mathematics and technology.
For instance, without proving it one of Riemann’s disciples George Boole invented from it the 0 and 1 or Boolean algebra which has torpedoed into computer science. The hypothesis can be used to shed light on computer science. I have already used it to resolve the computer science theory: P=NP? which has also been published in the Research Journal of Mathematics and Statistics. Granted the use of quarks and electrons as sources of analytic continuation, then the Riemann Theory is the resolution of the two frames of reference in Einstein’s relativity theory. After all, Einstein depended on Riemann’s recommendations that parallel lines do not exist as is in the Euclidean sense but that in the Riemannian geometry the so called parallel lines meet at a point to infinity and can be conformally mapped into the upper half of the plane as a unit circle.
You have also resolved the computer science theory P=NP, what is this about and what are its implications for the world?
P=NP? Is a conjecture on whether an algorithm can be found containing n strings that are executable in t time (called polynomial time or very fast time) within which a configured computer can verify any problem’s solution as fast as it can solve the problem? The computer science theory can be traced back to George Boole who invented the Boolean algebra, which has finally been put into reality as computer science, and Boole depended on Bernhard Riemann’s Hypothesis; hence it was home for me to naturally resolve the computer science theory using the general term of the Riemann zeta function. The proof suggests a Turing Machine (algorithm that a machine can use) with which super computers can be configured to perform tasks at extraordinarily fast speeds. Such computers can send spaceships to their fastest lanes for most efficient space shuttling that can veer to uttermost reaches of the universe to scoop information. Thus proof of P=NP? Takes man into an entirely new era of super computers and super-information gathering about every material thing the universe contains.
What nature of grants or support have you attracted since you started several works on mathematical and scientific issues?
I have attracted no grants whatsoever. I applied for ETF grants in order to resolve the P=NP? But the ETF committee at Benue State University has not allowed it to see the light of the day.
source: Nigerian Guardian Newspapers
Much kudos to the mathematician!
The best part of the above article is that it is the Holy Spirit that revealed the solution to Mr. Michael. I wonder why Nigerians like spiritualizing very simple things!