This beautiful piece of writing and perhaps one of my best discoveries, is intended to give an al... more This beautiful piece of writing and perhaps one of my best discoveries, is intended to give an alternate but also a direct proof of the Fermat's last theorem. The theorem being one of the most popular, if not the most popular was also notorious for being one of the most difficult to prove. In 1994-about 357 years after it was first stated by Pierre de Fermat and accompanied with series of failed attempts from several mathematicians, came the supposed breakthrough, notably by Andrew Wiles¹. His approach required very sophisticated mathematical concepts in number theory, especially the modularity theorem². His approach however, isn't a actually a direct proof per se, it just happens to rely on the connection between distinct branches of mathematics (elliptic curves, modular forms and Fermat equation), just like Galois proof of the impossibility theorem relied on the connection between group theory and polynomial equations.
In this article, a different approach is utilized, somewhat unorthodox, as it requires new fundamental mathematical techniques which also happens to have implications for the philosophy and foundations of mathematics. The proof can be thought of as direct and it doesn't actually require much advanced mathematics as with the case of Wiles proof. The results established in this article could come in handy to proving other related theorems/conjectures and possibly advancing mathematics for the better.
A relatively short essay on the question of whether we actually invent things or if it's an illus... more A relatively short essay on the question of whether we actually invent things or if it's an illusion.
In our previous article in reference [1], we were able to reformulate Maxwell's equations in a si... more In our previous article in reference [1], we were able to reformulate Maxwell's equations in a simplified and microscopic form. This article on the other hand is a follow-up of the aforementioned article but in this case it is shown that gravity may have electromagnetic origins, using as basis this reformulated Maxwell's equations. As a matter of fact, it is suggested in this article that thorough experimental investigations with neutrons could help us really understand gravity fundamentally. This however is based on the fact that a certain property of neutrons was calculated in this article using the assumption of the electromagnetic origins of gravity and this calculated value seems to correspond with the data that was obtained from an experiment performed some time ago (over 50 years ago) by Shull et al-see the article in reference [2]. Also, the rotation curve of galaxies, especially the spiral ones is revisited and it's shown that the assumption of the electromagnetic origins of gravity can explain it. This paper may also be handy to those who seek a unified/single theoretical framework for all fundamental forces.
The essence of this article is show that all quintic equations are solvable algebraically in te... more The essence of this article is show that all quintic equations are solvable algebraically in terms of radicals just like the quadratic, cubic and quartic equations.
We present the basic principles of thermoelectricity and statistical electricity, this is some... more We present the basic principles of thermoelectricity and statistical electricity, this is somewhat analogous to the principles encountered in thermodynamics. Just like how J.W.Gibbs [1] derived the basic laws of thermodynamics from statistical mechanics, the same is done using statistical electricity and a differential equation derived from both the equations of thermal conductivity and electrical conductivity.This however would later be extended to quantum thermoelectricity, using Schrödinger's wave equation as basis.
Prior to the solutions to the particle equation given in the article titled '' Electromagne... more Prior to the solutions to the particle equation given in the article titled '' Electromagnetism as the key to understanding the quantum world '' , we make little corrections and derive the same solutions in a much more rigorous mathematical approach, as the technique used previously appears to be ill-defined for the mathematically inclined, the author is sorry for such inconveniences. Also we show that this particle equation which can be sometimes called the electromagnetic field equation allows superposition principle, this is very handy when one begins to talk about field/particle structure of many charged particles and also the Laplace transform is derived.
Over the years observations has been made based on only what we perceive physically,this has howe... more Over the years observations has been made based on only what we perceive physically,this has however limited our ability to think outside the box.In this article we shall see that by restructuring the foundations of classical electromagnetic theories ( introducing new parameters), quantum mechanics is given a strong footing and also throwing more light into how our physical universe was designed.
We present a short communication on a new kind of differential group(s) non-galois in nature and ... more We present a short communication on a new kind of differential group(s) non-galois in nature and are of great importance in the study of homogeneous ordinary linear differential equations of order > 1 with exact solutions, exact solutions to differential equations are of great importance in applied mathematics, computational chemistry and physics, most especially quantum physics. However, in this article emphasis is made only on homogeneous second order linear ordinary differential equations and the results in this article are extensions of the works treated in the articles in references (1) and (2). In fact, the techniques employed in reference (2) and in this article can be applied to homogeneous linear ordinary differential equations of order > 2.
The main aim of science is to know and to know is to better understand this paradoxical univer... more The main aim of science is to know and to know is to better understand this paradoxical universe of ours.Then there is technology whose aim is to apply what we know to make the world a better place. However there are questions we ask ourselves everyday that science, despite it's success, has not been able to fully answer, could it be that our approaches has gotten to it's dead end or that our ignorance has taken the most out of us. Two subfields of science has promoted radical questions that challenges our knowledge of existence and reality, and they are quantum mechanics and artificial intelligence, the former challenging our understanding of reality and the later challenging our understanding of what consciousness actually is. Scientists have made us to believe so many things, but what if at some point they were wrong, what if at the classical world we experience quantum mechanical principles like entanglement, what if there is actually a multiverse and that we access/visit them and what if the interpretations of quantum mechanics can be resolved. The big bang theory explains how our present universe came into be but fails to tell us what caused it and how life came into be, what if this can be resolved too. From a philosophical perspective, what if consciousness and it's hard problems can be understood and resolved and lots more of what ifs. Get to find out ?, then get ready to get your minds blown 😱, as we explore these possibilities and resolve some of these paradoxical questions, using a novel approach that is not wildly known. But first you need to remember this '' The laws of the universe need not be complicated, all that is required are the right ingredients '' .
In this article the Maxwell's electromagnetic equations are reformulated in a simplified form, th... more In this article the Maxwell's electromagnetic equations are reformulated in a simplified form, this reformulation is as a result of the limiting case of the generalised particle equation, taking into account charge and current density/distribution and it is shown to be equivalent to the conventional Maxwell's equations in microscopic form.
In this article we show that the particle equation solution presented in the articles in referenc... more In this article we show that the particle equation solution presented in the articles in references 1, 2 and 3 is an approximate solution to a much more generalised equation of which is easily reduced to the modified Bessel equations. We shall see that the solution gotten from the generalised equation (modified Bessel equation) is a superior form of that presented in the stated articles above, the same physical predictions exist in this new function. Also we show that the consequences of special relativity and the basic quantum mechanical principles are indeed derivable from the equation and its solutions.
In this article we extend the theories provided in the article in references 1, 2 and 3 in establ... more In this article we extend the theories provided in the article in references 1, 2 and 3 in establishing some properties of atoms, most especially electron arrangement and shape of orbitals. Lastly a new quantum number is predicted.
In this short article we present the origin of the half and whole spin quantum numbers encountere... more In this short article we present the origin of the half and whole spin quantum numbers encountered in quantum physics, this in general leads to two classes of particles which are the bosons and fermions. The origin is explained from the consequences of the mathematical treatment and theoretical proposal presented in the articles in references 1 and 2 below, i would urge us to study those articles very well if we want to understand the content of this article.
In this article the major foundational quantum mysteries are resolved using an alternative mathem... more In this article the major foundational quantum mysteries are resolved using an alternative mathematical reformulation of the basic principles of quantum mechanics, this reformulation is as a result of the theories established in the articles provided in references 1 and 2 below.
In this article we present a short communication on a new technique in addition to the numerical ... more In this article we present a short communication on a new technique in addition to the numerical root finders in seeking a root to some polynomial/algebraic equations of degree > 2.
In this article we present important theories of differential equations, most especially ordinar... more In this article we present important theories of differential equations, most especially ordinary differential equations in terms of exact general solution seeking, using the powerful tool called variation of parameters.
The purpose of this article is to help make solution seeking of some homogeneous second order lin... more The purpose of this article is to help make solution seeking of some homogeneous second order linear ordinary differential equations easier and faster using well established theorems.
This beautiful piece of writing and perhaps one of my best discoveries, is intended to give an al... more This beautiful piece of writing and perhaps one of my best discoveries, is intended to give an alternate but also a direct proof of the Fermat's last theorem. The theorem being one of the most popular, if not the most popular was also notorious for being one of the most difficult to prove. In 1994-about 357 years after it was first stated by Pierre de Fermat and accompanied with series of failed attempts from several mathematicians, came the supposed breakthrough, notably by Andrew Wiles¹. His approach required very sophisticated mathematical concepts in number theory, especially the modularity theorem². His approach however, isn't a actually a direct proof per se, it just happens to rely on the connection between distinct branches of mathematics (elliptic curves, modular forms and Fermat equation), just like Galois proof of the impossibility theorem relied on the connection between group theory and polynomial equations.
In this article, a different approach is utilized, somewhat unorthodox, as it requires new fundamental mathematical techniques which also happens to have implications for the philosophy and foundations of mathematics. The proof can be thought of as direct and it doesn't actually require much advanced mathematics as with the case of Wiles proof. The results established in this article could come in handy to proving other related theorems/conjectures and possibly advancing mathematics for the better.
A relatively short essay on the question of whether we actually invent things or if it's an illus... more A relatively short essay on the question of whether we actually invent things or if it's an illusion.
In our previous article in reference [1], we were able to reformulate Maxwell's equations in a si... more In our previous article in reference [1], we were able to reformulate Maxwell's equations in a simplified and microscopic form. This article on the other hand is a follow-up of the aforementioned article but in this case it is shown that gravity may have electromagnetic origins, using as basis this reformulated Maxwell's equations. As a matter of fact, it is suggested in this article that thorough experimental investigations with neutrons could help us really understand gravity fundamentally. This however is based on the fact that a certain property of neutrons was calculated in this article using the assumption of the electromagnetic origins of gravity and this calculated value seems to correspond with the data that was obtained from an experiment performed some time ago (over 50 years ago) by Shull et al-see the article in reference [2]. Also, the rotation curve of galaxies, especially the spiral ones is revisited and it's shown that the assumption of the electromagnetic origins of gravity can explain it. This paper may also be handy to those who seek a unified/single theoretical framework for all fundamental forces.
The essence of this article is show that all quintic equations are solvable algebraically in te... more The essence of this article is show that all quintic equations are solvable algebraically in terms of radicals just like the quadratic, cubic and quartic equations.
We present the basic principles of thermoelectricity and statistical electricity, this is some... more We present the basic principles of thermoelectricity and statistical electricity, this is somewhat analogous to the principles encountered in thermodynamics. Just like how J.W.Gibbs [1] derived the basic laws of thermodynamics from statistical mechanics, the same is done using statistical electricity and a differential equation derived from both the equations of thermal conductivity and electrical conductivity.This however would later be extended to quantum thermoelectricity, using Schrödinger's wave equation as basis.
Prior to the solutions to the particle equation given in the article titled '' Electromagne... more Prior to the solutions to the particle equation given in the article titled '' Electromagnetism as the key to understanding the quantum world '' , we make little corrections and derive the same solutions in a much more rigorous mathematical approach, as the technique used previously appears to be ill-defined for the mathematically inclined, the author is sorry for such inconveniences. Also we show that this particle equation which can be sometimes called the electromagnetic field equation allows superposition principle, this is very handy when one begins to talk about field/particle structure of many charged particles and also the Laplace transform is derived.
Over the years observations has been made based on only what we perceive physically,this has howe... more Over the years observations has been made based on only what we perceive physically,this has however limited our ability to think outside the box.In this article we shall see that by restructuring the foundations of classical electromagnetic theories ( introducing new parameters), quantum mechanics is given a strong footing and also throwing more light into how our physical universe was designed.
We present a short communication on a new kind of differential group(s) non-galois in nature and ... more We present a short communication on a new kind of differential group(s) non-galois in nature and are of great importance in the study of homogeneous ordinary linear differential equations of order > 1 with exact solutions, exact solutions to differential equations are of great importance in applied mathematics, computational chemistry and physics, most especially quantum physics. However, in this article emphasis is made only on homogeneous second order linear ordinary differential equations and the results in this article are extensions of the works treated in the articles in references (1) and (2). In fact, the techniques employed in reference (2) and in this article can be applied to homogeneous linear ordinary differential equations of order > 2.
The main aim of science is to know and to know is to better understand this paradoxical univer... more The main aim of science is to know and to know is to better understand this paradoxical universe of ours.Then there is technology whose aim is to apply what we know to make the world a better place. However there are questions we ask ourselves everyday that science, despite it's success, has not been able to fully answer, could it be that our approaches has gotten to it's dead end or that our ignorance has taken the most out of us. Two subfields of science has promoted radical questions that challenges our knowledge of existence and reality, and they are quantum mechanics and artificial intelligence, the former challenging our understanding of reality and the later challenging our understanding of what consciousness actually is. Scientists have made us to believe so many things, but what if at some point they were wrong, what if at the classical world we experience quantum mechanical principles like entanglement, what if there is actually a multiverse and that we access/visit them and what if the interpretations of quantum mechanics can be resolved. The big bang theory explains how our present universe came into be but fails to tell us what caused it and how life came into be, what if this can be resolved too. From a philosophical perspective, what if consciousness and it's hard problems can be understood and resolved and lots more of what ifs. Get to find out ?, then get ready to get your minds blown 😱, as we explore these possibilities and resolve some of these paradoxical questions, using a novel approach that is not wildly known. But first you need to remember this '' The laws of the universe need not be complicated, all that is required are the right ingredients '' .
In this article the Maxwell's electromagnetic equations are reformulated in a simplified form, th... more In this article the Maxwell's electromagnetic equations are reformulated in a simplified form, this reformulation is as a result of the limiting case of the generalised particle equation, taking into account charge and current density/distribution and it is shown to be equivalent to the conventional Maxwell's equations in microscopic form.
In this article we show that the particle equation solution presented in the articles in referenc... more In this article we show that the particle equation solution presented in the articles in references 1, 2 and 3 is an approximate solution to a much more generalised equation of which is easily reduced to the modified Bessel equations. We shall see that the solution gotten from the generalised equation (modified Bessel equation) is a superior form of that presented in the stated articles above, the same physical predictions exist in this new function. Also we show that the consequences of special relativity and the basic quantum mechanical principles are indeed derivable from the equation and its solutions.
In this article we extend the theories provided in the article in references 1, 2 and 3 in establ... more In this article we extend the theories provided in the article in references 1, 2 and 3 in establishing some properties of atoms, most especially electron arrangement and shape of orbitals. Lastly a new quantum number is predicted.
In this short article we present the origin of the half and whole spin quantum numbers encountere... more In this short article we present the origin of the half and whole spin quantum numbers encountered in quantum physics, this in general leads to two classes of particles which are the bosons and fermions. The origin is explained from the consequences of the mathematical treatment and theoretical proposal presented in the articles in references 1 and 2 below, i would urge us to study those articles very well if we want to understand the content of this article.
In this article the major foundational quantum mysteries are resolved using an alternative mathem... more In this article the major foundational quantum mysteries are resolved using an alternative mathematical reformulation of the basic principles of quantum mechanics, this reformulation is as a result of the theories established in the articles provided in references 1 and 2 below.
In this article we present a short communication on a new technique in addition to the numerical ... more In this article we present a short communication on a new technique in addition to the numerical root finders in seeking a root to some polynomial/algebraic equations of degree > 2.
In this article we present important theories of differential equations, most especially ordinar... more In this article we present important theories of differential equations, most especially ordinary differential equations in terms of exact general solution seeking, using the powerful tool called variation of parameters.
The purpose of this article is to help make solution seeking of some homogeneous second order lin... more The purpose of this article is to help make solution seeking of some homogeneous second order linear ordinary differential equations easier and faster using well established theorems.
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Papers by Clinton O Onye
In this article, a different approach is utilized, somewhat unorthodox, as it requires new fundamental mathematical techniques which also happens to have implications for the philosophy and foundations of mathematics. The proof can be thought of as direct and it doesn't actually require much advanced mathematics as with the case of Wiles proof. The results established in this article could come in handy to proving other related theorems/conjectures and possibly advancing mathematics for the better.
Drafts by Clinton O Onye
Two subfields of science has promoted radical questions that challenges our knowledge of existence and reality, and they are quantum mechanics and artificial intelligence, the former challenging our understanding of reality and the later challenging our understanding of what consciousness actually is. Scientists have made us to believe so many things, but what if at some point they were wrong, what if at the classical world we experience quantum mechanical principles like entanglement, what if there is actually a multiverse and that we access/visit them and what if the interpretations of quantum mechanics can be resolved. The big bang theory explains how our present universe came into be but fails to tell us what caused it and how life came into be, what if this can be resolved too. From a philosophical perspective, what if consciousness and it's hard problems can be understood and resolved and lots more of what ifs. Get to find out ?, then get ready to get your minds blown 😱, as we explore these possibilities and resolve some of these paradoxical questions, using a novel approach that is not wildly known. But first you need to remember this
'' The laws of the universe need not be complicated, all that is required are the right ingredients '' .
Also we show that the consequences of special relativity and the basic quantum mechanical principles are indeed derivable from the equation and its solutions.
In this article, a different approach is utilized, somewhat unorthodox, as it requires new fundamental mathematical techniques which also happens to have implications for the philosophy and foundations of mathematics. The proof can be thought of as direct and it doesn't actually require much advanced mathematics as with the case of Wiles proof. The results established in this article could come in handy to proving other related theorems/conjectures and possibly advancing mathematics for the better.
Two subfields of science has promoted radical questions that challenges our knowledge of existence and reality, and they are quantum mechanics and artificial intelligence, the former challenging our understanding of reality and the later challenging our understanding of what consciousness actually is. Scientists have made us to believe so many things, but what if at some point they were wrong, what if at the classical world we experience quantum mechanical principles like entanglement, what if there is actually a multiverse and that we access/visit them and what if the interpretations of quantum mechanics can be resolved. The big bang theory explains how our present universe came into be but fails to tell us what caused it and how life came into be, what if this can be resolved too. From a philosophical perspective, what if consciousness and it's hard problems can be understood and resolved and lots more of what ifs. Get to find out ?, then get ready to get your minds blown 😱, as we explore these possibilities and resolve some of these paradoxical questions, using a novel approach that is not wildly known. But first you need to remember this
'' The laws of the universe need not be complicated, all that is required are the right ingredients '' .
Also we show that the consequences of special relativity and the basic quantum mechanical principles are indeed derivable from the equation and its solutions.