Related papers: Towards a Grand Unified Theory of Mathematics and …
Eugene Wigner famously argued for the "unreasonable effectiveness of mathematics" for describing physics and other natural sciences in his 1960 essay. That essay has now led to some 55 years of (sometimes anguished) soul searching ---…
Since ancient times, mathematics has proven unreasonably effective in its description of physical phenomena. As humankind enters a period of advancement where the completion of the much coveted theory of quantum gravity is at hand, there is…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
Wigner's famous and influential claim that mathematics is "unreasonably effective" in physics is founded on unreasonable assumptions about the nature of mathematics and its independence of physics. Here I argue that what is surprising is…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…
Many physicists, following Einstein, believe that the ultimate aim of theoretical physics is to find a unified theory of all interactions which would not depend on any free dimensionless constant, i.e., a dimensionless constant that is only…
Our conventional understanding of space-time, as well as our notion of geometry, break down once we attempt to describe the very early stages of the evolution of our universe. The extreme physical conditions near the Big Bang necessitate an…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
The physical models of a successful unified theory about the Universe must operate in different phase of matter evolution and different fields of physics. The attempts to build such wide range theory as a bunch of theories developed for…
Various 'optimistic' attempts have been made to reasonably explain the undeniable effectiveness of mathematics in its application to physics. They range over retrospective, historical accounts of mathematical applicability based on…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…
The ``unification'' of fundamental physical forces (interactions) imagines a ``single'' conceptual entity using which {\em all} the observable or physical phenomena, {\em ie}, changes to physical bodies, would be suitably describable. The…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
Eugene Wigner's much-discussed notion of the "unreasonable effectiveness of mathematics" as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…