“Why nature (or God) is mathematical is, again, a mystery.” - Richard Feynman
“You may object that by speaking of simplicity and beauty I am introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted by the simplicity and beauty of mathematical schemes which nature presents us. You must have felt this too: the almost frightening simplicity and wholeness of the relationship, which nature suddenly spreads out before us.”
“I think that modern physics has definitely decided in favour of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.”
- Werner Heisenberg
James Jeans Quotes
English physicist, astronomer and mathematician whose early career was in molecular physics, followed by an interest in astronomy and in later life he popularized science through books, radio broadcasts and lectures…..
“Today there is a wide measure of agreement, which on the physical side of science approaches almost to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a machine. Mind no longer appears to be an accidental intruder into the realm of matter...we ought rather hail it as the creator and governor of the realm of matter.” - James Jeans
“We have already considered with disfavour the possibility of the universe having been planned by a biologist or an engineer; from the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.” - James Jeans
“The universe can best be pictured as consisting of pure thought, the thought of what for want of a better word we must describe as a mathematical thinker.”
“The final truth about a phenomenon resides in the mathematical description of it; so long as there is no imperfection in this, our knowledge of the phenomenon is complete. We go beyond the mathematical formula at our own risk; we may find a model or a picture which helps us understand it, but we have no right to expect this, and our failure to find such a model or picture need not indicate that either our reasoning or our knowledge is at fault. The making of models or pictures to explain mathematical formulas and the phenomena they describe is not a step towards, but a step away from reality; it is like making a graven image of a spirit.”
“The concepts which now prove to be fundamental to our understanding of nature—a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation—or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time—all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material.”
Freeman Dyson - 'God appears to be a mathematician'
American-British physicist and mathematician, Freeman Dyson, was born in England in 1923. Aged 25, he relocated to Cornell University and has become known for his achievements in the fields of solid state physics, nuclear engineering and quantum field theory.
TRANSCRIPT: I find it a miracle. I mean, I don't pretend to understand it and I think it is absolutely marvellous that nature somehow thinks like a mathematician, that was what James Jeans said that... that God appears to be a mathematician. And it is astonishing that somehow all these weird mathematical ideas which we have invented for purely aesthetic reasons, essentially just as works of art, as intellectual constructions, turn up then unexpectedly to be used in nature. There're so many examples of this, of course. Of course the classic case was differential geometry which was invented by Gauss for very practical purposes, just for projecting maps from the spherical earth onto a plane, onto a piece of paper, so he invented this differential geometry as a way of representing curved surfaces on a flat plane. And then 50 years later Riemann applied that to a description of space and conjectured that space itself might actually be curved, but it was still sort of purely an intellectual hypothesis without any kind of physical basis. And then another 50 years later it turned out to be the essential tool for Einstein to understand gravitation. It is in fact what Einstein used for general relativity. So it's built... it's built deep into the structure of space-time. It's a miracle how that happened. So Gauss had developed this tool for totally other reasons. And that's happened again and again. Of course Lee invented Lee groups to understand classical dynamics, and it turned out to be, 100 years later, exactly what you need to describe particles, and I don't know why, but... so the world has deeply built into it these mathematical structures and there seems to be a kind of rule that anything mathematicians can invent, God somehow can use. So we hope that's also true of the Riemann hypothesis. We haven't yet found the Riemann hypothesis verified in nature, but maybe we will one day.
Exract from - The Mathematical Universe - by Max Tegmark
"Abstract: I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems." - Max Tegmark
Dr. Kaku addresses how physics has revolutionized mathematics
Dr. Kaku says we might imagine God as we know him to be a mathematician: "The mind of God we believe is cosmic music, the music of strings resonating through 11 dimensional hyperspace. That is the mind of God."
God is a Mathematician
Mathematics is abstract, symbolic, structured and precise. It is true everywhere and always and mathematical laws cannot be violated, ever. Math sounds a lot like the attributes of God—eternal, omnipresent and omnipotent. According to theoretical physicist Michio Koku, “The mind of God we believe is cosmic music, the music of strings resonating through 11-dimensional hyperspace. That is the mind of God.”i Vern Poythress, who teaches New Testament in Cambridge University and has two doctorates, a PhD in mathematics from Harvard and a doctorate in Divinity, argues in his book Redeeming Mathematics: A God Centered Approachii, that “the harmony of abstract mathematics, the physical world of things and our thinking depends on the existence of a Christian God.” Srinivas Ramanujan, on whose life the book and the movie “The Man who knew Infinity”iii are based is known to have said that “an equation to me has no meaning unless it represents a thought of God”.
The structures of the universe, from the tiniest (subatomic) to the largest (cosmic), can be visualized as networks or webs of connections. And, these networks are interlocking, pulsating particles, exchanging, sharing and transforming energy from one form to another. Physics today is understood through mathematics. Scientists have long used mathematics to describe the physical properties of the universe, but physicist Max Tegmarkiv goes even further and believes that the universe itself is math. In Tegmark’s view, everything in the universe — humans included — is part of a mathematical structure. All matter is made up of particles, which have properties such as charge and spin, but these properties are purely mathematical, he says. And space itself has properties such as dimensions, but is still ultimately a mathematical structure.
Mathematics, numbers, symbols, information and energy are different ways by which physicists have attempted to describe the universe. Modern theories in physics are abstract and mystifying to most. For many, faith in the divine origin of the universe provides more certitude than modern physics does. Faith gives one certainty which physics is unable to do, this is the appeal of faith for many. Certainty in an uncertain world is comforting.
Scientific knowledge has an asymptotic relationship to truth or Truth. Scientists are getting closer to the Truth but, I suspect, will never reach it. Scientists are like Adam reaching out to touch the hand of God but not making it, as depicted in the frescov on the ceiling of the Sistine Chapel.
Physicists are peering into the outer reaches of the cosmos and probing deep into the inner sanctum of atoms, discovering realms that are beyond the reach of our senses. For most of us, these realms are difficult to comprehend, because we cannot see, touch or feel them. No one has seen a quark or been able to visualize Einstein’s four-dimensional space and time. Hence, to some, modern physics is incomprehensible, abstract, hard to relate to, and indistinguishable from a myth.
Thankfully, we do not rely just on our senses to understand the universe, if we did, we would still be in the dark ages. Physicists are looking for a single theory or, as Michio Koku states, “an equation about six inches long,” which can explain all phenomenon, from the largest (cosmos) to the tiniest (subatomic particles). The holy grail in physics is to find a theory that reconciles general relativity and quantum physics. Science is in search of ultimate unity, the God Particlevi, as Nobel Laureate Leon Lederman wrote in his book of the same name. Particle physicists keep building bigger and bigger particle accelerators, like the one at CERNvii, in search of the God particle. At CERN, in the Large Hadron Collider, energy at the point of collision of the protons approaches the energy moments after the Big Bang, in the hope of finding the God particle.
The truth is that the Truth might not be a particle. Truth might not be a thing. It might be an abstraction, like an “idea in the mind of God”, as some have suggested, or perhaps as Max Tegmark posits, “There’s something very mathematical about our Universe, and the more carefully we look, the more math we seem to find. ….. So, the bottom line is that if you believe in an external reality independent of humans, then you must also believe that our physical reality is a mathematical structure. Everything in our world is purely mathematical – including you.”
Theologists, scientists and philosophers seem to agree that Reality, absolute truth, or God, if you will, is an abstract reality. Not a reality that can be detected by our senses or known through our intellect. In this view mathematics are an expression of the mind of God. She is a mathematician!
Sunil Mehrotra has an MS in Aeronautical Engineering from Purdue University and an MBA from The University of Chicago. He has held senior executive positions at Fortune 500 companies and has been a CEO and founder of two start-ups. He has also taught at Pepperdine University in Malibu, California.