http://www.pbs.org/wgbh/nova/blogs/physics/2015/04/great-math-mystery/
The puzzle of the power of mathematics is in fact even more complex than the above examples from electromagnetism might suggest. There are actually two facets to the “unreasonable effectiveness,” one that I call

*active* and another that I dub

*passive*. The active facet refers to the fact that when scientists attempt to light their way through the labyrinth of natural phenomena, they use mathematics as their torch. In other words, at least some of the laws of nature are formulated in directly applicable mathematical terms. The mathematical entities, relations, and equations used in those laws were developed for a specific application. Newton, for instance, formulated the branch of mathematics known as calculus because he needed this tool for capturing motion and change, breaking them up into tiny frame-by-frame sequences. Similarly, string theorists today often develop the mathematical machinery they need.

Passive effectiveness, on the other hand, refers to cases in which mathematicians developed abstract branches of mathematics with absolutely no applications in mind; yet decades, or sometimes centuries later, physicists discovered that those theories provided necessary mathematical underpinnings for physical phenomena. Examples of passive effectiveness abound. Mathematician Bernhard Riemann, for example, discussed in the 1850s new types of geometries that you would encounter on surfaces curved like a sphere or a saddle (instead of the flat plane geometry that we learn in school). Then, when Einstein formulated his theory of General Relativity (in 1915), Riemann’s geometries turned out to be precisely the tool he needed!

...

NOVA:

The Great Math Mystery
Is math invented by humans, or is it the language of the universe? NOVA takes on this question in a new film premiering April 15, 2015 at 9pm on most PBS stations.

NOVA:

Describing Nature with Math
How do scientists use mathematics to define reality? And why? Peter Tyson investigates two millennia of mathematical discovery.

The Washington Post:

The Structure of Everything
Learn more about the “unreasonable effectiveness of mathematics” in this review of Mario Livio’s book “Is God a Mathematician?”

http://math.northwestern.edu/~theojf/FreshmanSeminar2014/Wigner1960.pdf
The Unreasonable Effectiveness of Mathematics in the Natural Sciences

Richard Courant Lecture in Mathematical Sciences delivered at New York University,

May 11, 1959

EUGENE P. WIGNER

Princeton University

Hello Jim Smith

I have not had time to follow up on the links etc but I want to ask your opinion on something re math

I agree with your analysis that pure consciousness is not part of the physical universe

I call it 'presence-awareness' to indicate two of its essential qualities - beingness and awareness

It also has the essential quality of intelligence

Presence-awareness is a primary or essential reality - ie Divine

The body and its nervous system is part of the objective physical universe

What we experience as human mind is an effect or product of the encounter between presence-awareness and the nervous system

Mind is a sort of holographic emergence from that encounter; an effect of incarnation

Human mind is not a primary or essential reality - ie not Divine

The qualities of human mind are a mix of those it derives from physical reality (specifically the nervous system)

and from presence-awareness or pure consciousness

Math I suggest is a product of human mind

The reason it maps onto physical reality is because human mind and therefore math is partly a product or effect of matter

The other part or aspect of human mind being presence-awareness or pure consciousness

If we examine the neuron, the basic operational component of the nervous system, we find it is functionally a biological digital device

in the sense that it either fires or it does not fire - the action potential

The nervous system and the brain is functionally a biological digital mechanism

Math is a mental product made possible by the inherent digital nature of the nervous system

Not sure if I have presented that clearly

Any thoughts?