Mr. Raja,

Deep question indeed!

In my opinion, mathematics is the rule book of  the nature. It is integral part of nature. Nature does not do mathematics or calculations. Rather we have found and understood a 'part' of this rule book and we use it to solve 'some' part of the deep secrets of nature. We call it the subject 'Mathematics'.

For examples, laws of mass, charge, energy and momentum conservation. Nature commands these laws. They are held by default in order to sustain the universal framework and distribution of energy across the universe.

You take example of our digestive enzymes in the body.

Did we make them for our purpose???

Absolutely not!!! They were there since our inception. We do not 'use' them. rather they are basis and the sole cause of our existence on the planet.

I think I could express it!

Regards,

MKD 

Dear Raja N A Khan, thank you for invitation,

1/ Mathematics needs only for describing those processes which are studied by Physics...2/ in General in nature mathematics appears in Geometrical forms… 3/ Nature of mathematics is only a mental tool for operations… Exist lot of example: crystals form,  soap bubble, etc.. 4/ The nature do not need mathematics….5/“Mathematics and Time” both are same, just a mind base tools for understandings of quantification of events….

7/ Math is not more than a key of estimation and calculation; even the geometry and image orders are under calculation just by a way of understanding of brain….8/there do not exist any link between Energy and Mathematics.

Best regards,

Dear Raja:

I think mathematics "are", in a way, in the physical world AND in human mind. Knowledge --including mathematical knowledge-- is a mechanism of adaptation of humans to the physical environment. Human brain was developed through adaptation during natural evolution. Action on the environment shaped neural connections. Then, logical and mathematical relationships are a product of the adaptive behaviors selected throughout human (and pre-human) evolution. That's why mathematics seem to emerge mysteriously from our mind and adapt --no less amazingly- to the physical world. (I owe this argument to Jean Piaget's genetic epistemology)

Concerning the relationship between mathematics and nature, the following link is one of the most useful references:

https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Question is good. In principle I agree with Jose Eduardo and with Jean Piaget. But the mystery is still there for me and always has been, despite the fact that every day I live among mathematical formulas. I understand that I can deeply understand the world only if I will be able to describe it mathematically. But I don't understand and I'm afraid that I will never understand why this is so.

With regard to mathematics as a means of adaptation to the world, which arised in the evolution. I know a lot of people, for example among humanitarian professions, who do not know mathematics, don't understand it and even fear it. However, many among them are well-adapted to this world, and much better than any bright mathematical mind.

Thanks to Tatsuo for the reference. I did not know this article of  Wigner. 

Mathematics is a tool  created by humans to describe, to understand and to explain how and why nature is so perfect, to be able to manipulate natural elements for a better life. So mathematics is in every place, in every natural process where you can discover it.

Galileo Galilei (1564–1642) said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth."

https://en.wikipedia.org/wiki/Mathematics

"Math has the illusion of being effective when we focus on the successful examples, But there are many more cases where math is ineffective than where it is effective. - Derek Abbott. ©2013 IEEE

"Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its "mother tongue," and that this mathematics has its own existence that is out there waiting to be discovered? This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.

Derek Abbott, Professor of Electrical and Electronics Engineering at The University of Adelaide in Australia, has written a perspective piece to be published in the Proceedings of the IEEE in which he argues that mathematical Platonism is an inaccurate view of reality. Instead, he argues for the opposing viewpoint, the non-Platonist notion that mathematics is a product of the human imagination that we tailor to describe reality..."

http://phys.org/news/2013-09-mathematics-effective-world.html

The universe and everything in it is based on mathematics. We were placed in it as curious creatures. Mathematics allows us to calculate what is going on. Whether or not it is correct, has to be proved through experiments that can be duplicated. If you are mathematically clueless, you are probably proficient in the subtleties of language. Both mathematics and language can mean things that aren't immediately recognizable. Einsteins's Theory of Relativity is a prime example.

Mathematics occur in nature as an abstraction of the facts.