# What is the relationship between Mathematics,Science and Nature?

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in".

When mathematical physicist Paul Dirac was asked what he believed, without hesitation he replied that the laws of nature should be expressed in beautiful equations.

As we learn more about nature, it becomes increasingly apparent that an accurate statement about nature is necessarily mathematical. Anything else is an approximation. So, mathematics is not only science but is also an exact science.

Because nature is mathematical, any science that intends to describe nature is completely dependent on mathematics. It is impossible to overemphasize this point, and it is why Carl Friedrich Gauss called mathematics "the queen of the sciences."

Conclusion: Nature is innately mathematical, and she speaks to us in mathematics. We only have to listen.

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It has been said that "mathematics is science without limit" and that "mathematics is the language we write science".

What do you think is the relationship between mathematics, science and nature?

## Popular Answers

Issam SinjabI want now to present an example that illustrates this in a beautifully way and make another equally important conclusion.

Because of quantum theory we now have two kinds of physical theories, those that work at a large scale and those that work at the scale of individual atoms. these theories are incompatible — the very successful theory of relativity isn't expressible in quantum terms, and vice verse.

Currently,we don't have a theory that works at all scales-unified theory. However, an element of such a theory is an equation written by Paul Dirac in 1928. Dirac's equation successfully predicts the behavior of particles moving at relativistic velocities, so to some degree it reconciles the relativistic and quantum views of reality.

While writing his equation Dirac realized it had two possible roots. At that point, Dirac could have decided his equation was only an approximation of reality (there are plenty of those), or he could claim his equation accurately described nature, therefore nature allowed two different kinds of matter, with positive and negative signs. Dirac decided his equation described nature and in so doing his equation implied the existence of a new form of matter, antimatter.

Dirac realized he could rewrite his equation to eliminate the negative root, but that equation would have been complex and unattractive, solely to eliminate the strange possibility that nature allowed two kinds of matter. Acting primarily on instinct, Dirac decided his equation accurately reflected nature, and he described the possibility of something he called "antimatter." Within a few years antimatter had been observed in 1932 by Carl Anderson. Carl discovered a new particle called "positron"(like electron but with positive charge).

Dirac did not invent his equation, if he did then this implies nature subsequently obeyed Dirac' equation and this will make Dirac some kind of a creator! But Dirac is not a creator, Dirac discovered his equation and he found it in nature. This clearly demonstrate that nature speaks to us in mathematics and equally importantly, that mathematics was discovered not invented.

The question of this thread was inspired by the reference below and the above is an extract from it:

http://arachnoid.com/is_math_a_science/index.html

Louis Brassard·