What is the relationship between Mathematics,Science and Nature?

Nobel Prizewinner Richard Feynman had this to say about mathematics:

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

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?