The Numbers in Science

"God used beautiful mathematics in creating the world." - Paul Dirac

When we start studying science, we come across many numbers, many equ
ations. While many assume that we do so because the teachers and the books say so but to some this maybe a grave concern that why we use numbers to describe something like a waterfall, a rainbow, flying kites and even hopping rabbits. And nearly nobody finds out 'why'.
Though these should be the first things to be taught in the class but Alas! They weren't.  So now I'll try to answers some of these fundamental questions.

What is mathematics?

Mathematics can be thought of as a language. But it isn't like any of the mainstream languages. It is a language that describes patterns. And mathematics has this unique ability because it itself is made of numbers and operations that occur in patterns themselves for example 0, 10 and 20 all have the same last digit i.e 0, and this repetition occurs after regular intervals of 10 i.e in a pattern.

Since when is mathematics a part of our sciences?

Early science was basically providing a reason for a certain physical happening with no awareness that these happenings despite being apparently different, converge to a single fundamental phenomenon because of lack of a fundamental mathematical base or model for everything. Sir Isaac Newton was the first physicist who started from scratch and created the first mathematical foundations that we still use today. What he did is still mind boggling, because it took such a leap of imagination and understanding to look out at the universe and find the simple mathematical equations that could govern the things that he was observing and we've been following his footsteps eversince.

How do these patterns describe everything?

For reasons unknown to humans as of now, it is observed that everything in this universe from neutrinos at one end and the galaxies at the other, and even the universe itself follows certain patterns. All processes in the universe occur in a certain manner that is replicable over and over again. And that's what mathematics is well suited for. For embodying and describing patterns that don't change over long intervals of time.

How does math describe an object?

One of the biggest achievements of math is that it by virtue of it's numbers and equations, it can describe an object, that is real and tangible. And these equations can be modified to embody any of the physical objects found in the universe. And this achievement was made possible by dividing all objects into a few fundamental particles of which everything was made e.g electrons, protons or better yet quarks. Equations were developed to describe these particles. Once these particles were described, now everything made of these particles can also be described by simple modifications of these basic equations.

How do numbers describe an event?

When describing an event, we first describe what event actually occurred. This can be described as a combination of a few fundamental processes already described such as the conservation of energy, the conservation of momentum or the application of a force. This ideology is similar to the one described in the previous question. Second we describe where and when it occurred. This can be described completely using our three dimensions of space and one dimension of time and these coordinates are themselves described by numbers and equations.

Is mathematics the only language to describe everything?

It is possible that mathematics is not the only language with the ability to describe everything. One day we may come across an approach far superior than math to understand reality. It may even be possible that mathematics is not the right approach at all. But as of today we have a couple of hundred years of experience that shows us that math is a sure footed guide to the nature of reality. In fact some of the equations predicted results that were initially believed to be absurd but later observations revealed that the math was right and it predicted things some couple of years ahead of time. Famous examples are the expanding universe and the black holes which were predicted by Einstein's theory of general relativity.