**— William Paul Thurston, American mathematician**

In a previous blog, I spoke a lot about what mathematics isn’t. However, I don’t think I spoke quite enough on what mathematics truly is.

Here's how I began that blog.

"When we’re young we begin by learning
the steps to add – we’re given the rules and we must learn to repeat them – no
questions asked. Why does carry forward work the way it does? Well, *no
questions asked."*

However, I believe that the essence of
truly understanding mathematics lies in the questions you ask – and the first
one, the most fundamental one, is also probably one of the hardest questions
you would and could find – What really *is* Mathematics?

Something that differentiates explaining
what mathematics is from explaining a lot of other concepts is that mathematics
was not really ever *invented*. If a young student angry about excessive
math homework was given a time machine, he would not know how to use it to
prevent the presence of math in their homework. Mathematics has been around
ever since humanity has been around. Probably even before. Various
philosophers, scientists and mathematicians have made their contributions to
the subject. But mathematics is something that has been discovered over time,
not invented.

One of the most important misconceptions about mathematics is that mathematics is well – like addition, subtraction of numbers and like stuff related to that. This claims math to be about using different operations on numbers and in a sense, we almost always need to use these in one form or another. However, the distinction is that what has been described is arithmetic, and not mathematics.

Essentially all arithmetic does is providing you with a certain basic set of tools which you can use in your study of the subject of mathematics. So, mathematics is not about additions, or subtractions. Multiplications, or divisions. Mathematics lies in how you put these powerful tools together to build a world of your own.

According to Po Shen Loh,

“If you ask me what math is, I’ll say math is actually the distilled heart of thinking. It’s logic. As you learn how to assemble these chains of logic, you can use that skill for anything. So, my real goal is to help the world become a more thinking place”

This is really the way I like to think about mathematics. As an art of thinking. As an art of problem solving.

And that’s my answer to what mathematics really is. An art of thinking.

However, many of the people reading may feel that the description above is extremely vague. Of course, we couldn’t be using mathematics when we’re thinking about what to write in an English composition. Or could we?

Maybe a better definition could be the art of problem solving. In its essence, the two really mean the same thing but this description allows one to better understand what exactly is meant. What the subject of mathematics really aims at doing is make the world a more thinking place – a place where we have a greater ability to solve real life problems.

As a child, all of us must have been intrigued by the question on whether we were left-brained or right brained. If you’re mostly analytical and logical in your thinking, the theory says that you’re left brained. If you tend to be more creative or intuitive, you’re right-brained.

A sensible conclusion would be that a mathematician falls into the left brained category. However as weird as this may sound, creativity, intuition and imagination are ideas imbedded in the heart of mathematics – an idea a majority of people never really realise. It is for this reason that invoking the spirit of mathematical thinking is so important in today’s day and age. Mathematics has the potential to be our greatest asset in teaching the future generation to meet the future with curiosity, creativity and courage.

I’ll end this blog the same way as my blog earlier, to emphasize on the importance of the very idea.

Mathematics really is a subject that can change the world – and it is unfortunate that a lot of students do not ever get to see much of its magic in their education. If every student gets to see the power of mathematics, a subject where we create, we imagine and we innovate - maybe the day is not very far away when every student would come back home and say,

“Math? – Oh, who doesn’t love math.”

I'll sign off with this thought.

Until next time,

Rushil :)

PS: I would love to know how all of you see the subject of mathematics - what you love about it, and how your opinion differs from this so feel free to comment below!

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