Create Your Syntax

Among the many wishes of some people, the most celebrated wish is to be a creative mathematician. What does one mean by ‘creative mathematician’? Being creative with mathematics implies going beyond the existing rigours of the language and creating art works that can be explained through the same language of mathematics. The notations do not change but you use them to express ideas that are novel. This makes you a creative mathematician. The art work is not as easily understood as poetry or as easily appreciated as music because the reader looks at the notations and symbols as part of Maths as defined or practiced by institutions. They do not realize that your art work is a creative expression.

You can transcend truth in the human context only through abstraction. This abstraction or the abstract can be expressed through natural language or formal language. Mathematics is a formal language. You can also write about Mathematical concepts the way you do about your favourite song. You can review and unravel mysteries the same way you review a story and unravel the implications. It is a boon to the students of Mathematics who wish to appreciate the elegance of its structure. One can never really go wrong in Mathematics because when you work within the framework in your own way, you will still find a hidden pattern and an insight. If you try to solve a problem and get it wrong, you open more perspectives and questions related to the problem at hand. If you get the answer right and find a solution, then you also shut down different scenarios that can be realized only when you get it wrong. In Mathematical thinking, there is no concept of right and wrong. There is always an idea that is realized. It is only on this plain of abstraction that perfection is ever realized be it natural or formal language. A natural language say English when used to express ideas creatively, will become formal but it will have the signature of an artist or philosopher. This artist is a mathematician of natural language as much as a mathematician is an artist of formal language.

Writing about Mathematics activates subtle logic that creates the framework in the first place. Academicians do not realize that the frameworks of modern mathematics would never have existed without subtle logic and intuition.  The rationale occupies a small portion of the thought process used to weave ideas.

It is like taking notes in your diary. We do not have to have a standard way of taking down notes.

Practice writing about mathematical concepts and set your own rules. You will always find insights, which can be expressed through the rigours of formal mathematics. You have the insight! All you need is syntax. Create one!