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!
