Since writing about my 3D OpenGL Project, I've been recently wondering why I have a growing appreciation of Mathematics. What is it that I appreciate specifically?
It may be obvious but I feel that answering these types of personal, inward and exploratory questions is the best at helping you discover your innate drive and motivations.
Over the last couple of years, I've started to realise that while Mathematics can be difficult to interpret at times, this is due largely I feel, primarily due to the lack of contextual and background understanding which is then required to interpret its notation and syntax. This might seem obvious but what this means is that the majority of Mathematics must happen in your head, not on paper, and that the primary activity is conceptual manipulation of ideas and thinking. My education never highlighted this, and equally, I didn't see it.
I was of the impression growing up that mathematics was firstly and primarily learnt through syntax and notation, and that through notation and syntax, we derive mathematical understanding. For example, that it is through the manipulation of fundamental rules that are represented as particular algorithms and syntactical notation.
A part of my growing interest in Mathematics is having realised that its syntax is not of primary importance, and it has been detrimental for me up to this point to learn and gain an understanding of mathematics by seeing it this way. I've also realized that understanding is a very time-consuming process but learning notation is lightening fast.
For example, I took at least 6-8 months to understand the ideas behind Calculus but the mathematic syntax, algebra, algorithms and rules only took maybe half a page. And for all the manipulation of those algorithms, they never provided actual understanding or insight. This might seem obvious to some but I only really realised this recently.
The opposite is true: insight is achieved without syntax, and the most effective way to understand it is through conceptual thinking and manipulation of ideas without requiring pages of ink.
Having said that, the reason why I've tried to understand my deficiencies is that I see Mathematics as fundamentally important to me because of its utility in representing ideas and my growing interest in understanding them.
I like the idea of representing ideas. For example, I usually represent conceptual ideas as code every day using syntax and notation for the particular programming language I'm using. Those ideas live an entirely separate life from their final representation in code. I spend more time thinking and trying to understand the implications of what I'm planning to represent/do, and coding that thinking and understanding into the syntax and notation is merely a brief formality. The same is true of Mathematics.
I've come to realise the link between Mathematical notation and Programming too. They both represent ideas.
Mathematics is a programming language used to define ideas using rules to confine/define them.
Thus to answer my question, why do I appreciate Mathematics? I appreciate Mathematics for its ability to define and represent ideas.
What a wonderful realisation.