HOW I SEE MATHEMATICS

                                              

Can you still remember those days that we started to raise our fingers or may be pointing the fingers towards certain objects and shouting ONE TWO THREE... out loudly and that very moment where we started our counting process, which led us to put a strong foundation at our primary age, when dealing with numbers. Numbers were a worrisome sight for sure. And i don't think there was someone in our childhood who was allured and was interested in numbers as they were in fairy tales or playing, which is quite acceptable because the childhood was always milky and we all wanted to see pretty things which make us happier and sweets which bring us taste. So it was quite an obvious fact that neither numbers nor counting things brought what we wanted in that childhood, even though we had to deal with the process, because it was more of a constant process which every child had to be fulfilled in that age. So you should have been wondered about how things have changed and gone up to now, when you look at the present circumstance compared to what you and i experienced in our childhood, related to the continuous progress of Mathematics.

Think for a while. Numbers were there to get us used to the smell of Mathematics. That was the core and the necessary factor to be made, if you want to go further and further. Then there will be mathematical operations, equations with unknown variables, geometry, trigonometry and more. And once you looked back along the path, you have made so far, you will find out that the process has been made upon an ordered sequence like a chain. Numbers are certainly a prime toggle of it. And the toggles are yet unbreakable   and wouldn't be in future as well, because of the standardization and everything has made upon Mathematics, which was built on axioms. That's something which i always astonished and continuing to be so, because of that strong foundation (axioms) brings the stability to Mathematics unlike in other subjects. Also it's amazing when you think about certain mathematical methodologies and expressions ,  that are used to represent certain phenomena in a shorter form with a bunch of variables that were mixed with integration, differentiation, inequalities, logic and many more operations which lead us to solve many more paradoxical matters in easier way. I think that's why the concept "NUMBERS" becomes even more praise worthy and useful in the context of Mathematics.

Though it's not all about numbers and equations. If my memory goes back to that golden era, the ancient Greek history which has been a major part in modern Mathematics, probably with the rise of philosophical ideologies and most of them have made a considerable impact on modern Mathematics too. Especially in that time, logical reasoning and arguments were controversial additions and created a much more interesting face to the subject. Logic has always been a one of the very interesting modules. Some arguments made a plenty of bizarre instances among olden Greek philosophers and still they do and at times the things that looked probable (practically) appeared to be as highly impossible because of that. Zeno was a one of those Greek philosophers, who did challenge people with nice logical proofs and arguments. He was certainly a genius at that time and enabled to make various philosophical interpretations on certain phenomena in a logical way. Imagine how wonderful would have it been to prove something complicated in a logical way rather than using a heap of variables with operations or to prove something in a non-mathematical way rather than using a complicated mathematical model. Something like, if you have to determine whether a given monotonic sequence is a divergent or a convergent one and the value that the sequence approaches when n(number of terms in the sequence) goes to infinity? ,then you probably have to know the concept of a monotonic sequence, definitions of the divergence and the convergence of a sequence and more importantly the concept of limit, if you are going to solve it using the techniques of modern Mathematics. But what if someone gives you the same question in more of a practicable way rather than a mechanical way and asks you to explain the phenomena philosophically or logically (may be to prove the contradiction)?. It's probably hard for us but that is what Zeno did(related to "The Arrow paradox") at most times. So the numbers and logic have been the forefront of Mathematics and i believe this variety is something that keeps our interest more and more in the subject.

I always eager to see the abstruseness of the concepts, bigger equations, number patterns and geometrical sketches whenever i look at Mathematics regardless of how abstract its concepts have been. For you, the fact may be different. But we always have something in us, which tempt us to be attached in particular things. And i always believe that Math shows us more than what we expect it to be and more than what we learn under the label "Mathematics". But most of us don't have that interest to search the underlying core, which is a disappointment for sure. We only look at numbers, variables, operations and theorems more often than not. But we don't want to see what those concepts are all about, why have these variables, numbers and operations put there? and don't try to build a physical interpretation or more of a coherent image according to those contents in Math. I think that's why there has been an unconsciously held delusion about Mathematics among most of the students .But what requires is the passion and the interest to make sure that you wouldn't let yourself down and wouldn't give up in doing Math over and over again.

HESHAN ARAVINDA

2011/2012