K Sreram

There
are many who keep themselves unclarified form this doubt and convince
themselves with some solution that does not actually hold well optimally.
The common answer a random person would give is: “mathematics is a subject that
involves heavy reasoning and IQ skills which could later be used for general
reasoning in everyday life and people who are good at it can be labeled: genius”. But I differ from this view! I want to point out that mathematics is a unique discipline separate from social life skills and an expert mathematician cannot become a skillful survivor in his social life consequently. Before going any further with
this article, let me make it clear that I am just a computer science
student and don’t have any prior knowledge on general psychology or social psychology or pedagogical psychology (though stuff I am going to talk about topics that can
be classified into these subjects) or any other related subject. All that I put
forth in this article are my own views on these subjects and might contain
facts that are wrong (excuse me for that).

Mathematics
is a subject which has unique applications in our everyday life. Whenever
mathematics is referred to, people tend to imagine it to be a subject filled with
numbers and calculations. But let me tell you, mathematics is not such a
subject. Schools and universities teach us how to solve problems instead of
letting us solve those problems ourselves. People have misunderstood the phrase “solution
to mathematical problems” (especially in schools in universities); they
believe that formulating a solution is same as learning a “universal algorithm” to
obtain the solution to a family of problems. That’s not what mathematics is about. It’s about finding an optimal solution for a problem and not just learn
an existing algorithm to solve that problem. Mathematical intelligence requires
two main intellectual qualities: creativity and calculative ability, like we
humans need two eyes to perceive an extra dimension in space (with only one eye
we just perceive just two dimensions, but with 2 eyes we see the third
dimension: depth).

There
are people with just one such ability: creativity or calculative ability. In
schools and institutions, we are taught to master the calculation part.
Creativity is rarely acknowledged in our dynamic social lives, and in our educational institutions.
People with just creativity and no calculative ability tend to get involved
more into arts like music, drawing, poetry, authoring stories. People who are good at being calculative end-up becoming engineers and engineering subject teachers.
But people with both these qualities end up becoming physicist or
mathematicians.

Before
I go about answering the main questions, let me tell you that by using the word
“ability” I don’t mean that that person has to be born with it. I believe that any person can cultivate any talent or ability by investing rigorous work effort in doing so for an extended period of time. We don’t
get something we don’t work for.

Let
me answer the questions given as this article’s title. Why do we need
mathematics? We need mathematics (which is an enormous collection of solutions
to various unique and unimaginably breath taking problems built up from several
centuries of human life) to solve problems. So as simple as that, why do we
need to learn mathematics if we are actually going to solve a problem
ourselves (ground-up)? The answer to this questions is that we don’t need to solve a
problem from the scratch. Because if we were to do that, it would take
centuries! Imaging a mathematical subject like vector geometry; the underlying
concepts that were used to create that subject dates back to several centuries.
Human lifespan is short; we can’t waste our lifetime “re-inventing the wheel”
(but taking up small challenges is not wrong). So we use the concepts human
have developed before to analyze and obtain our solution to most problems. The main requirement
of mathematics is to quantize our nature and prove or derive physical or
chemical or biological scenarios. Why do we need to quantize? Though our common sense can predict theories to some precision, it loses to
scenarios that are so in-differentiable. For example, Isaac Newton discovered
that the same force of gravity that pulls the apple to the ground (and that
hurt his head!) Pulls the planets in our solar
system towards the sun. But our common sense says: “no! How is that possible!
If the sun was to pull our Earth like how Earth pulls the apples, then should
our earth be pulled into the sun?” That’s not actually true and yet the
scientists in Newton’s time rejected his work refusing to accept his theory. But Newton did
not give up, he created a set of mathematical formulations that proves that Earth
doesn’t have to go into the sun!

Newton laid down certain mathematical proofs to state that the planet moves in
elliptical orbit because the sun pulls the earth towards it and also because at
any point in time, the earth has a particular amount of potential energy and a
particular amount of kinetic energy. At all times, the sum of the potential
energy and the kinetic energy equals a constant value. Let me omit the proof
here to maintain the lucidity of this article. You might ask how Newton came to
know about that (that the gravitational force is responsible for the
elliptical movement) without using
the mathematical derivations himself. Newton was smart enough to understand that without needing any math. But when he wanted to convey his findings to the scientists in his
time, he cannot just be talking about his imagination and say: “hello
everyone! In my imaginary simulation of the planetary system I can picture our
Earth moving tangentially when it’s closest to the sun (as we all know from our
observation). As it’s pulled towards the sun, its tangential velocity pushes it
away! And again in my imaginary simulation it changes direction towards the sun
following a curvilinear path and forms an elliptical orbit!” (I made this up
myself. Newton did not speak these words). Scientists don’t need vague stories and imaginations, they want the precise description or proofs for the proposed theory. They want you to express every detail there is to express.
Conveying such critical details becomes hectic using an ordinary language, so a
language like maths is needed!

So
let me go to the last part of the question. Is maths required for our everyday
life? The straight forward answer is no. But indirectly, yes. The basic
underlying principles in our technologies that we use today dates from the
beginning of mathematics! Of course if the law of gravity and the Newton
mechanics was not accepted by the scientific community, we won’t have any of
these technologies we enjoy today. Does this mean that mathematics is just a mere
language used to satisfy scientists and not more than that? As I said before,
mathematical expressions define the system while any explanation written in an
ordinary language only shows the viewpoints of the author. So to put it
elegantly mathematical formulations proving your findings record more
information than you intend to record. And this information will be hidden
under your own derivations and equations and it could take a while to get
reviled; either by you or someone else. So more than acting as a language, it
acts as the best method to capture complex situations thoroughly.

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