The real reason why mathematics is considered difficult/boring

Mathematics is a construct that enables us to try and solve problems in the simplest way possible and arrive at concrete answers.  Contrary to the mindset of mathematicians and experts , most of us who aren’t fond of rigid logic or have been intimidated by its presence in our curriculum, bear a common notion – that it is difficult or boring but is it though? Perhaps, the term “mathematics” brings back memories of boring lecture sessions or constant failure in written exams, that has managed to burn our confidence to the ground. Perhaps, a bundle of old exam sheets bear testimony to how numbers got muddled up in our head, or how formulas got lost in the dark recesses of our mind. Whatever be its reason, this article tries to analyze the primary reason behind such hatred.

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THE SUBJECTIVE NATURE OF BOREDOM AND DIFFICULTY

It is important to understand that difficultly of any discipline, is nothing more than an interpretation which more than often stems from a very narrow set of bad experiences. Every problem revolves around a rigid logical structure. At no point, will x + x, hold a value more than or less than 2x. It is in a way formally establishing what already exists. The truth of a statement holds irrespective of whether it is proved, which is more than often, a reflection or implication of some real-life event. So why is this considered “boring”?

The primary reason behind labelling this as “difficult” is the mundane and lifeless nature it gets introduced to us from early on.We appreciate the value of things, when we understand the reason behind doing things, and for mathematics its no different.

It more than often, becomes a chore and something to get over with, rather than appreciating its strange, yet consistent framework that is a reflection of truth. The theorems and formulas of mathematics was designed to solve problems, but sadly becomes the problem itself for those who find it incredibly hard to sit through lectures. Unlike many other disciplines, mathematics looks for precise objective answers, and the road towards a solution mostly comprises application of previously established theorems.

The boredom associated with associated with mathematics stems from a lack of an understanding beyond purely mechanical steps, formulae and well-established equation, not to mention the lack of an objective beyond arriving at a clear-cut answer. It is no different from cramming a text of history without understanding a single word.

The difficultly of mathematics is perhaps debatable by those who have made it a mission to stay away from it, but it is without a shred of doubt, an indispensable branch of study which have served as a cornerstone in furthering of scientific studies. Mathematics brings order to chaos, it finds patterns in the most disconnected and vague aspects of the world, yet strangely enough, it holds true.

INTERPRETING A MATHEMATICAL EQUATION
The following example, illustrates the contrast between the apparent mundane nature of a series and what it implies. Let’s say one has been asked to find out the sum of the following infinite series:

1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......\infty

Assume that a person running at “constant speed” has to cover a unit distance on the number line from 1 to 0.
Let’s also assume that it takes the person 1 unit of time to cover half the distance.
Now since the person is running with constant speed it is certain that for the next one-fourth he will take \frac{1}{2} unit of time.
Similarly for the next one-eighth he will take \frac{1}{4} unit of time.
So in general, the portion from
\frac{1}{2^n} to \frac{1}{2^(n+1)} will take \frac{1}{2^n} units of time.
Adding up all these time intervals gives us our desired infinite series
1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......\infty
But then if we think physically, since the runner was running at constant speed and has covered \frac{1}{2} the distance in 1 unit of time.
To cover the entire unit distance he should take just twice the time.
So he should take 2 units of time to cover the entire distance.

1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+......\infty=2 !!

But how can the sum of an infinite series be finite!! How can something as absurd and incomprehensible as infinite make sense to us in the simplest way possible – an integer?

 

To understand why we need to dig deep into the subject and accept its importance.

Click here to understand the concept of infinity and infinite series.

This is precisely the perspective from which the concept of “convergence” is better understood, than just solve endless problems. The whole point behind discussing this example is that the above example piques interest because it can be related to, on an intuitive level, that natural makes us ask further questions.

Often in class we get introduced to convergence through a classical \epsilon definition rather than being told why convergence needs to be introduced.

Mathematics, ideally shouldn’t be looked upon as a burden or duty by teachers, rather as the most essential accessory of scientific studies. The joy of mathematics can be experienced only if we try and explore the hidden meaning behind equations, how mathematics has so far been responsible for our progress, and its application in other disciplines.

 

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