Hi there!!!

For some people, it is Mental Abuse to Humans. For others, it is the Most Amazing Thing in History. Truly, the word MATH is possibly the one which elicits the most varied response from students all over the world.

The entire student community is split into three, regarding this subject. The first type includes fanatics of the first degree, who would live, eat, sleep and breathe mathematics, away from other trappings of the material world (I count myself among them).

The second type are ambivalent towards the subject, as prepared to hate it as to love it.

The third type are the math haters (grrr), the people who would make all kinds of excuses, appointments and emergencies, just to avoid a date with the subject.

Like it or not, mathematics is an essential field in today's life. People may not like it consciously, but they would baulk if they were to find out how much maths they actually use subconsciously in real life. Like the proverbial octopus, mathematics has spread its hypothetical tentacles across fields and spheres of life. Without it, life as we know it...would not remain as we know it.

Nevertheless, in all these years of mathemania, we have unearthed some very interesting ideas, incongrous to what we know and so powerful, that if they were true, the fabric of mathematics would come undone.

For instance,

Let a = b = 1.

Then, a = b

or, ab = b²

or, ab – a² = b² – a²

or, a(b – a) = (b + a)(b – a)

or, a = b + a

or, 1 = 2

Ouch.

For those who did not understand how this is possible, a word of advice. This is NOT possible. To find the error in this seemingly sound argument, just substitute the values in the expression.

You will find that to reach the 6th line of the (ahem) proof, you are dividing the whole equation by (b – a), i.e. 0, which is not possible.

In another case, let's take a right triangle.

Now, we all know that the side c can be given as a² = b² + c², which is the Pythagoras Theorem.

Now, consider this case:

Now, the sum of all the small bits and pieces of the lines is equal to (a + b), agreed? Please understand this statement to comprehend what I shall state now. No matter how many small pieces I make, the sum of their lengths shall always be equal to (a + b).

So, if I make infinitely small pieces of those pieces, we can assume that it will form a right triangle just like this:

in which case, a = b + c. Which we know is wrong. So, where's the mistake?

If one argues that you just can't take an infinite no. of sides as a single side, then tell me, shouldn't the entire branch of calculus - that is based on the assumption that something can be divided into an infinite no. of parts which can be worked upon, and vice versa - be wrong?

Like these problems, there are numerous fallacies in mathematics which provide a lot of mind-scratching and brain-boggling to the casual reader. In this way, we do find abnormalities in mathematics. But then, we the students find abnormalities everywhere. 

Still, I would maintain that mathematics is the most correct and effective form of communication, because everyone understands the language of mathematics. Like one little known scientist once said before he gained renown, "Pure mathematics is, in its way, the poetry of logical ideas." That man was Albert Einstein.

I would be very interested if you can share any more interesting and strange problems you know of and would like to share.

Till next week, then.

Yours in absolute abstraction
A student

Hello people!

Everyone reading this has gone through the cycle of education at least once. The fact that you can read this proves that statement, and the fact that you are reading this on a computer shows that your education was - and still is - successful. Parents end up getting going to school more than once, thanks to their charges.

Having said that, there are a lot of contradictions one comes across in his or her schooling life. A lot of instances arise where the student is left scratching his head as to what is right and what is wrong, what to do and what not to do, what to study, what to leave. Basically, it is in situations like these in which the student seriously doubts his mental capability and asks, "Why am I here?"

For instance, the study of atomic structures. Since grade 5, we have known that an atom is like a ball with very small balls rotating around it. This theory got a name and refinement in ninth grade, and Dalton became the father of chemistry for us. The next year, we were told that his thory was all wrong and J.J. Thompson actually knew what the atom is. Fine. We can live with that.

Before that thought could take root within our minds, however, that theory was also rubbished, and Rutherford came in with a new model. Here, the roots of frustration were planted. The syllabus forced us to learn about alpha-rays, gold foil experiment, angular momentum and whatnot, and yet, there was an underlying feeling that this too, could be flawed.

Our fears were confirmed when, in the 11th grade, Rutherford was pushed out to give way to Neils Bohr, who gave the first really concrete theory about the structure of an atom. After arming ourselves to the teeth with formulae regarding atomic radius, energy of electrons and quantum numbers, we felt reassured. Surely, after all these shenaniguns, there was nothing more elaborate and correct than this.

But no, he too was wrong. The current theory of the structure of the atom - which talks about Schrodinger's wave equations and Hamiltonian operators and electron clouds - is what is accepted today. However, the mass emotion among science students now is that of skepticism. Surely, there will be another theory that shall herald itself as the final word in chemistry, and everything else be damned.

Have you heard of the saying, "Against stupidity, even the gods contend in vain"? Well, we have but only just begun to understand its complications.

Until next time, then.
Yours in utter confusion
A student