It takes two to make a quarrel! It takes two to make a dialogue. I have, during the past two months been writing letters to mathematicians of prestigious universities but my arguments seem to carry no conviction with those who are supposed to listen as and when challenged and file their answers. I had summed up my distrust of current state of mathematics in the form of a paper which needs to be evaluated by the students of mathematics. The consensus of silence amongst the guardians, who are supposed to defend the integrity of mathematics, is appalling. Have the mathematicians gone too far in popularising fake mathematics? Have they reached a point of no return? Is accepting truth so painful and revolting?
Since my monologue is not flowering into a dialogue, I have for the time being stopped doling out new ideas. So the discussion about plane and point, as promised at the culmination of last chapter will not proceed.
As young students we were exposed to the tyranny, truth inflicted on a king who was very fond of clothes. Yes, I am talking about the story, Emperor’s New Clothes! It is a typical story weaved by the author around temptation of a powerful person who turns logic of argument into an undeclared order for silence. So starts the story of the king who had a new coat for every hour of the day. Like European mathematicians, two persons posing as weavers swindled him and made him a laughing stock at the same time. The silence of all and sundry around him was deafening till a child in his innocence says that which was true but unthinkable.
Nicholas Sparks in his book The Notebook says “We sit silently and watch the world around us. This has taken a life time to learn. It seems (that) only old are able to sit next to one and another and say anything and still feel content. The young brash and impatient must always break the silence. It is a waste, for silence is pure. Silence is holy. It draws people together because only those who are comfortable with each other can sit without speaking. This is the great paradox.”
Paradox! But the pain inflicted on the young minds due to the consensus of silence is real. The parents are made complicit in this conspiracy of silence. They part with their hard earned money but purchase misery for their kids. After all, how many students pursue mathematics seriously after class 10. And after class 12, not even 0.1% students study mathematics. The tragedy is that the rest of the students clean their minds of all mathematical junk collected by them as young seekers of knowledge.
I have before me class 5 book published by NCERT. At the level of class 5, we were supposed to sit in a combined test at divisional level! Our knowledge of mathematics, as I recall was much superior than what the new age authors are trying to inflict on students. The basic problem with new age math authors is that they can’t make a difference between teaching math as a skill and using the skill as a tool for solving math related problems. This book far from teaching anything to students confuses even math graduate mothers. It means that mothers who can home teach their children are rendered helpless. The book, in order to look big has only figurative presentation which confuses the kids. Simple concepts like LCM & HCF become beyond the comprehensive capabilities of the students. They can’t do math even mechanically. The connection between knowledge and understanding not only bypasses the young ones but also scholars. We shall see this disconnect clearly when I shall analyse the realty of a solved problem.
It is not only that mathematics in its present avatar sabotages the efforts of the national leadership to educate Indian masses. Teaching of the English language, which is so important for the budding students also suffers from the same malady. At present learning the english language occupies a premium position in knowledge gathering matrix. A good knowledge of English language of the students helps them to come to terms with the world as they grow up. Or when exporting skilled human resource opportunities arise, English language comes handy. But the new age authors have dealt a mortal blow on the practice of teaching it by their presumptuousness. In our time, as is won’t in Europe, translation from one language to another served as the kingpin of learning of this language. We were supposed to think locally or in our mother tongues and then translate the sum and substance of the ideas into the English language. This practice slowly but steadily made us to come to grips with the idiom of the written and spoken word of both the English as well as Hindi language. But some gentleman, powerful and convincing like the two fake weavers, came up with the idea of direct learning. Thus practice of translation was given a goodbye in school curriculum. The results are before us. The frugal understanding of the English language affects the capacity of the students to learn the new and complex additions to knowledge pool. This infirmity deprives them of capability to reproduce correctly nuances of learnt information.
Any reform in education sector in India should start with the following executive order:
- Re-introduction of practice of translation from English to vernacular and vice versa
- Simplifying teaching of math skills and postponement of problem solving till class 4.
I shall now reproduce one letter addressed to Dr Arjun K Rathie the visiting faculty (Mathematics) of the University of Kerala.
shibhan lal pandita <firstname.lastname@example.org> Oct 11
Today is Vijayadashmi. Happy returns of the day!
Post retirement, a near divine intervention pushed me into the rough and tumble of mathematics by an innocuous remark of my granddaughter- “I hate mathematics”. She was then in class 3. So I tried to understand the reasons which made this subject beyond the reach of almost all the students. My efforts led me to draft a paper titled: Mathematics- the Critique.
While drafting this paper I stumbled upon an easier way to roll almost the entire arithmetic into one ‘ field of mathematical deception’ which if introduced in math curriculum can make a difference. In fact arithmetic will demote to a mental math activity.
Since March ’16, I have been moving from pillar to post to convince universities as also the HRD Ministry, to look into the malaise but to no avail. I therefore invested in the web site surprisemajor.com to get in touch with the world at large. My method of testing the mathematical waters is simple. I have put together a set of questions and am seeking answers. Amazing that even Prof. J R Patadia- IMS, has raised his hands. There is particularly one wrong derivation which puts the entire calculus under shade.
Today I started my day by going through the life story of Bhaskaracharya and came to know about the mathematician Pell. There I saw the following equation:
61x2 + 1 = y2 I could not follow the argument but a look at the equation told me not only how to do it but also solved it. Trust me Sir! I did it in 2 minutes!
The answer is x=1/30 and y= 31/30
It was through Twitter that I came to know about the mathematician Dr C K Raju (ckraju.net). I have found that he has a wonderful understanding of mathematics. Curse, I don’t have the e mail address of Prof. Raju. He simply distrusts the European math and argues that when the Europeans began to get mathematically trained and thought of contributing to the coffers of mathematics they had to do so in such a way as not to come in conflict of the Christian Theology. Hence argumentative math in place of empirical math! I think our ideas converge.
Sir, I invite you to go through my web site with an open mind and alert other scholars as well in case you find merit in what I am trying to say. You can skip reading my tale of woes Chapter 1 Part 1 and go straight to parts 2 &3 to save time.
I am from Kashmir, now like a refugee in my own country. Dr Homi Bhabha Is said to have spoken these words: The truth belongs to a migrant’s double vision! Let the truth be spoken even if it is bitter!
S L Pandita