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Was Shakuntala Devi a Mathematician? Or The Nature of Polynomial Click-Baits

Try this.Quickly multiply 221 and 36. Did you reach out for a pen or worse, start Excel?

By I Kid You Not , in Opinion , at September 22, 2020 Tags: ,

Try this.

Quickly multiply 221 and 36. Did you reach out for a pen or worse, start Excel? Before you do any of that, try working this in your head.

At this point, you’ll either give up this exercise as pointless or make an attempt to remember the 2 numbers. If you are the former type, you do not care much for the Shakuntala Devi’s professional motivation question, but you seem to like this wrong rabbit hole in which you seem to marching in.

Let’s start by taking a look at the numbers, one of the numbers looks suspiciously like part of Sherlock Holmes’s mailing address, and the other an estimated age at which Holmes met Dr. Watson. Mnemonics help in memorization, and the technique can be a doorway to more interesting pursuits.

Now let’s focus on the multiplication question at hand, you might be doing the following in your head,

221
36 X
_____
1326
663
——–
to arrive at – 7956 

Or, you might have done, 221 x (40 – 4) = 8840 – 884 = 7956 (if you can do all that computation in your head, you are nudging towards Devi status, at an infinitesimal pace). And there are multiple approaches that make it simpler and quicker (Vedic mathematics or Trachtenberg system anybody?). Shakuntala Devi was a wizard at these kinds of computations. She could do these and more complicated computations like, “What’s the 23rd root of a 67 digit number?” without breaking a sweat and nothing but Ragi Mudde (Cultural food fact: Just a ball of Ragi, i.e., ground finger millet ball, in the morning can keep one going through the day without any energy bars) as her power source.

Now, If you framed a question, what is (2 Y2 + 2 Y + 1) * (3 Y + 6)? And then expanded that to 6 Y3 + 12 Y2 + 6 Y2 + 12 Y + 3Y + 6, which is equal to 6 Y3 + 18 Y2 + 15 Y + 6. And if you seek further to understand, what if the variable Y is 10 and then calculate,

                                    = 6 * 1000 + 18*100 + 15*10 + 6
= 7956

You constructed a single variable polynomial, found a variable value that produces 7956.

Aha! You have created a generalizable pattern.

Now, if you go on to explore the characteristics of the polynomial, you have formally entered the world of mathematicians. You are a number theorist! You are enamored by polynomials as a category as opposed to a specific number.

Now if you created a 3 variable polynomial like, Xn + Yn = Zn , you belong, without any doubts, to the world of mathematicians. Pierre de Fermat, about 400 years back, conjectured that the above polynomial does not hold for n >2. When you plug in n=2, it is the familiar Pythagoras theorem. For n>2, it is a hairy monster. Andrew Wiles proved the Fermat conjecture couple of decades back. A simple looking bait and the hunt lasted 400 years. The mathematics that was created to solve this Fermat conjecture is now the scaffold for the next super-structure in the world of mathematics.

If you ask a question, but why bother? Stop for a moment and ponder on the fact that computers became part of our life in the mid-20th century but the mathematics behind it, like Boolean algebra, prime number factorization, etc. was done couple centuries back. A good Mathematician has this nose for exploring problems that have seemingly no practical use until it has!  In conclusion, Ramanujan or Gauss or Sophie Germain, were all famously computation-obsessed, but the better part of their life was spent on mathematics which enthralled generations of mathematicians while Shakuntala Devi thrilled scores of her contemporaries with her powers of computation.

Written by Prasad S.

Prasad is a mathematics aficionado by night and a global business leader by day. If you feel compelled to share your views, do write to skprasad99@gmail.com

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