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Questions, questions, and more questions!

Recently, I attended a camp called Anvika conducted by the IIST, Thiruvananthapuram for students from across the country. We had a very interesting class there - where we spent an entire 2 hours trying to find as many questions  based on an experiment he showed us as we could. While the experiment in itself wasn't too interesting (in my opinion, atleast), this thought of asking questions  sparked within me and I had a couple of very interesting questions over the camp which I  tried answering along with some of my friends there. On one of the nights, we saw a satellite in the sky one night, and it was moving quite fast. In fact, it seemed to practically cover a third of the visible sky in about a minute. The following thought came to my mind: if the satellite covers the entire sky in about 3 minutes, does it mean that it completes a revolution around the Earth in just 6 minutes?! Even accounting for errors, this would mean that the satellite covers a revolution of the ...
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Maybe a Deewangi is all we need

Around a little more than a year ago, when I was deciding where I should study in class 11, I had a meeting with the head of a certain school, who wished that I joined his school. He was quite nice to me, and really wished that I did well. However, when I told him that I wished to focus on the mathematical olympiads as well, he said the following: “Beta, math olympiads toh deewangi hai – iske jageh astronomy karle na?” Translated into English, “Son, mathematical olympiads is just a crazy obsession – why don’t you do astronomy olympiads instead?” When he said this, I just smiled, and replied, “I’m sorry sir, but I’m not going to be leaving math olympiads anytime soon.” Deep down, my parents as well as I already knew that I wouldn’t be joining that school. Mathematical olympiads for me, was (and still is) as he said, a somewhat crazy obsession – a deewangi. When he suggested that I do astronomy, his logic was that getting a gold medal in the international astronomy olympiad was ...
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Mathematics - An art of thinking

  "Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding." — William Paul Thurston, American mathematician In my previous blog ( here ), I spoke a lot about what mathematics isn’t. However, I don’t think I spoke quite enough on what mathematics truly is. Here's how I began that blog. "When we’re young we begin by learning the steps to add – we’re given the rules and we must learn to repeat them – no questions asked. Why does carry forward work the way it does? Well,  no questions asked." However, I believe that the essence of truly understanding mathematics lies in the questions you ask – and the first one, the most fundamental one, is also probably one of the hardest questions you would and could find – What really  is  Mathematics? Something that differentiates explaining what mathematics is from explaining a lot of other concepts is that mathematics was not really ever  invented . If a young student angry abo...
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Algorithms, or mathematics

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 When we’re young we begin by learning the steps to add – we’re given the rules and we must learn to repeat them – no questions asked. Why does carry forward work the way it does? Well,  no questions asked. To some extent, it is important to know how exactly to do a certain set of things while first learning maths. We may not be able to get anywhere in a subject if we’re unable to learn a few basic rules and know how to use them. However, after a certain point it is important to bring in the spirit of mathematical thinking within each student too – something missing in almost every form of school math education. Mathematical miseducation is so common, we wouldn’t even see it. We practically expect a math class to look like repetition and memorisation of disjointed technical facts. A teacher might teach you the quadratic formula – invented by some very smart person somewhere in the world, and we’re simply supposed to apply it. Often what we really learn in school math classes i...
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