This year at the 52nd International Mathematical Olympiad, a team member of India got a Gold Medal; an event that had been missing from our performance for about a decade. Hence, this is an appropriate moment for me to write a bit about Mathematics in general.

The first thing I wish to say about maths, is that it deals with figments of our imagination and thoughts. And no two people can actually have the exact same thoughts. Then what does it mean, to know the Pythagoras theorem? And more importantly, what does it mean to say that the Pythagoras theorem I am thinking about, is the same one that you are? How can people actually have intelligent conversations and write even books on what might mean different things to different people?

So, my own explanation for this is: If one could somehow instruct the whole world to simultaneously think about the Pythagoras theorem for a while, we would all be (probably) thinking of this property of a right angled triangle. Of course, the mental picture or dimensions of the triangle will vary wildly from person to person. The content of our thoughts may be different, but the form is the same. So in a way, **mathematics is a living example of collective memory at work. **And knowing the Pythagoras theorem, is tantamount to nothing other than being part of this collective memory. So, whenever you teach somebody the Pythagoras theorem, you are not just saying the words to him; you are including him to also share the collective memory that millions of people already have in common.

If art is considered as the purest form of human expression, I think mathematics is the purest form of human thought. And often I wonder whether the analogy between maths and arts can be taken further. For instance, it is a generally accepted fact, and does not come to us as a surprise that not all people have the same level of appreciation of art. But for some reason, when we see students who don’t like maths, we consider that as a failing of our education system. Sure, one can train people to be able to do some basic calculations, just the way anybody can be mechanically trained to play a piece of music. But true appreciation of maths, just like art, is an inherent quality of each person, and cannot be created out of nothing. Then, is it wise for educators all over the world, to strain their brains to create better ways to make children like maths more and more?

To conclude: the thirst for maths is like the quest for gold.. And the true location of the treasure has been given by Paulo Coehlo in *The Alchemist*: One has to look within.

One thing that I realized over the last few weeks was that we hardly use the formal system in our proofs. We don’t even know the formal deduction rules properly, yet we ‘prove’ theorems – based purely on our interpretations, and strongly believe that our proofs are correct. But what education has achieved is that it has taught students the interpretations, leaving the formalism totally out of the picture. Hence everyone has “the same content” in their thoughts. The form is implicitly the same anyway.

But it would be interesting to see how kids schooled only in formalism, and then set free to interact would develop their interpretations.

Also, it’s great to hear about the IMO results this year.