Mathematical Foresight

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Hitesh Gakhar, HLF13 participant: As both an undergraduate student and budding researcher, I am unsure as to how to express my immense gratitude towards being selected for HLF 2013. Even before the event had started, I knew that meeting people of such intellectual stature would certainly change something inside of me.

Thinking back to my days in high school, I remember being introduced to the concept of a real line. Now back then, for some reason, I had the striking intuition that a real line might not be the best construction. It might be better (for certain purposes) if it were a number circle instead! One would obtain such a thing by identifying positive and negative infinity as the same point.

The inspiration behind this rather vague thought was that in the new space, certain trigonometric functions (like tan) become continuous – what a grand idea! Soon after, in the early years of my college life, I was introduced to the so-called ‘one point compactification of real line’, which is precisely the same idea that had already found its way into my head.

Now when you formulate an idea, and you later find that this idea has already been extensively studied and formalised, it gives you a strong sense of mathematical foresight. It’s somewhat trickier in this day and age to have a truly original mathematical idea, and this is even more true when you’re an undergraduate. So predicting a powerful piece of maths before you’ve seen it can be an encouraging experience, as it shows that your thinking is aligned with that of the greats.

And now, at Heidelberg, I’m already having more of these revolutionary experiences.

On Tuesday, I attended Avi Wigderson’s lecture on Randomness. Now, being a lover of probability theory, I had already developed a few of my own notions and intuitions about the world.

In particular, I had often considered the grand question: is the world deterministic or probabilistic? Well, as long as we are ignorant, randomness exists. In other words, it’s the lack of information which generates randomness and not the observed phenomenon itself. Once you have dug out every piece of information, you can predict everything with utmost certainty.

This is exactly what Avi’s talk was about. He verified precisely the thoughts which I once had. I was correct, or at least I had the same thinking as one of the great minds of our times. I felt joyous, proud and motivated. It was one of the best feelings I have had in a long time.

And there is still a lot that is yet to come.

Courtesy of Hitesh Gakhar

Hitesh Gakhar was born on March 25, 1991 in Faridabad, India. He has been a mathematics lover since the beginning. Currently, he is working on his masters-thesis(in functional ananlysis). Hitesh also has been a stage actor, a photographer and an amateur comic maker. His math-comic page on facebook is called ‘Dr. Isomorpheus‘.

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