My Experiments in Mathematics

For those of you who do not know, I am a Mathematics graduate. That's what I did before enrolling for the MCA degree that made me a software developer. Mathematics is something that always intrigued me, something that I felt a passion for, in spite of the fact that one of my Professors thought otherwise. Fermat's Last Theorem, Russel's Paradox, Group Theory... it's a wonderfully weird and completely abstract yet totally real world out there. There is Mathematics everywhere... it forms the base for a lot of what goes on in Physics, in Computer Science, in Finance... so it's very closely related to our daily lives. And yet it's so abstract to the core. Let's think about where it all begins. Numbers. Is there anything around you that you can pick up and say "This is a number."? No. Because it's a concept that exists only in our minds. You can relate natural numbers and rational numbers to the quantities in which a certain commodity is available in a certain place, but, it's still three apples, or two-thirds of a pie, or twelve bottles of paint, not three, or two-thirds, or twelve. And what happens to negative numbers, or real numbers, or complex numbers? And yet, theories that explain everyday, real life phenomena, like gravity and demand vs supply need these numbers.

There's also a point of contention on whether Mathematics is an Art or a Science. Alfred Nobel did not think it was a Science, because you could not conduct practical experiments in Mathematics, like you could in Physics or Medicine. He also did not think it could benefit humanity. The University of Delhi, from where I graduated, offers both a B.Sc. and a B.A. degree in this subject, depending on the subsidiary subjects you choose to study alongside. Oxford and Cambridge stick with B.A. degrees. I think it's a bit of both. That's part of the beauty of the subject. It brings the worlds of Art and Science together. You need a scientific mind to understand Physics, and an artistic mind to understand literature. But you need a blend of both these outlooks to understand Mathematics in the true sense.

An interesting anecdote that comes to my mind here. I once appeared for an interview for a scholarship to finance higher studies in Mathematics. It was a diverse interview panel. There was one person from a Physics background, one from fashion design, one from Economics... There was an American on that panel who did not have any background in the subject. He asked me to explain Group Theory to him, beginning from the very beginning. I started out with sets, then functions, operations, then commutativity and associativity, and after a good ten minutes I hoped I hadn't let my Professor of Group Theory down. She was one of the best Profs and one of the best human beings in the Mathematics Department back in College. But as it turned out, my interviewer told me, "I feel like Alice Through the Looking Glass." That was the third and last scholarship interview I had at hand. And I walked out of there, being unable to familiarize Lewis Caroll's fans with Mathematics. Interestingly enough, Lewis Caroll himself was a distinguished Mathematician but his talent at delighting children with his word play overshadowed all his other talents.

I always found the more abstract realms of Analysis and Algebra more interesting than the less abstract, applied areas such as Numerical Analysis. Because that's what pure Mathematics is. Abstract. An infinite space where you can spend hours on end looking for solutions to problems or looking for new problems to solve. A space where a restless mind in Brownian motion finds its due.