Often, people ask me, “Electronics kyon chhoda? usme maths use hota hai na.. OR finance mein ja; usme maths bahut lagta hai….” My answer to them is farily simple: “Lekin Maths mein electronics ya finance nahi lagta.”

I am lucky to be able to pursue PURE maths. I have finally entered the league of mathematicians. We jokingly claim – We may not do everything useful like the physicists and chemists, but at least what we do is pure!

I used to joke: that if a day comes when the world believes me to be a good mathematician, and I have enough money to sponsor Parab prize for pure mathematics, then I shall award it to a deserving candidate. But once an application has been found for his theorem, I shall take away that prize! Since the application is discovered, there would exist physics and economics prizes for him to be bestowed upon.

Recently, a collegue friend of mine doing MSc Math@IITB was awarded a prize for good performance in his BSc Mathematics at Mumbai University. He had actually completed his Msc (part one) from IIT Roorkee. He then left the course incomplete and came to IIT Bombay to pursue MSc in pure maths. I asked him, why he didn’t get the BSc prize last year as he had completed his Bsc two years ago. He replied that his course at IIT Roorkee was in APPLIED Mathematics; so having deviated from pure maths, they say he didn’t deserve the prize then. I was amazed and equally proud. A true mathematician’s aesthetic sense lies as much in hating differential equations and statistics (and the like) as in appreciating the beauty of the celebtated Euler equation exp(i*pi) + 1 = 0

(I have been carried away, so let me explain: This equation has five great constants- e, i, Pi, 1, 0 that come together with basic operations +, * and exponent, each used exactly once!)

At an interview for Phd in Maths at TIFR, another friend of mine was asked to evaluate a particular limit. He couldn’t solve it using first principles and hesitantly, resorted to the L’Hopital Rule. The interviewers were frustrated at his using the unromantic way of solving it.

Indeed, when many pure mathematicians (at least in India) hear of “differential equations”, I have seen their faces turn sour. We don’t call the consequence of a theorem as its “Application”, but label it as “Corollary”. We don’t want applications, we want results; romantic results!

As mathematician G H Hardy puts it:

Beauty is the first test: there is no permanent place for ugly mathematics. (It will be replaced by elegant mathematics.)

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October 9, 2008 at 13:40

AnonymousI had read somewhere

“Winners dont do different things they do things differently…”

but sometimes u need to do different things..like pursuing Pure maths.. which dont really make u a loser…u r d winner Parab..hats off to u for doing things which noone else dare to do..that makes u a winner!!

Ameya

November 25, 2008 at 11:47

arunJust one nit about — Differential equations. Much of mathematics that developed in the last century were inspired by real world problems and differential equations is one of them which is now no less maths than group theory or for that matter any other subfield of maths. There is plenty of interest in the field and the subject has gone through a heavy dose of abstraction to lift it up to the standards of 20th century maths. It is now widely used in other areas of maths. A result comes to my mind is the proof of the poincare conjecture (that won grisha perelman the fields medal)– this was solved with a help of PDE like the heat equation. Navier stokes (PDE again) is another of the hot problems around. Russians I believe know how to attract interest in differential equations since it has produced plenty of pure mathematicians who have done spectacular work in differential equaions and dynamical systems — vladimir arnold and pontryagin come to my mind. Both front-rate mathematicians, they were unafraid to tackle the nastiest of problems in differential equations/calc of variations and even indulge in empiricism (which you find repugnant) and have contributed immensely.

I read recently in our library that Pontryagin tossed and turned in his bed for two days without sleep to discover one of his most beatiful results — The maximum principle. The idea came to him after he invited engineers to discuss their problems in aircraft control. How much poorer the world would have been without this result is very subjective question but for me — it is just great maths i came here to look for.

Unfortunately here in our college diff eqns is a topic that has been relegated to the sidelines with only some `un-glamorous’ mathematicians working on it. We have been taught differential equations as a collections of results to remember (like in calculus) to be accepted and regurtitated on exams. (I hope to better understand the subject in the third semester with PDE)

We accept maths as beatiful and among the things that is endearing to us is the richness of diverse fields. Even more mystifying are the connections between them. Yes, Group theory is used in dynamical systems see arnold’s book on diff eqns for example. Topology courses are taught with applications in differential equations.(Poincare-bendixson theorem for example).

How boring it would have been if maths were just group theory or just PDE, just topology. Yikes, it makkes me cringe :-|.

These connections are for me the reason maths is worth pursuing, every now and then we find some unexpected relation some unifying principle keeping our interest alive.

December 8, 2008 at 16:22

Abhishek ParabWell said, Arun! Hope I will also learn PDEs with a new vigour!