The Mathematics that I wanted to learn : The trajectory of an average mathematician ( Part-1)

One of the most incomprehensible thing for me is that I am in the mathematics profession. With a little apprehension I would like to call myself an average mathematician. In fact I was possibly never cut out to study mathematics. I was the worst student of mathematics in my batch in school till the eighth standard. I did not even know what a factor was, what is the meaning a multiple of a number and so forth. I had failed most of my exams on mathematics till then. But possibly as “Don Corleone” had said everyman has but one destiny, I was destined to fall in love with mathematics. In my eighth standard I was lucky to have Mr Nilachal Samanta as my teacher. He told me that he used  to fail in mathematics and later on  excelled in it and had the chance to attend the lectures of the great theoretical physicist S. N. Bose at the University of Calcutta. He used give a lot of time to me and spoke to me about mathematics as if he was telling me a story. He largely spoke about geometry. At that age when kids are more bothered about their next football match I learnt about the Babylonians, about Euclid, about Archimedes, about Apollonius, about Brahmagupta and so on. One afternoon I suddenly felt that I was understanding what my teacher was telling me and was even enjoying it. That evening I went back to my  hostel room and started looking at the exercises on geometry. They were called riders in our days. To my surprise I found that I could effortlessly apply the the correct theorems, do the correct constructions and solve the riders. I went back the  next day and told my teacher that ” I have fallen in love with mathematics”. He patted my back and said, ” now you can go your own way”. I remain forever indebted to him. My love for mathematics continues to remain as strong as it was on that fateful day and seems to grow more with every passing day. To my surprise I shunned every other choice of a profession and went to study mathematics at the St. Xavier’s College of Calcutta University.  There I learned modern algebra, real analysis, linear algebra, analytic geometry, probability and statistics, linear programming and even the mathematics of astronomy.  However two subjects actually caught my fancy. One was Newtonian mechanics and the other was real analysis. I still remember Professor Ram Ghosh starting his lectures on real analysis with the sentence…let epsilon be greater than zero no matter how small. Mechanics was fun. You essentially had to set up the differential equations and solve them and these differential equations are nothing but simply the Newton’s second law of motion. What we really lacked while studying mechanics was the stress on the physical intuition. We simply resolved the forces and never asked questions about why we ignore some types of forces and not others, while setting up the differential equations of motion. Our prescribed text was by a local mathematician and the reference text was the famous ( or dreaded) book on mechanics by S. L. Loney. The book by Loney was more that 100 years old and the problems were really challenging. The challenge was not in the physics but in the algebraic manipulations. I was bored of that text and thus one day went in search of a good text on mechanics in the famous book district of Calcutta called the ” College street”. I found one and that was by Smith and Smith. I had enough money to buy that from Sarat book house which probably is the best address in India for books on maths and physics. I really loved that book. It gave the physical intuition, and studied everything using vectors, and that fascinated me. I truly learnt about Newtonian mechanics from that book, and it indeed saved me from being thrown out from  the list of the  select number students who retained their honours in mathematics in their B.Sc. ( Bachelor of Science ) Part-I examination. This was way back in 1990.  The book is still on my bookshelf. I faired poorly in the examination. Some of my friends were surprised looking at my marks since they knew among them I was probably one of the most passionate about mathematics. One my friends Sandip Banerjee ( now a faculty in mathematics at the Indian Institute of Technology, Roorkee) told me that I did not take a proper approach to the University examination. The technique was to try and solve the question papers that appeared in the last 10 years of the University examination and one was bound to get questions which would get repeated and one can just vomit the answer without any thinking. So in mathematics there was no credit for thinking. It reminded me what Richard Feynman said of the education system in Brazil in the late fifties: ” I cannot understand how could anyone get educated by this self propagating system of education where everybody was passing the examination and teaching others how to pass the examination”.  We were basically in the same state even in the early nineties and  probably we are still the same now. It goes without saying that I did heed Sandip’s advice and prepared properly for my Part-II examinations. In fact during the first two years when my friends were solving the question papers of the last ten years I was busy reading ” Topology and Modern Analysis” by G. F. Simon’s and Mechanics by P. C.  Smith and R. Smith. Using my pocket money I had bought some excellent texts from a store in College street which sold very cheap books by Mir Publishers, Moscow. Those books were written by excellent Russian and erstwhile Soviet mathematicians and were of very high quality. I spent most of my time with these books rather than really preparing seriously for the exams. I had a much smoother run in my Part-II and finally got out from the Calcutta University with a second class honours in Mathematics. I understood that the most inevitable thing for me was to flee from Calcutta University. I was really lucky that I got through the examination for a 2 year master’s degree in IIT Kharagpur.  However St. Xavier’s college was indeed fun and my teachers were truly kind. I fondly remember my teachers there and specially Dr T. K. Chakravarty. The mathematics environment of St. Xavier’s was filled with the legend of Father Goreaux, a renowned mathematician , and was also said to be one of the last students of Albert Einstein.  Now I know that Father Goreaux  may not have been a Phd student of Einstein since according to Abraham Pais, Einstein’s biographer, Einstein, did not have a Ph.d. student. I remember talking to him several times and he also gifted me an analysis book my the famous mathematician De-La-Valle-Poussion. I felt very elated that day but I never had any courage to ask Father Goreaux about his interactions with Einstein. Of three central themes of my blog two of them would be from my school and college. One would be to again feel the hidden pleasures of Euclidean Geometry and the other would be to regain the lost joys of classical mechanics. In the second part of this article I will tell you the my experiences as a graduate student in IIT Kharagpur.