Prime Obsession by John Derbyshire is about the Riemann Hypothesis - one of the greatest unsolved problems in mathematics. I read about a dozen or so pages of the book before I bought it, and from that preview it seemed to be a book along the lines (actually, it seemed to be a lot better) of Fermat's Last Theorem by Simon Singh - a book for people who don't need to have a background in advanced mathematics but do have an aptitude and an inclination towards the subject.
In the first chapter or so, the author explains his basic mathematical concepts so beautifully that even someone who has little aptitude for the subject can understand what he's talking about. He has his readers interested and waiting for more.
But after that preview is over, it gets rougher. Perhaps because the subject of the book is a lot more complicated than Fermat's Last Theorem or any of the other popular unsolved problems in mathematics. Perhaps because the author talks too much about the history of all the mathematicians and the places involved. It doesn't hold my attention that well.
I'm about halfway through this book - and this is the first book in a few years that I feel like leaving halfway - and I can't understand some of the mathematical ideas in it. Not like I don't know how he arrived at a certain conclusion, but like I firmly believe the conclusion is wrong. Well, some of this is because he's not presenting rigorous mathematical steps in a book that's not meant for rigorous mathematicians, but, even so, it leaves gaps in my understanding.
I must say that the author has made fairly commendable attempts to explain rather complicated concepts to readers with insufficient background in the subject. It just seems that a reader who wants rigorous mathematical proofs should look for a different book.
Showing posts with label The Mathematics Dream. Show all posts
Showing posts with label The Mathematics Dream. Show all posts
Thursday, June 10, 2010
Tuesday, September 8, 2009
On Teacher's Day
Okay, I know this post got a little delayed but, well, these days, my weekends are reserved for my husband and my household chores.
I was just thinking about some of the teachers I've had. I wrote a post about my college lecturers and professors a while age and there's not much I want to add about them. But there are some other people I want to talk about.
My mother. She taught me to read, got me into the habit of reading on an almost daily basis. I was a bit of a brat who refused to go to school and she would patiently take me to school and wait around and make sure I was okay.
My grandmother. I don't think I would have been able to scrape through my Hindi and Sanskrit exams if it wasn't for her. Or be good at Mathematics. She helped me out with all the subjects that she was capable of teaching, and she did it every day after school.
My class eight Mathematics teacher, Mrs Renuka Mahani. She was the one who ignited the spark in me that took me all the way to an undergraduate degree in Mathematics. She had her own ways of teaching, different from the rest of the teachers I'd come across. She got all her ideas through, and made me want to study.
My class eight English teacher, Mrs Sonia Chhabra. She did the same things with English Literature. We had our own English textbooks, which Mr Lewis compiled, but she taught them in a way that I liked. I still remember her reciting Mark Antony's speech to us and getting us all excited about Sherlock Holmes mysteries. It was lovely.
There are actually others I may want to write about as well, but I will save them for a future post.
I was just thinking about some of the teachers I've had. I wrote a post about my college lecturers and professors a while age and there's not much I want to add about them. But there are some other people I want to talk about.
My mother. She taught me to read, got me into the habit of reading on an almost daily basis. I was a bit of a brat who refused to go to school and she would patiently take me to school and wait around and make sure I was okay.
My grandmother. I don't think I would have been able to scrape through my Hindi and Sanskrit exams if it wasn't for her. Or be good at Mathematics. She helped me out with all the subjects that she was capable of teaching, and she did it every day after school.
My class eight Mathematics teacher, Mrs Renuka Mahani. She was the one who ignited the spark in me that took me all the way to an undergraduate degree in Mathematics. She had her own ways of teaching, different from the rest of the teachers I'd come across. She got all her ideas through, and made me want to study.
My class eight English teacher, Mrs Sonia Chhabra. She did the same things with English Literature. We had our own English textbooks, which Mr Lewis compiled, but she taught them in a way that I liked. I still remember her reciting Mark Antony's speech to us and getting us all excited about Sherlock Holmes mysteries. It was lovely.
There are actually others I may want to write about as well, but I will save them for a future post.
Tuesday, February 17, 2009
Of Theorems, Conjectures And Me
Like I promised in my post on Fermat's Last Theorem, here is my post on my time as a Mathematics student. This is neither the first nor the last such post, just one of many.
I first heard of Fermat's Last Theorem when I was in class nine, I think. At that time, I read a little bit about it, but probably not enough to get me really interested in it. In class eleven, I happened to land up on something called the Beal Conjecture. The statement of this conjecture is on similar lines to Fermat's Last Theorem. Incidentally, until a statement is proved, it should be called a conjecture, not a theorem. Fermat's Last Theorem was always referred to as a theorem instead of a conjecture, for over three hundred years when it stood without a proof.
I was rather intrigued by the Beal Conjecture. I was in touch with a Professor from the University of North Texas over e-mail, doing some background research, and trying to figure out if I could attempt to actually prove it. I told him I wanted to study the proof for Fermat's Last Theorem, and asked him to suggest references. He pointed me in the right direction, but I guess I did not know enough Mathematics then to be able to figure it out.
As an undergraduate student of Mathematics, I attended a workshop where a Professor from Berkeley gave us an overview of the proof. He did it in a fraction of the time that Andrew Wiles spent at the Newton Institute for the same task, but the overview was enough for me to be interested and confident enough to make another serious attempt to figure it out. I did, to an extent, but was never able to grasp it fully, because of the sheer bulk of the thing, and I no longer remember any of it, except that it was based on elliptic curves. This I remembered before Simon Singh's book reminded me of it.
Somewhere along the line, I gave up Mathematics, and forgot all about Fermat and Beal. After reading this book, I do have a bit of renewed enthusiasm. Maybe I will take up that stuff all over again. It won't necessarily be fruitful, but it just might be fun.
I first heard of Fermat's Last Theorem when I was in class nine, I think. At that time, I read a little bit about it, but probably not enough to get me really interested in it. In class eleven, I happened to land up on something called the Beal Conjecture. The statement of this conjecture is on similar lines to Fermat's Last Theorem. Incidentally, until a statement is proved, it should be called a conjecture, not a theorem. Fermat's Last Theorem was always referred to as a theorem instead of a conjecture, for over three hundred years when it stood without a proof.
I was rather intrigued by the Beal Conjecture. I was in touch with a Professor from the University of North Texas over e-mail, doing some background research, and trying to figure out if I could attempt to actually prove it. I told him I wanted to study the proof for Fermat's Last Theorem, and asked him to suggest references. He pointed me in the right direction, but I guess I did not know enough Mathematics then to be able to figure it out.
As an undergraduate student of Mathematics, I attended a workshop where a Professor from Berkeley gave us an overview of the proof. He did it in a fraction of the time that Andrew Wiles spent at the Newton Institute for the same task, but the overview was enough for me to be interested and confident enough to make another serious attempt to figure it out. I did, to an extent, but was never able to grasp it fully, because of the sheer bulk of the thing, and I no longer remember any of it, except that it was based on elliptic curves. This I remembered before Simon Singh's book reminded me of it.
Somewhere along the line, I gave up Mathematics, and forgot all about Fermat and Beal. After reading this book, I do have a bit of renewed enthusiasm. Maybe I will take up that stuff all over again. It won't necessarily be fruitful, but it just might be fun.
Saturday, February 14, 2009
Fermat's Last Theorem
Last night I stayed up to finish reading Fermat's Last Theorem by Simon Singh. Bhatti had told me that if I'd read this one during the years when I was studying Mathematics, I would never have given up Mathematics. Turns out, he was probably right. The way this guy has illustrated the passion that mathematicians have for their subject, the way he has put forth the mystery, the intrigue of the subject, it's all pretty brilliant. He takes you on a beautiful journey through the ages, telling you the story of Fermat, number theory, and Mathematics in general.
Let me put a disclaimer here. You don't need to be a mathematician to be able to read, understand, and appreciate this book. You just need a bit of mathematical aptitude and inclination. The author doesn't really talk too much about the actual theories and concepts that went into proving the Last Theorem, and even when he does, the concepts are such that you can do without understanding them.
I loved the book. It reminded me of a lot of things that happened during the years when I was studying Mathematics, in school and in College. I'll do a separate post about that stuff. Until then, all I'd say is that anyone who has the slightest bit of interest in the subject should most certainly read this one.
Let me put a disclaimer here. You don't need to be a mathematician to be able to read, understand, and appreciate this book. You just need a bit of mathematical aptitude and inclination. The author doesn't really talk too much about the actual theories and concepts that went into proving the Last Theorem, and even when he does, the concepts are such that you can do without understanding them.
I loved the book. It reminded me of a lot of things that happened during the years when I was studying Mathematics, in school and in College. I'll do a separate post about that stuff. Until then, all I'd say is that anyone who has the slightest bit of interest in the subject should most certainly read this one.
Friday, January 2, 2009
How Does Your Mind Work?
This is probably the first time I've thought of writing a post based on some thoughts I gathered from the comments space of a post on someone else's blog.
Your mind doesn't work the same way, or equally actively, at different points of time during the day. Or at different places. Or during different phases of your life. There are some things you can do better in the afternoon, and some that are better taken care of late in the night. And then there are some which refuse to let you have a moment's peace until you take care of them.
There was a certain lecturer we had in College, who used to tell us that, no matter where we are or what we are doing, our minds should always be looking for a solution to a Mathematical problem or the proof of a theorem. He used to tell us things like, if you are hanging on for dear life from the door of a DTC bus, and the conductor asks you to buy your ticket, you should tell him to wait until you figure out the solution to the metric spaces problem that's been bothering you all day. He narrated this incident when he, after much effort, came up with the solution to such a problem, and began to dance around in his balcony for the benefit of his amused and startled neighbours.
In those days, I was sufficiently enthralled with Mathematics to be able to relate to all this. There were times when I tossed and turned a problem in my head on the bus ride home. Times when I woke up in the middle of the night with a sudden breakthrough. Or, if my brother is to be believed, mumbled things like a(n) tends to l in my sleep.
You know when I get most of my ideas? When I am taking a bath. It's the only time during the day when I shut the door, literally and figuratively, on the rest of the world, do away with my worries, and relax. And only a relaxed mind can figure out that last remaining step in the proof of a theorem. Or the last line that fits into a poem that I've been trying to write. Or the subject for my next post. This is mostly applicable for my evening bath, because mornings are generally a little rushed, given the fact that I need to get to work, and that I certainly don't like making my carpool friend(s) wait. This is the major reason why I do most of my blogging late in the evening. All through school and college, I made it a point not to study beyond eight or so in the evening. But when I was worked up over something interesting, something Mathematical, it would, more often than not, come to me late in the night.
On the other hand, I can hardly, if ever, write code in the later phases of the day. That, by the way, is, supposedly, what I do for a living. Apparently the relaxed mind works very well at what it does, but it does only things that it likes to do. And the tense, tired mind grows relaxed if it does those things.
I've read a number of articles in Reader's Digest and in other places that tell you to figure out when your mind is most active and when it slumps, and organize your day accordingly in order to maximise efficiency. Tasks that don't need your mind to be too active, like sorting your mail, should be taken care of post lunch, when you're feeling a little drowsy. And code should be written whenever your mind is at its wakeful best.
I think this stuff makes a lot of sense, and I try to abide by it as much as I can. But what I find more important than all of this, is that, each day, everyone needs to schedule some time exclusively for an activity that relaxes their mind, makes them happy, and gives them a sense of achievement. If you're one of the lucky souls who get all this from whatever it is that you do for a living, great. Otherwise, you need to mark some time for this in your daily calendar. It works wonders.
Your mind doesn't work the same way, or equally actively, at different points of time during the day. Or at different places. Or during different phases of your life. There are some things you can do better in the afternoon, and some that are better taken care of late in the night. And then there are some which refuse to let you have a moment's peace until you take care of them.
There was a certain lecturer we had in College, who used to tell us that, no matter where we are or what we are doing, our minds should always be looking for a solution to a Mathematical problem or the proof of a theorem. He used to tell us things like, if you are hanging on for dear life from the door of a DTC bus, and the conductor asks you to buy your ticket, you should tell him to wait until you figure out the solution to the metric spaces problem that's been bothering you all day. He narrated this incident when he, after much effort, came up with the solution to such a problem, and began to dance around in his balcony for the benefit of his amused and startled neighbours.
In those days, I was sufficiently enthralled with Mathematics to be able to relate to all this. There were times when I tossed and turned a problem in my head on the bus ride home. Times when I woke up in the middle of the night with a sudden breakthrough. Or, if my brother is to be believed, mumbled things like a(n) tends to l in my sleep.
You know when I get most of my ideas? When I am taking a bath. It's the only time during the day when I shut the door, literally and figuratively, on the rest of the world, do away with my worries, and relax. And only a relaxed mind can figure out that last remaining step in the proof of a theorem. Or the last line that fits into a poem that I've been trying to write. Or the subject for my next post. This is mostly applicable for my evening bath, because mornings are generally a little rushed, given the fact that I need to get to work, and that I certainly don't like making my carpool friend(s) wait. This is the major reason why I do most of my blogging late in the evening. All through school and college, I made it a point not to study beyond eight or so in the evening. But when I was worked up over something interesting, something Mathematical, it would, more often than not, come to me late in the night.
On the other hand, I can hardly, if ever, write code in the later phases of the day. That, by the way, is, supposedly, what I do for a living. Apparently the relaxed mind works very well at what it does, but it does only things that it likes to do. And the tense, tired mind grows relaxed if it does those things.
I've read a number of articles in Reader's Digest and in other places that tell you to figure out when your mind is most active and when it slumps, and organize your day accordingly in order to maximise efficiency. Tasks that don't need your mind to be too active, like sorting your mail, should be taken care of post lunch, when you're feeling a little drowsy. And code should be written whenever your mind is at its wakeful best.
I think this stuff makes a lot of sense, and I try to abide by it as much as I can. But what I find more important than all of this, is that, each day, everyone needs to schedule some time exclusively for an activity that relaxes their mind, makes them happy, and gives them a sense of achievement. If you're one of the lucky souls who get all this from whatever it is that you do for a living, great. Otherwise, you need to mark some time for this in your daily calendar. It works wonders.
Thursday, October 9, 2008
Cleaning Up...
Today I spent the better part of my day cleaning out some of my closets. This is an almost annual activity for me, but I normally refrain from throwing out any of my stuff. Today I'd decided to be ruthless in deciding what to throw out and what to keep. Not to say that I would ever throw out something like my College Yearbook. No way, not even in a fit of extreme ruthlessness. But today I did throw out a lot of stuff I'd been hanging on to for five or six years for no apparent reason, except that I am a bit of a pack rat. By the way, for those of you unfamiliar with the term "pack rat," I looked it up on Wikipedia, and here's what their article says: "This article is about the rodent. For the human behavior, see compulsive hoarding."
Coming back to my point, I did find so many things that I should have thrown out six years ago, but I did find so many others that I would want to keep for the next sixty (if I do live that long, that is). There is so much stuff in my closets that reminds me of who I really am, of what I once wanted to be, of what I once was. The many issues of my school magazine that I edited and wrote articles for, the issue of Teens Today that reminds me that I do have what it takes to be a published writer, the innumerable prospectuses (I actually did not know the plural form of prospectus. This is what Merriam-Webster and wiktionary say.) of British Universities that I gathered towards the end of my undergraduate degree, when I was planning to apply for higher studies in Mathematics, the offer letters from the Universities of Oxford and Cambridge (the only ones I actually applied to), the sketches I drew in the days when I was aspiring to go to NIFT and be a fashion designer. Now these are the things I can never throw away. (Except the prospectuses. I kept the ones from Oxford and Cambridge, but got rid of the rest.) This is the stuff that forms such an integral part of my identity that I can never imagine doing away with any of it. I even managed to dispose of the first job offer letter that I ever got (from Flextronics), because I don't think that that defines me half as strongly.
And then, of course, there is all the miscellaneous memorabilia. The College Yearbooks, the cards and stuff I got from various friends on various occasions, the photo albums, the large school-leaving group photograph, the lovely picture of me as a chubby two-month old in my mother's lap, the pictures from the school farewell, the College Fests, Graduation Dinner, the Tech Fest we organized during our MCA years... it is such a good feeling to recount all those memories.
I'm not sure why I am writing this on my public blog, because it does seem like something that's meant basically for me. But these are things that all my good friends should certainly know about me. And for the others, well, like I do say sometimes, I enjoy irritating people by making them read stuff that is of no consequence whatsoever to them!
Coming back to my point, I did find so many things that I should have thrown out six years ago, but I did find so many others that I would want to keep for the next sixty (if I do live that long, that is). There is so much stuff in my closets that reminds me of who I really am, of what I once wanted to be, of what I once was. The many issues of my school magazine that I edited and wrote articles for, the issue of Teens Today that reminds me that I do have what it takes to be a published writer, the innumerable prospectuses (I actually did not know the plural form of prospectus. This is what Merriam-Webster and wiktionary say.) of British Universities that I gathered towards the end of my undergraduate degree, when I was planning to apply for higher studies in Mathematics, the offer letters from the Universities of Oxford and Cambridge (the only ones I actually applied to), the sketches I drew in the days when I was aspiring to go to NIFT and be a fashion designer. Now these are the things I can never throw away. (Except the prospectuses. I kept the ones from Oxford and Cambridge, but got rid of the rest.) This is the stuff that forms such an integral part of my identity that I can never imagine doing away with any of it. I even managed to dispose of the first job offer letter that I ever got (from Flextronics), because I don't think that that defines me half as strongly.
And then, of course, there is all the miscellaneous memorabilia. The College Yearbooks, the cards and stuff I got from various friends on various occasions, the photo albums, the large school-leaving group photograph, the lovely picture of me as a chubby two-month old in my mother's lap, the pictures from the school farewell, the College Fests, Graduation Dinner, the Tech Fest we organized during our MCA years... it is such a good feeling to recount all those memories.
I'm not sure why I am writing this on my public blog, because it does seem like something that's meant basically for me. But these are things that all my good friends should certainly know about me. And for the others, well, like I do say sometimes, I enjoy irritating people by making them read stuff that is of no consequence whatsoever to them!
Sunday, September 14, 2008
Happiness
Why do we value something only if we can't have it, or have lost it? Why is it so difficult for us to appreciate and be thankful for what we do have? We have this tendency to set our eyes on something we think we want, need or like, and then decide that that is the only thing that will make us happy.
I've discovered that you don't always get what you want. You generally get something completely different. When I wanted to be a journalist, I set out to be a Mathematician. And I was happy being one. When I had my heart set on Mathematics, I landed up in the software industry. And I am happy here too. There's no telling if I'd have been any more or less happy if I'd got what I originally thought I wanted. I mean, writing makes me really happy, but only because I write exactly when I want to, as much as I want to, and about what I want to write about. Writing in a constrained environment may not have kept me as happy as my current job keeps me.
There are other areas in life where this is equally applicable. But I don't feel like talking about them right now. I just feel like telling everyone who's reading this, and myself, to be happy with whatever cards life deals you. Appreciate the good things in your life. Don't hang on to thoughts of the "If only..." kind that make you upset. Not to say that you should let go of your dreams. Most certainly not. Go after them, by all means. But know where to draw the line. Know how to distinguish between what you really need or want and what you can be happy without, if only you put your mind to it.
I've discovered that you don't always get what you want. You generally get something completely different. When I wanted to be a journalist, I set out to be a Mathematician. And I was happy being one. When I had my heart set on Mathematics, I landed up in the software industry. And I am happy here too. There's no telling if I'd have been any more or less happy if I'd got what I originally thought I wanted. I mean, writing makes me really happy, but only because I write exactly when I want to, as much as I want to, and about what I want to write about. Writing in a constrained environment may not have kept me as happy as my current job keeps me.
There are other areas in life where this is equally applicable. But I don't feel like talking about them right now. I just feel like telling everyone who's reading this, and myself, to be happy with whatever cards life deals you. Appreciate the good things in your life. Don't hang on to thoughts of the "If only..." kind that make you upset. Not to say that you should let go of your dreams. Most certainly not. Go after them, by all means. But know where to draw the line. Know how to distinguish between what you really need or want and what you can be happy without, if only you put your mind to it.
Saturday, June 21, 2008
What They Taught Me In College
The Profs in the Mathematics Department back at St. Stephen's were an interesting set of people... each leaving an indelible mark in my memory for her or his own specific reason. These are the people who led me to be fascinated with Mathematics. They were also the people who taught me some important values. And, of course, my friends and I did have quite a lot of fun at their expense behind their backs - as is quite usual in any teacher - student setup in urban India. But in spite of all that, I have a huge amount of respect for all of them. And I want to write about all of them here. And about the stuff they taught me.
Quite possibly, it is simplest to describe Dr Geeta Venkataraman. She was this really sweet, calm, confident person. I never once saw her lose her cool. I also do not remember anyone being annoying enough in her class to cause her to lose her cool. GV, as she was referred to, commanded that kind of respect. And at the same time, she made you comfortable enough to talk to her like you would to a friend. She was a great motivator. At least I found her to be so.
At the opposite end of the spectrum, as I see it, sits Dr Sanjeev Aggarwal. Aggy, as he was fondly referred to, was probably the most complicated character in our department. Extremely outspoken. Totally encouraging and extremely discouraging at the same time. Notorious for hardly ever awarding marks in double digits in the January Tests, which were marked out of fifty. One of my classmates once commented that, in our immediately senior batch, if you added up what the entire class got in Aggy's Jan Test, you would still not add up to fifty! Immodestly speaking, what I got on his Jan Test constitutes Douglas Adams's answer to the question of Life, The Universe and Everything.
During his tutes he would completely insult anybody and everybody, but in a way in which we never really took it to heart. When I was applying to Oxford, I went to him for a recommendation. He was known to be a little brutal in writing recos, but I was feeling adventurous enough to take the risk. Aggy and GV had both themselves graduated from St. Stephen's and post-graduated from the University of Oxford. When I went to Aggy for a reco, he told me: "One needs two things to pursue a career in Mathematics. One is talent. The other is passion. I have absolutely no doubt that you have the talent you need. About the passion I'm not so sure." He also said that the interest you feel for Mathematics is much like romance. You feel it quite passionately, but it dies out, much like real life romance. I never really agreed with his views on anything, but I always found them interesting. By the way, in spite of the lack of passion and the fact that I did ask him to write me a reco anyway, I did make it through to my first preference college at Oxford. The reason why I did not go there probably demands a separate post which I may or may not write at another time.
Aggy had this remarkable passion for his subject. He used to tell anecdotes of his college days when, you know, if he figured out the solution to a problem he'd been working on for a while, he'd start dancing around in his balcony with his neighbours staring at him. He encouraged all of us to be that passionate. He firmly believed that we all needed to be passionate about something in life, if not Mathematics.
Then there was Dr Mathur. Completely opposite to GV in a different respect. Remarkably quick at flying off the handle. He'd lose his temper about once during every lecture. Possibly because he was one of the most senior people in the department (he retired a little before we got our farewell). At that age, people tend to be quite set in their ways and not too open to change. Changing culture, changing attitudes. He had his own ideas on how ladies should behave and on just about everything else. He was really good at remembering people. After perhaps three or four days of college, he never once called out names while marking attendance. He'd just look at everyone during the lecture and mark it all on his own. So no scope for proxies there!
The thing about him that I remember most distinctly was that, no matter how angry he got with you in class, he'd be back to his sweet self the instant you were talking to him outside of class. If you apologised to him, he'd accept it most gracefully.
Okay, so my classmates from St. Stephen's who are reading must be eagerly awaiting this. Dr Amber Habib. I think he was the only one in the department who did not graduate or post graduate from St. Stephen's himself. He'd done an integrated MTech from IIT Kanpur and spent a few years teaching at the University of Berkley. He was this really sweet, simple and humble person. Most of my close friends did not like him or his teaching style too much. I never quite understood why. Because I did. I liked him a lot. And I found his teaching style interesting. Inevitably, when all my friends were engrossed in making fun of him, I'd stick up for him. So I came to be accused of having a crush on him.
He was a man of varied interests. Mathematics, Computers, painting, butterflies... there's a long list. My friends who did not like him did find him and his antics interesting in a strange kind of way. There was this white kurta that he used to wear sometimes which used to provoke them into poking any amount of fun at him. Aarti has immortalised that kurta in the yearbook write-up she wrote for me.
Then there was Dr Ranjit Bhatia. He is a former Olympic athlete. By the time we were in our first year, which was his last year of service to the College where he'd studied too, he'd developed a pretty serious case of Parkinsosn's. But he was still very independent, financially and otherwise.
And of course, I cannot possibly miss out Nandita Naraian. Ms Naraian is actually enough to require a separate post, but this one would be grossly incomplete without her mention. She was a lot more than a teacher. Ordinarily, the Profs at St. Stephen's stay away from the Delhi University Teacher's Association (DUTA) (as do the students from DUSU), but Nandy, as we called her, was one active member. She always took the lead in any protest that DUTA or the public at large was making against anything that she considered worth protesting against. Be it a candlelight vigil or a hunger strike or just a procession, she'd be there. But she had her own ideas about the methods of protesting. She did not believe in conventional strikes. Because they'd put the students at a loss for no fault of theirs. There was this strike that happened in 1983 that she loved to talk about over and over again. I do not remember what they were protesting against then. But I do remember the way they did it. Nandy used to take portable blackboards and all her students to the India Gate grounds and teach them there, where she could get all the media attention she wanted and needed. She described how she and the entire class of students used to hop around from one bus to another from College to India Gate. She made it sound like we'd missed an adventure of a lifetime by not being part of it. She once asked us how old we were in 1983. She was noticeably disappointed to find out that the vast majority of the people in our batch were only a year old back then.
Anyway, we were actually lucky enough to experience a slightly toned-down version of that adventure. When we were final year students, there was some talk of increasing the working hours of lecturers in the University without increasing their compensation. DUTA was obviously protesting against that. Nandy and GV participated in that protest by teaching us in the grounds right outside the Vice-Chancellor's Office. These grounds were actually almost adjacent to one of the College gates, so we did not get to hop around between buses. But it was still an experience of a lifetime.
When I asked Nandy for a reco for applying to Oxford and Cambridge, she was totally thrilled. To know that I wanted to pursue higher Mathematics. Immodestly speaking, I was one of her favourite students. I do sometimes feel I let her down by giving up all that.
Nandy had a huge amount of passionate concern for the environment, the country, society, her students, world peace... there's a long list here. She was a fiercely independent woman. And she was a brilliant teacher. She used to say that teaching was like oxygen for her. She could not live without it.
So, you know, I learnt a lot from all these people other than Analysis and Algebra and all that stuff. I learnt that you need to be passionate about whatever you do in life. I learnt that as long as you think you can, you can be completely independent. I learnt that we all need to learn to care about others and about society, and we all need to make our own contribution, small or large, towards making it a better place to live in.
Quite possibly, it is simplest to describe Dr Geeta Venkataraman. She was this really sweet, calm, confident person. I never once saw her lose her cool. I also do not remember anyone being annoying enough in her class to cause her to lose her cool. GV, as she was referred to, commanded that kind of respect. And at the same time, she made you comfortable enough to talk to her like you would to a friend. She was a great motivator. At least I found her to be so.
At the opposite end of the spectrum, as I see it, sits Dr Sanjeev Aggarwal. Aggy, as he was fondly referred to, was probably the most complicated character in our department. Extremely outspoken. Totally encouraging and extremely discouraging at the same time. Notorious for hardly ever awarding marks in double digits in the January Tests, which were marked out of fifty. One of my classmates once commented that, in our immediately senior batch, if you added up what the entire class got in Aggy's Jan Test, you would still not add up to fifty! Immodestly speaking, what I got on his Jan Test constitutes Douglas Adams's answer to the question of Life, The Universe and Everything.
During his tutes he would completely insult anybody and everybody, but in a way in which we never really took it to heart. When I was applying to Oxford, I went to him for a recommendation. He was known to be a little brutal in writing recos, but I was feeling adventurous enough to take the risk. Aggy and GV had both themselves graduated from St. Stephen's and post-graduated from the University of Oxford. When I went to Aggy for a reco, he told me: "One needs two things to pursue a career in Mathematics. One is talent. The other is passion. I have absolutely no doubt that you have the talent you need. About the passion I'm not so sure." He also said that the interest you feel for Mathematics is much like romance. You feel it quite passionately, but it dies out, much like real life romance. I never really agreed with his views on anything, but I always found them interesting. By the way, in spite of the lack of passion and the fact that I did ask him to write me a reco anyway, I did make it through to my first preference college at Oxford. The reason why I did not go there probably demands a separate post which I may or may not write at another time.
Aggy had this remarkable passion for his subject. He used to tell anecdotes of his college days when, you know, if he figured out the solution to a problem he'd been working on for a while, he'd start dancing around in his balcony with his neighbours staring at him. He encouraged all of us to be that passionate. He firmly believed that we all needed to be passionate about something in life, if not Mathematics.
Then there was Dr Mathur. Completely opposite to GV in a different respect. Remarkably quick at flying off the handle. He'd lose his temper about once during every lecture. Possibly because he was one of the most senior people in the department (he retired a little before we got our farewell). At that age, people tend to be quite set in their ways and not too open to change. Changing culture, changing attitudes. He had his own ideas on how ladies should behave and on just about everything else. He was really good at remembering people. After perhaps three or four days of college, he never once called out names while marking attendance. He'd just look at everyone during the lecture and mark it all on his own. So no scope for proxies there!
The thing about him that I remember most distinctly was that, no matter how angry he got with you in class, he'd be back to his sweet self the instant you were talking to him outside of class. If you apologised to him, he'd accept it most gracefully.
Okay, so my classmates from St. Stephen's who are reading must be eagerly awaiting this. Dr Amber Habib. I think he was the only one in the department who did not graduate or post graduate from St. Stephen's himself. He'd done an integrated MTech from IIT Kanpur and spent a few years teaching at the University of Berkley. He was this really sweet, simple and humble person. Most of my close friends did not like him or his teaching style too much. I never quite understood why. Because I did. I liked him a lot. And I found his teaching style interesting. Inevitably, when all my friends were engrossed in making fun of him, I'd stick up for him. So I came to be accused of having a crush on him.
He was a man of varied interests. Mathematics, Computers, painting, butterflies... there's a long list. My friends who did not like him did find him and his antics interesting in a strange kind of way. There was this white kurta that he used to wear sometimes which used to provoke them into poking any amount of fun at him. Aarti has immortalised that kurta in the yearbook write-up she wrote for me.
Then there was Dr Ranjit Bhatia. He is a former Olympic athlete. By the time we were in our first year, which was his last year of service to the College where he'd studied too, he'd developed a pretty serious case of Parkinsosn's. But he was still very independent, financially and otherwise.
And of course, I cannot possibly miss out Nandita Naraian. Ms Naraian is actually enough to require a separate post, but this one would be grossly incomplete without her mention. She was a lot more than a teacher. Ordinarily, the Profs at St. Stephen's stay away from the Delhi University Teacher's Association (DUTA) (as do the students from DUSU), but Nandy, as we called her, was one active member. She always took the lead in any protest that DUTA or the public at large was making against anything that she considered worth protesting against. Be it a candlelight vigil or a hunger strike or just a procession, she'd be there. But she had her own ideas about the methods of protesting. She did not believe in conventional strikes. Because they'd put the students at a loss for no fault of theirs. There was this strike that happened in 1983 that she loved to talk about over and over again. I do not remember what they were protesting against then. But I do remember the way they did it. Nandy used to take portable blackboards and all her students to the India Gate grounds and teach them there, where she could get all the media attention she wanted and needed. She described how she and the entire class of students used to hop around from one bus to another from College to India Gate. She made it sound like we'd missed an adventure of a lifetime by not being part of it. She once asked us how old we were in 1983. She was noticeably disappointed to find out that the vast majority of the people in our batch were only a year old back then.
Anyway, we were actually lucky enough to experience a slightly toned-down version of that adventure. When we were final year students, there was some talk of increasing the working hours of lecturers in the University without increasing their compensation. DUTA was obviously protesting against that. Nandy and GV participated in that protest by teaching us in the grounds right outside the Vice-Chancellor's Office. These grounds were actually almost adjacent to one of the College gates, so we did not get to hop around between buses. But it was still an experience of a lifetime.
When I asked Nandy for a reco for applying to Oxford and Cambridge, she was totally thrilled. To know that I wanted to pursue higher Mathematics. Immodestly speaking, I was one of her favourite students. I do sometimes feel I let her down by giving up all that.
Nandy had a huge amount of passionate concern for the environment, the country, society, her students, world peace... there's a long list here. She was a fiercely independent woman. And she was a brilliant teacher. She used to say that teaching was like oxygen for her. She could not live without it.
So, you know, I learnt a lot from all these people other than Analysis and Algebra and all that stuff. I learnt that you need to be passionate about whatever you do in life. I learnt that as long as you think you can, you can be completely independent. I learnt that we all need to learn to care about others and about society, and we all need to make our own contribution, small or large, towards making it a better place to live in.
Sunday, May 25, 2008
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.
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