It's been quite a while since I posted. And yes, life has become a bit more demanding since the time I returned from Wardha. The flurry of ambivalent thoughts have clogged a brain which was already set in a pattern of thoughts arising out of the consequences of the past few months with a tinge of foresight into the future. And wrestling through these thoughts, I, after quite a long struggle finished one of those books which I am pretty sure shall have a long standing impact on my thoughts. I shall continue my posts on Sevagram trip soon, but I must admit that the time is running out for me, for Independence Day is not far away, and the timing shall be perfect if I can finish it by then.
The name of the book is "A Mathematician's Apology" - written by Prof. G H Hardy - a brilliant mathematician who is called one of the foremost "pure" mathematicians (read on to know what it means) - better known to many as the Professor who presented Srinivasa Ramanujam to the world - a Professor who in his own words - "I still say to myself when I am depressed, and find myself forced to listen to pompous and tiresome people, 'Well, I have done one thing you could never have done, and that is to have collaborated with both Littlewood and Ramanujan on something like equal terms
'" - always felt proud to be associated with his collaborations for he considered the other two to be better mathematicians than he was. The ranking of mathematicians given by Hardy is still one of the things in the folklore of History of Mathematics.
Why would such an accomplished mathematician have to offer an apology? And to whom should he apologise and for what reasons ? - Questions, Questions of concern, of logical importance given the context. Prof. Hardy not only answers these with a verve that one can see in the writings of great litterateur but also gives us a glimpse of his mind and his beliefs which make this book a great work to study. Definitely one of those which one would like to chew and digest.
"Exposition, criticism, appreciation, is work for second-rate minds"
declares Prof. Hardy. It's hard for me to digest this, for all my life, at least till this time, I was engaged in more or less these three things - and work for second- rate mind?? This must definitely have some strong reasons. And the Prof. explains to us in as clear terms as possible that he is sad because at his age - around sixty - when he wrote the book, it becomes difficult to be the same "creative" person as you once were - and according to him, as a mathematician his job is to work on being creative - recognising, working on patterns - which is what he considers mathematics is about - a creative art that works with wonderful abstract patterns. Of course there are many other views that he talks on, I think this is the best of the views that suits this context. He says that he is forced to write on mathematics as he is not in a position to develop it and henceforth he would like to putforth an apology to Mathematics.
And the master that he is, what an apology it turns out to be! For all those who would wish to have a glimpse of what clarity of thought could be - here's a book that I found, which - in the manner of its construct, in the manner of its pacing, in the manner of its ordering - shows it in every respect possible.
One reason why one can definitely read this book is for the quotes - quotes that flow from his thought as well as the quotes that he handpicked to include it in his apology to the field to which he has devoted his life. I shall try and present a few of them in this post.
In the process of his monologue, he tells us the reasons why he considers mathematics superior for he considers it important to justify his existence and his activities - which in essence have shaped his life - and that justification is a real beauty. He says that one would have to answer such questions as
"...whether the work which he does is worth doing; and the second is why he does it, whatever its value may be"
- and henceforth this apology helps all those who wish to take a look at what to do in their future decide their future better.
Let me give an example of the kind of argument he gives on encouraging the individual talents - so here it goes -
This view was endorsed by Dr. Johnson -
"When I told him that I had been to see [his namesake] Johnson ride upon three horses, he said "Such a man,sir, should be encouraged, for his performances show the extent of the human powers...""
In the process of answering the two questions that he raised he tells us more about his views on mathematics - as a harmless subject - at least his domain - Theory of Numbers - which he then considered of no practical use but definitely one of those which was really beautiful for all the patterns that it helps him come up with. It is another matter that today we know that the Theory of Numbers is the key on the basis of which Theory of Computation gave birth to Cryptography and the whole security related aspects.
His comments on research are one that have really intrigued me. I quote :
There are many highly respectable motives which may lead men to prosecute research, but three of which are much more important than the rest. The first
(without which the rest must come to nothing) is intellectual curiosity
, desire to know the truth. Then, professional pride
, anxiety to be satisfied with one's performance, the shame that overcomes any self-respecting craftsmen when his work is unworthy of his talent
, the desire for reputation, and the position, even the power or the money, which it brings.
It is interesting to note that he follows it up with this sentence :
"It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the sufferings of the others , but that will not be why you did it"
I really feel that these statements are really worth pondering upon. I happen to take this course on "Research Methodologies" - which in its only class till now has more or less raised certain questions close to this. The other course I have taken - Adv. ToC - is another course which thanks to Prof. Prasad Jayanti has raised some really interesting questions that Prof. Hardy touches upon. A good news is that all the classes of this course are going to be recorded, and I foresee a great benefit of those recordings. It really helps if somebody who is as good lectures you on those things which a mathematician of Prof. Hardy's stature has expounded.
Getting back to the book, Prof. Hardy then considers the beauty of mathematics - gives us certain glimpses - the Euclid's proof for the existence of an infinity of prime numbers , the Pythagoras proof of irrationality of sqrt(2) (I think I must learn from Paresh how to add these Math elements into my posts. Click here
- I somehow am not in a mood to do it after a long night- it's already about to be 6 :o) - and it is the argument that he provides for the greatness that he intends to attach to it - the certain generality and certain depth -
is something that is definitely worth a read for any audience. The examples are chosen such that it requires little mathematical rigour but elementary understanding of mathematics to appreciate his idea of greatness.
A comment on 'piling of subtlety of generalization upon subtlety of generalization' (from Alfred Whitehead's Sciends and the Modern World)
not being the achievement of mathematics to his comment on "pure" mathematics as he would call all that abstract work which does NOT have to do with any constraints as are imposed on the mathematics which works on describing the world - the physical mathematics as he puts it - to the statement that he makes that only elementary mathematics is useful to the common man in general - it is tale which unfolds in a wonderful manner - and I think what I am writing now would make more sense once one reads the book. Hopefully the earlier paragraphs made some sense.
The notions on physical reality and a bit of his philosophy - with very interesting anecdotes - I cannot but appreciate - though I agree that I have done a lot of second-rate work for the past few hours.
I definitely consider that a work of this kind is one of the first rate literary creation from a master of patterns though however he would like to look at it as his second-rate work. It is his prerogative to consider that Mathematics stands at a higher pedestal than poetry or any other form of art - and it need not be mine. And I do think however that the more I think of it, I tend to agree with him on the first and second rate works - and there is the other part of my mind which tells me that without the help of expounding, criticism and appreciation - one may not be creative to solve the problems of the world - which is what I wish to do as a going to be engineer - and Prof. Hardy creations are in his own realm which never get restricted by any such constraints - a thought which has caught me by fire more and more.
There is one more reason why one would want to read this book. And that is the wonderful Foreword provided by C P Snow about Prof. Hardy's life and times and his experiences with Prof. Hardy.
I am sorry for all you folks for having kept this book with me for the past few months - and I think it's time to give it back to the library with a fine attached :(