### A Note To Myself

This post is 'addressed' to a young lad of a generation ago who evolved into what I am today. I wish wistfully - if only I had then got to meet someone like what I now am or at least got to read something like *this*.... Of course, if that had happened, this post would never have been written!

I grew up in Kerala, among popular science books idolizing Albert Einstein. The 'Sastra Sahitya Parishad', a Mallu organization I have mentioned in some earlier posts, had built up a virtual cult around the Master - indeed if I were to say he was a grand-fatherly figure for self and a whole host of Mallu schoolers of my generation, I would not be exaggerating one bit.

Projecting Einstein as the one Scientist who really counted, 'Parishad' fed us verbalized and romanticized - and indeed, dumbed-down - interpretations of Relativity theory thru half a dozen books on the life of Einsten (one of these hagiographies began: "Dear children, each one of you would want to be a scientist, not just a scientist but a very big scientist, right? Here is the life-story of the greatest scientist of them all; try to be like him!") and countless articles which kept appearing in their Students' Magazines. To give an example of the impact all this had, I could confidently make statements like "gravity is the curvature of the space-time-continuum" at the age of 10 - and I was nowhere near being a child prodigy!

Although I developed grand dreams of becoming a Theoretical Physicist, I was never quite comfortable with Mathematics - and was clearly less than sharp at manipulating algebraic expressions. A fear slowly grew witin - what if I am fail to do lengthy calculations - to fill page after page with all those messy equations, how will I do Einstein-class work?... Then, towards the end of junior college, I read 'The Physicists' by C.P.Snow. And the following bit sank deep:

"The reader may wonder if to be a top-flight physicist, one also has to be great with Mathematics. Well, not necessarily! Indeed, more than facility with Mathematics, a profound physical intuition is what marks out an outstanding physicist. Of course, Dirac could have been any type of Mathematician, of the highest level. Feynman, Pauli and Dyson were also formidably gifted in Mathematics. But Einstein, who was bored with Mathematics, had to pick up on the way whatever Mathematics was needed in his theoretical work..."

Wow, the great Einstein (the greatest of them all!) was no great shakes with Math - and did not like it much either! Ergo, I too had a chance, if could really hone my 'physical intuition' to the required sharpness. And when, a few weeks later, I had to choose my future career, I confidently declared to Pop: "I am going to study pure Physics!". I remember using the English word 'sublime' somewhere there.

Several years passed and despite all efforts (sometimes optimistic, sometimes desperate), my Physics Research petered out; and the love affair with the subject had ended long before a certain eminent (and loud) theoretical physicist made a public declaration which went: "Our Institute has many good students. But there are also a few mediocrities and one or two deficient guys. And finally, of course, there is a certain Nandakumar!"

Utterly disillusioned, I switched to hacking software to earn a living... to continue the main story, over the next few years, thanks to a fairly rigorous study of computer programming - and the internet - I discovered Mathematics (yes, I am not saying 'rediscovered' because I never really knew it before!) and noted with considerable surprise that I was actually *liking* it!

And I found out C.P.Snow was plain wrong (perhaps I am being uncharitable here, but I even suspect he lied) - Einstein might have been no great Mathematician but he certainly greatly loved Mathematics (and he was definitely not BORED with it!). And Mathematics is a subject that returns love with the deepest fulfillment; and without connecting - viscerally - with this fulfillment, one simply cannot do anything worthwhile with any Mathematical Science, Physics included - and viewing Math as a necessary evil, as I used to, is to put it mildly, bad tactics! My discoveries also had a reassuring element: to relate to Math at gut level, one does not need to be a Math Wiz; even I could do it! Snow and the 'Parishad' books had not only missed this vital point about the quintessential nature of Math but had hopelessly - and unpardonably - obscured it.

I want to emphasize that it is simply not necessary to be 'gifted' or even terribly well-trained to make a nontrivial contribution to Mathematics. Indeed, one could say this is one crucial difference between it and Physics: the days when an energetic amateur could hope to do ground-breaking work in Physics are almost certainly over; but with Math, the scene, even now, is: "there (still) are theorems .... which have never been proved and which any fool could have guessed." From personal experience, I am very much in agreement with this quote by G.H.Hardy, although I can't share his snobbery - perhaps Hardy, having been a genius, could afford to be a bit snobbish.

Mathematics is one subject where the quality of teaching is crucially important (I can only think of Music as an area where the teacher has a comparably critical role to play) and in our country, Math remains a very poorly taught subject, including at the highest levels. One other serious problem with the way Math is introduced in our system is the element of competition it always and essentially involves. There are some who are naturally quick and sharp and there are some who are naturally competitive. And I belong to neither category. Moreover, Geometry, an area of Math which I found (quite late in life) I could relate to much more naturally than, say, Analysis, is nowadays much neglected - for example, IIT-JEE, the ultimate Desi test of *real* mathematical ability, usually has zero questions on pure geometry.

David Hilbert once remarked: "Mathematics is often confused with juggling numbers". One could rephrase it, in the context of modern Indian academia: "Mathematics is almost always confused with juggling equations - at speed!".

And I think computer programming is a very useful means to get to love Math, especially for those who are less than facile with equations. Indeed, programming and geometry were what enabled me to get to the heart of Math - more accurately, Mathematics entered my heart via programming and geometry.

I sign off with a very reassuring and more to the point, true statement (at least a hell of a lot truer than the stuff I got to read in more innocent times) on Mathematics that I heard from one of our leading experts: "It is not that Mathematicians find the subject easy. Trust me, that is just not the case. They don't find the subject easy at all. Indeed, the whole idea is not to do Math with ease or to do it better than everybody else, but to love it and to enjoy doing it!"

I grew up in Kerala, among popular science books idolizing Albert Einstein. The 'Sastra Sahitya Parishad', a Mallu organization I have mentioned in some earlier posts, had built up a virtual cult around the Master - indeed if I were to say he was a grand-fatherly figure for self and a whole host of Mallu schoolers of my generation, I would not be exaggerating one bit.

Projecting Einstein as the one Scientist who really counted, 'Parishad' fed us verbalized and romanticized - and indeed, dumbed-down - interpretations of Relativity theory thru half a dozen books on the life of Einsten (one of these hagiographies began: "Dear children, each one of you would want to be a scientist, not just a scientist but a very big scientist, right? Here is the life-story of the greatest scientist of them all; try to be like him!") and countless articles which kept appearing in their Students' Magazines. To give an example of the impact all this had, I could confidently make statements like "gravity is the curvature of the space-time-continuum" at the age of 10 - and I was nowhere near being a child prodigy!

Although I developed grand dreams of becoming a Theoretical Physicist, I was never quite comfortable with Mathematics - and was clearly less than sharp at manipulating algebraic expressions. A fear slowly grew witin - what if I am fail to do lengthy calculations - to fill page after page with all those messy equations, how will I do Einstein-class work?... Then, towards the end of junior college, I read 'The Physicists' by C.P.Snow. And the following bit sank deep:

"The reader may wonder if to be a top-flight physicist, one also has to be great with Mathematics. Well, not necessarily! Indeed, more than facility with Mathematics, a profound physical intuition is what marks out an outstanding physicist. Of course, Dirac could have been any type of Mathematician, of the highest level. Feynman, Pauli and Dyson were also formidably gifted in Mathematics. But Einstein, who was bored with Mathematics, had to pick up on the way whatever Mathematics was needed in his theoretical work..."

Wow, the great Einstein (the greatest of them all!) was no great shakes with Math - and did not like it much either! Ergo, I too had a chance, if could really hone my 'physical intuition' to the required sharpness. And when, a few weeks later, I had to choose my future career, I confidently declared to Pop: "I am going to study pure Physics!". I remember using the English word 'sublime' somewhere there.

Several years passed and despite all efforts (sometimes optimistic, sometimes desperate), my Physics Research petered out; and the love affair with the subject had ended long before a certain eminent (and loud) theoretical physicist made a public declaration which went: "Our Institute has many good students. But there are also a few mediocrities and one or two deficient guys. And finally, of course, there is a certain Nandakumar!"

Utterly disillusioned, I switched to hacking software to earn a living... to continue the main story, over the next few years, thanks to a fairly rigorous study of computer programming - and the internet - I discovered Mathematics (yes, I am not saying 'rediscovered' because I never really knew it before!) and noted with considerable surprise that I was actually *liking* it!

And I found out C.P.Snow was plain wrong (perhaps I am being uncharitable here, but I even suspect he lied) - Einstein might have been no great Mathematician but he certainly greatly loved Mathematics (and he was definitely not BORED with it!). And Mathematics is a subject that returns love with the deepest fulfillment; and without connecting - viscerally - with this fulfillment, one simply cannot do anything worthwhile with any Mathematical Science, Physics included - and viewing Math as a necessary evil, as I used to, is to put it mildly, bad tactics! My discoveries also had a reassuring element: to relate to Math at gut level, one does not need to be a Math Wiz; even I could do it! Snow and the 'Parishad' books had not only missed this vital point about the quintessential nature of Math but had hopelessly - and unpardonably - obscured it.

I want to emphasize that it is simply not necessary to be 'gifted' or even terribly well-trained to make a nontrivial contribution to Mathematics. Indeed, one could say this is one crucial difference between it and Physics: the days when an energetic amateur could hope to do ground-breaking work in Physics are almost certainly over; but with Math, the scene, even now, is: "there (still) are theorems .... which have never been proved and which any fool could have guessed." From personal experience, I am very much in agreement with this quote by G.H.Hardy, although I can't share his snobbery - perhaps Hardy, having been a genius, could afford to be a bit snobbish.

Mathematics is one subject where the quality of teaching is crucially important (I can only think of Music as an area where the teacher has a comparably critical role to play) and in our country, Math remains a very poorly taught subject, including at the highest levels. One other serious problem with the way Math is introduced in our system is the element of competition it always and essentially involves. There are some who are naturally quick and sharp and there are some who are naturally competitive. And I belong to neither category. Moreover, Geometry, an area of Math which I found (quite late in life) I could relate to much more naturally than, say, Analysis, is nowadays much neglected - for example, IIT-JEE, the ultimate Desi test of *real* mathematical ability, usually has zero questions on pure geometry.

David Hilbert once remarked: "Mathematics is often confused with juggling numbers". One could rephrase it, in the context of modern Indian academia: "Mathematics is almost always confused with juggling equations - at speed!".

And I think computer programming is a very useful means to get to love Math, especially for those who are less than facile with equations. Indeed, programming and geometry were what enabled me to get to the heart of Math - more accurately, Mathematics entered my heart via programming and geometry.

I sign off with a very reassuring and more to the point, true statement (at least a hell of a lot truer than the stuff I got to read in more innocent times) on Mathematics that I heard from one of our leading experts: "It is not that Mathematicians find the subject easy. Trust me, that is just not the case. They don't find the subject easy at all. Indeed, the whole idea is not to do Math with ease or to do it better than everybody else, but to love it and to enjoy doing it!"

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