Page 20 - Ramanujan Yatra

processes for growing Ramanujans, we will have to examine more closely the path of Ramanujan’s own growth and his courses of self instruction. We are familiar with his earlier part of life – how he worked all alone through Carr’s ‘Synopsis of Pure Mathematics’, as a school student, and the later part (after 1914), in partnership with Hardy. But not much has been written about his courses of self study between 1902 and 1913.
One of the great mathematics teachers of the 20th century, Prof. W.W. Sawyer writes, “The essential quality for a mathematician is the habit of thinking things out for oneself. That habit is usually acquired in childhood. It is hard to acquire it later.”
In a beautiful book about how to grow mathematicians titled ‘Prelude to Mathematics’, Sawyer defines mathematics as ‘the classification and study of all possible patterns’. He has used the word ‘Pattern’ in a way that not everybody may agree with. It is to be understood in a very wide sense, to cover almost any kind of regularity that can be recognized by the mind.
Thinking things out for himself, experimenting with, observing patterns and recognizing regularities in his objects of study – be they numbers, infinite series, continued fractions, integrals, special functions – is just what Ramanujan did, with passion and determination, to become Ramanujan.
Prof. Sawyer has written an important article ‘Catering to the Extremes’ on the kind of education needed to nurture students with exceptional mathematical ability (available on the website www.wwsawyer.org). He cites an article on Alan Turing written by Turing’s math teacher Canon Eperson, who wrote:
“I believe my deliberate policy of leaving him mainly to his own devices, and standing by to assist when necessary, allowed his mathematical genius to progress uninhibited.... he read and understood books on advanced topics, such as Relativity.”
Sawyer continues...“The article about Turing reminded me of the mathematical education that some of us were fortunate enough to receive in the 1920s. It was based on a policy that had been thoroughly tested and had proved highly satisfactory. It seems to have been recognized and used only in a very restricted sector - the mathematically strongest public schools.....what service did the teachers of the 1920s do for their pupils, and how can their contribution be replaced in the different circumstances of to-day?
(1) Their greatest service was being responsible for letting the young mathematicians take control of their own lives and forge ahead at their own rate. It is very hard for someone who has not had the experience of independent
Ramanujan
YATRA
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