Ramanujan (continued...)- Part 2.

So where were we earlier? A young boy of 17 infatuated with mathematics... unsatiated with what the school curriculum or available textbooks of that era provided.... with acumen and originality par excellence, was hungry for more. An answer came in the form of an old and outdated textbook titled, `Carr's Synopsis of Pure and Applied Mathematics'.

Actually it was hardly a textbook, not even close to being one. It was only because of Ramanujan that we know of this book today, else it was already out of print 50 years before Ramanujan's time.

Carr, an englishman and the author of the text, was not a professor in a university nor a very competent mathematician. He was, in fact, a private tutor of mathematics who coached students preparing for the Mathematical Tripos. The Tripos was a highly tough and competitive examination in mathematics which was taken by college students aged 20-21. Excelling in the Tripos was considered a great honour and the toppers in this examination were called 'Wranglers'. Being a Wrangler more or less guaranteed you a full scholarship to pursue Mathematics at Cambridge or Oxford or any college of your choice. The Tripos is one of the oldest examinations in the world, and though it has changed in format and structure, it still exists. Infact great english mathematicians like James Clerk Maxwell (who formulated the first comprehensive mathematical theory on electromagnetism and is famous for the 4 Maxwell's equations of electromagnetics) , G. H. Hardy (who shall feature in this monograph later), Lord Kelvin (famous physicist who worken on electricity and thermodynamics) and Geoffery Taylor (one of the greatest fluid mechanicians ever) were senior Wranglers in their time, just to name a few.

So coming back to Carr, who himself had passed the Tripos, though not as a Wrangler, was a popular tutor for the examination and ran classes around 1840-1860. It was for these classes that he had prepared the Synopsis which was more of a compilation of 5000 theorems in algebra, integral and differential calculus, the theory of equations, number theory, continued fractions and trigonometry. It was hardly a text book, in the sense that it contained very little theory. But what it did have was a step-by-step chronology of mathematical theorems each a little more challenging than the previous one. Since this was not a textbook, the author had not bothered to provide detailed proofs anywhere throughout the text. Most formulae and theorems were simply stated and for some difficult ones, a couple of lines attempting to delineate the rough solution strategy were provided. It was with this primitive text that Ramanujan began his adventure into advanced mathematics. It is probably one of the most intriguing facts that such a primitive book should trigger the genius of a man, as he began working through each problem in the book, each solution being a piece of original research for him. More importantly, as Ramanujan churned mathematics out of the book, the book inspired mathematics out of Ramanujan. He started filling up his `notebooks' (which would later become famous as his legacy and remain as poseidon's treasure for mathematicians of the 20th century) with original theorems of his own working with force and vigor. By the time he was 20, he had developed his own special methods of constructing magic squares, his own theory of modular equations and continued fractions and his own theory of divergent series (which though later found to have a lot of inconsistencies was nonetheless remarkable to have originated from an amateur mathematician). There is one last time I should like to mention about Carr and his book. Other than extracting the genius out of Ramanujan, the book had another singular effect upon his methodology of working out problems that has left its mark in his notebooks. Throughout his notebooks, Ramanujan does not care to write detailed proofs for any of the 3000 theorems that he conjured himself. He barely outlines the proof and it hardly makes any head or tail to the innocent reader. Ever since his death many mathematicians tried to work through his notebooks, most of them giving up because they found it eating up their time. It is just recently, after work for more than 20 years that Bruce C Berndt, a mathematics professor at UIUC released a 5 book series that provides a detailed exposition of Ramanujan's work as an amateur mathematician which is hidden in his notebooks. His work as a professional mathematician is yet to be mentioned.

(To be continued.....I try to be regular at this but I'm afraid of losing inspiration and leaving it half baked!)