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RAMANUJAN’S EARLIER NOTEBOOKS AND HIS LOST NOTEBOOK

Since the centenary of Ramanujan's birth, a large amount of Ramanujan's mathematics that had been ensconced in his earlier notebooks and in his lost notebook has been brought to light. In particular, in 1987, only one book had been written on Ramanujan's notebooks [2], but now several have appeared [2], [1]. We now have a larger portion of Ramanujan's mathematics to appreciate, evaluate, analyze, and challenge. The challenge is to ascertain Ramanujan's thinking and motivation and to properly place his work within contemporary mathematics. Since other writers in this series of articles are focusing on Ramanujan's lost notebook, we give more concentration in this paper on his earlier notebooks. For most of his life, both in Kumbakonam and later in Madras, Ramanujan worked on a slate. Paper was expensive for him, and so he recorded only his final results in notebooks. Writing down his proofs in notebooks would have taken precious time; Ramanujan was clearly anxious to get on with his next ideas. Moreover, if someone had asked him how to prove a certain claim in his notebooks, he undoubtedly was confident that he could reproduce his argument. We do not know precisely when Ramanujan began to record his mathematical discoveries in notebooks, but it was likely around the time that he entered the Government College in Kumbakonam in 1904. Except for possibly a few entries, he evidently stopped recording his theorems in notebooks after he boarded a passenger ship for England on March 17, 1914. That Ramanujan no longer concentrated on logging entries in his notebooks is evident from two letters that he wrote to friends in Madras during his first year in England [5, pp. 112–113; 123–125]. In a letter of 13 November 1914 to his friend R. Krishna Rao, Ramanujan confided, " I have changed my plan of publishing my results. I am not going to publish any of the old results in my notebooks till the war is over. " And in a letter of 7 January 1915 to S. M. Subramanian, Ramanujan admitted, " I am doing my work very slowly. My notebook is sleeping in a corner for these four or five months. I am publishing only my present researches as I have not yet proved the results in my notebooks rigorously. " Prior to his journey to England in 1914, Ramanujan prepared an enlarged edition of his first notebook; this augmented edition is …