Ramanujan, Srinivasa — G. H. Hardy | The mathematician's second appearance in print in the West

Ramanujan, Srinivasa, G. H. Hardy, et al

The Messenger of Mathematics. Vol XLIV. [May 1914–April 1915]. Cambridge: Bowes & Bowes, 1915

8vo (213 x 136 mm). Very minor pale spotting, mostly to the endpapers, a short tear at the top edge of the front free endpaper, a few pencil annotations, an old bookseller's invoice laid in. Original patterned brown cloth, gilt-titled spine; spine ends and corners softened, a few rubbed spots at extremities.

First and only edition of a rare mathematics journal featuring one of Srinivasa Ramanujan's earliest appearances in print in Europe. It includes three papers by the mathematical autodidact, written soon after he arrived in Cambridge, as well as his mentor G. H. Hardy's proof of one of the equations.

In late January of 1913, Cambridge mathematician G. H. Hardy received an envelope sent from Madras, India. The cover letter began:

"I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. I have had no University education but I have undergone the ordinary school course. After leaving school I have been employing the spare time at my disposal to work at Mathematics. I have not trodden through the conventional regular course which is followed in a University course, but I am striking out a new path for myself. I have made a special investigation of divergent series in general and the results I get are termed by the local mathematicians as ‘startling’... I would request you to go through the enclosed papers. Being poor, if you are convinced that there is anything of value, I would like to have my theorems published. I have not given the actual investigations nor the expressions that I get but I have indicated the lines on which I proceed. Being inexperienced I would very highly value any advice you give me."

What followed were nine pages of mathematical formulae on infinite series, improper integrals, continued fractions, and number theory. Despite initially dismissing the letter, Hardy took a second look at the equations with his colleague J. E. Littlewood. They realized the work was sensational, its author a mathematical genius. Some of the results were entirely novel and extremely advanced, stumping even the esteemed Cambridge professors. Hardy eventually managed to arrange for Ramanujan to come to Cambridge as a research fellow. Arriving in 1914, Ramanujan stayed at the University under Hardy's tutelage, publishing articles, and making substantial contributions to the field. In 1918 he was elected to the Royal Society. He was one of the youngest fellows in its history and the second Indian person ever admitted. After falling ill, he returned to Madras, where he died in 1920 at age 32. After his death, Ramanujan would be recognized as one of the most important mathematicians of the twentieth century, and by far the most compelling.

Volume XLIV of the Messenger of Mathematics (Cambridge: Bowes & Bowes, 1915) contains three papers by Ramanujan—“Some definite integrals” (pp. 10–18; followed by Hardy's 3-page proof of the formula), “Some definite integrals connected with Gauss’s sums” (pp. 75–86), and “Summation of a certain series” (pp. 157–160). It is of particular note that Ramanujan's first paper appears alongside Hardy's proof of it. This is emblematic of their mathematical partnership, where Ramanujan would provide a highly intuitive insight, and the professor would formally prove it. Additionally, Hardy's proofs of Ramanujan's formulas acted as a stamp of approval in the mathematics community. This cannot be overstated — Hardy was the premier mathematician in England at the time, while Ramanujan had only just arrived.

This journal was among the earliest glimpses that the Western mathematics community would see of Ramanujan's prodigious genius. The Collected Papers of Srinivasa Ramanujan, edited by Hardy, includes a list of Ramanujan's papers and a bibliography. He dates the first two papers that appear in this journal to 1914 and puts them first and second on his list. As such, it appears that these papers were the first ones that Ramanujan wrote after arriving in England and receiving instruction in modern math. However, according to the bibliography, Ramanujan's earliest publication to appear in Europe was "Modular equations and approximations to π," in The Quarterly Journal of Mathematics (1914). Before leaving India, Ramanujan had published nine papers in the Journal of the Indian Mathematical Society starting in 1911.

While we are able to locate a handful of copies of this volume of The Messenger of Mathematics in institutional libraries, we cannot find any record of this volume having been sold at auction, or any copies in the trade.

REFERENCES

Ramanujan, Srinivasa and G. H. Hardy, editor. Collected Papers... Cambridge University Press, 1927

PROVENANCE

Possibly A. Hodge Esq. (scrawled name written on laid in invoice from A. C. Curtis Limited, Godalming, dated 20 September 1915)