Early Indian Mathematical Pilgrims to Cambridge

Early Indian Mathematical Pilgrims to Cambridge K. Razi Naqvi Department of Physics, Norwegian University of Science and Technology N-7491 Trondheim, Norway During the nineteenth and the early part of the next century, the University of Cambridge (UoC) was the Mecca of Mathematcis for students from the British Isles and other parts of the British Empire. UoC concentrated on undergraduate teaching; its examination system, particularly the Mathematical Sciences Tripos (hereafter abbreviated as MathTrip), served as a launch pad for re- munerative and influential careers in law, church, politics, even medicine, and various adminis- trative organs of the British Raj. Most examiners were not engaged in research, and few examinees dreamt of qualifying as a high wrangler, or of becoming a creative mathematician. The purpose of this article is to scrutinise the performance of the few Indian students who completed one or both parts of MathTrip, the career choices they made after returning to India, and their efforts, if any, towards the diffusion of modern mathematics in Indian schools and colleges. Almost all of the returnees became functionaries of the colossal British bureaucracy. Rejuvenation of Indian mathematics was carried out mostly by other enthusiasts, among whom Muslims are conspicuous by their scarcity. “Whether good mathematicians, when women and a handful of men from other they die, go to Cambridge, I do not parts of the British Empire were two mi- know. But it is well known that a large nority groups, whose members performed [?] number of men go there when they equally well. I am concerned here essen- are young for the purpose of being con- tially with those who came from the In- verted into senior wranglers and Smith’s dian subcontinent, and even out of this prizemen.” I would have been happier to small group, I will only speak of those who quote this remark if its author, the eccen- passed MathTrip during the period 1898– tric Oliver Heaviside, had used small in- 1909. One of my purposes for selecting stead of large. When these words were writ- this group is to ask what contribution, if ten [1], British men did indeed form the any, they made to mathematical research bulk of the students aspiring to complete and to promotion of mathematical educa- the Mathematical Tripos (for short, Math- tion in India; another is to see what frac- Trip), but most candidates knew that they tion of the graduates had identifiably Mus- would not be able to reach the peaks men- lim names. I will subject to closer scrutiny tioned by Heaviside, and did not think of the credentials of two individuals, namely themselves as good-mathematicians-to-be, Inayat Ullah Khan (also Inayatullah Khan; let alone senior wranglers. Quite a few hereafter abbreviated as IUK) and Ziaud- 1 din Ahmad (alternative spellings of the first Both Parts of the Examination are held in June. component: Zia Uddin or Zia-ud-Din or InPart I the namesare in order of merit, the names Zia-ud-din); my motive is to see whether being bracketed in all cases of equality. In Part II. the claims made by their devotees about they are arranged in each Division in alphabetical their academic achievements in Cambridge order. and/or a European university are sup- To paraphrase the above: The list of the ported by such facts as cannot be reason- men who obtained Honours in Part I (Math- ably disputed, and to ask whether it is rea- Trip1) of a given year was grouped in three sonable to call either of them a mathemati- classes (Wranglers, Senior Optimes and Ju- cian or a scientist. nior Optimes), the names in each class being placed according to the marks awarded by the examiners. 1 MainSources Among the wranglers, those placed at the first and second position were called Se- It will suffice to examine two documents nior Wrangler (SW) and the Second Wran- titled Historical Registers, one covering the gler (2W), respectively; after these came period 1753–1910 [2] and the other the fol- the Third Wrangler (3W), Fourth Wrangler lowing decade [3]. The scope of both com- (4W), and so on. Two or more wranglers pendia can be summed up by quoting the who got the same marks were bracketed to- first and the last paragraph of the preface to gether by a closing brace “}”. the second: In the list for Part II (MathTrip2), each Fist paragraph: “The publication of The His- candidate was placed in one of three classes torical Register of the University of Cambridge (First, Second, Third), each class itself being followed upon a decision of the Syndics of the further divided into three divisions (First, Press to lighten the ever-increasing bulk of The Second, Third); the names in each category Cambridge University Calendar by transferring followed alphabetical ordering. Success in the historical information hitherto contained in it Part II is to be seen as a postgraduate quali- to a separate volume. That volume, published in fication. 1917, contained historical records from the earliest times up to and including the year 1910, the fruit of diligent research on the part of its editor, Dr J. 3 AFewExamples R. Tanner.” Last paragraph: “In order to make this volume In the Introduction to the collected works of as self-contained as possible, indexes to the Tripos G. H. Hardy, we find the following descrip- Lists, to the winners of University Scholarships tions: and Prizes, and to the holders of University ap- Hardy was fourth wrangler in 1898, R. W. H. pointments during the period 1911–20 have been T. Hudson being Senior Wrangler, with J. H. Jeans included in it.” and J. F. Cameron, later Master of Gonville and Caius, bracketed next. He took Part II of the Tri- pos in 1900, being placed in the first division of 2 New Regulations the first class, Jeans being then below him in the second division of the first class. In the same year In 1886, new regulations came into effect [2, he was elected to a Prize Fellowship at Trinity, and p. 549], which are quoted verbatim below: his early ambition was thus fulfilled. Hardy and Jeans, in that order, were awarded Smith’s Prizes Those who have obtained Honours in Part I. in 1901. are admissible to the Examination in Part II. following. In 1899, the top four wranglers were G. 2 Birtwistle (SW), R. P. Paranjpye (2W), S. B. years. In certain respects his position was McLaren, and P. V. Bevan. In Part II of the unique, for he was a link between the older following year, six candidates were placed theoretical physics and the new.” in the First Class: P. V. Bevan, G. Birtwistle, Among the Indians, Paranjpye (1876– G. H. Hardy, and R. P. Paranjpye (all in the 1966) became an administrator in the British First Division), J. H. Jeans and S. B. McLaren Raj, was knighted and served as India’s (both in the Second Division). High Commissioner to Australia during the In 1900, there were 16 wranglers, of period (1944–7). Hoon Balak Ram, whose whom Balak Ram was 4W. There were 26 last name is sometimes spelt as Balakram wranglers in 1905; J. E. Littlewood and (1876–1929) also joined the prestigious In- J. Mercer (both of Trinity College), were dian Civil Service, and was appointed as bracketed as SW, and F. M. Khan (of St. a judge in the Bombay High Court shortly John’s College) was 23W; I have come to before his death. Both Paranjpye and Balak conclude that his full name must have been Ram participated in the revival of mathe- Fazl Muhammad Khan. matics in India [6], and played an active The 1909 list for MathTrip1 has 31 wran- role in the Indian Mathematical Society [7]; glers, the top four of whom are: P. J. a recent book on Catalan numbers men- Daniell, E. H. Neville, L. J. Mordell, W. E. tions the latter’s contribution to number H. Berwick, and C. G. Darwin; on Nr. 14 theory and gives a biographical sketch [8, stands the name of G. S. Chowla, and two p. 69]. S. M. Sulaiman (1886–1941) was scholars are bracketed under Nr. 27: Inayat- knighted in 1929, served as the Chief Jus- ullah and J. R. Stickland. In the second class tice of Allahabad High Court, and spent (Senior Optimes), four names are bracketed the last few years of his life as one of the in the tenth place, among them S. M. Su- three judges of the Federal Court at Delhi, laiman. established in 1937. Sir Shah Muhammad Sulaiman did not lose his interest in science, and spent his spare time in formulat- 4 What Happened to Most of ing a unified theory of physical phenomena Those Named Above and a non-Einsteinian theory of relativity [9–12]. I reproduce an excerpt from an obit- A few became well known mathematicians uary written by C. V.Raman for Nature [13]: or mathematical physicists. In this group Sulaiman studied mathematics and physics at fall G. H. Hardy (1876–1947), J. H. Jeans Cambridge, taking Part II [sic] of the Mathemati- (1877–1946), J. E. Littlewood (1885–1977) cal Tripos in 1909. During his subsequent career and C. G. Darwin (1887–1962). The careers as a practising barrister and as a judge at Alla- of Hudson (1875–1904), Bevan (1875–1913) habad, he continued to retain a general interest and McLaren (1876–1916) might have been in the progress of physical science. Later in life, just as productive and distinguished if they the stimulus of contact with the University staff at Allahabad and Aligarh led him actively to un- had lived longer.

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