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I. Mathematicians in Cambridge in the late 1870s.
Part of a version of an address to the South-West Wales Branch of the Mathematical Association, Swansea, on 2 March, 1935, by Andrew R Forsyth. It was published in The Mathematical Gazette 19 (234) (1935), 162-179.
Mathematicians in Cambridge in the late 1870s.
A beginning may be made by naming some of the men of mark at Cambridge in that day.
There was Stokes, who held the chair that once was Newton's: the successor of Young, Poisson, Fresnel, in the line of mathematical physicists (to be followed, in my judgment, by Horace Lamb who died recently). We knew some of the work of Stokes, published many years earlier, on the sums of periodic series. But we could not then know how much work, silent in its anonymity, fell to him as Secretary of the Royal Society in saving the Transactions of that learned body from the occasional paradoxes of less accomplished physicists. Nor could we know then that he was the scientific Master of Sir William Thomson - the title of respect with which Kelvin, to his latest days, was wont to describe Stokes in public references. We students attended one course of his lectures - on Physical Optics: it was the single professorial exception allowed, even enjoined, by tutors of all grades - and delightful the lectures were, none the worse because they were of no profit in a Tripos Examination.
There was Cayley, deemed a wonder in pure mathematics, not then held in favour at Cambridge. He had achieved marvels in analysis and high algebra, all beyond us: marvels in the geometry of curves and surfaces, in a range of which we knew nothing; also in the beginnings of the hypergeometry of ideal space: Maxwell described him as the man
Whose soul, too large for ordinary space,Even our college manciple, a fine character in an old-world type of college servants, had his own appreciation of the great man: one day, when expounding some of the glories of Trinity to passing visitors, he halted before Cayley's picture in the dining-hall and solemnly assured them "he's that exact, he could take the earth in his hand and tell you its weight to a pound". Not for undergraduates was there to be attendance at Cayley's lectures, any one of which often contained results his research had obtained only since the preceding lecture; there, he never gave a thought to the Tripos: and rarely indeed did examiners pay the least heed to Cayley's work. But there was one rather wayward undergraduate of my year who, greatly daring, went to a course of lectures by Cayley: he had gone with the acquiescence of his college tutor, to the surprise of one or two lecturers of his college, and against the prudent warning of his coach that such expenditure of time would be unprofitable for the Tripos. That undergraduate was out of his depth after a few minutes of the first lecture: he took what notes he could: sought information somehow: delved hard (and often unwisely) in strange places, with a determination to learn something in that range of knowledge; and he then succeeded in making a beginning of the pure mathematics which, in varying forms, has absorbed a large part of a life that has not been idle.
In n dimensions flourished unrestricted.
There was Adams. He had discovered the planet Neptune thirty years earlier, by a great and long-sustained calculation first conceived by him when he was an undergraduate. We knew something of the inadequate treatment of his work in 1845 meted out by Airy, who had passed from Cambridge to Greenwich and who still was Astronomer Royal in our day. But the work of Adams was not for us: he had passed into the limited cohort of great classics, whose works are not read but to whose names men pay a willing, if uncritical, homage. Seemingly unambitious, he moved supreme in his own domain and was known to us as Father Neptune. Diligent in research, he did not publish much, but all the published work was sound: his main satisfaction appeared to be the attainment of knowledge. Thus, when G W Hill's work in the lunar theory first became known, Adams was found to have all the main results in his own possession, even to familiarity with those infinite determinants which long deterred even the most courageous souls.
We saw Maxwell, intellectually known to be great: we could not surmise how much greater he was yet to become even than the reverent estimate of an awakening world. His great treatise (Electricity and Magnetism) was still fairly recent: its range seemed to have little in common with the electricity of the blackboard and the examination paper: indeed, many of the students (I was one) could then hardly tell - except in a glib vocabulary sufficing for the examination - the difference between a conductor and a condenser. And I have heard Maxwell lecture, a declaration that now can be made by few: for he died in 1879, while still in the prime of life as men count years.
On rare occasions we saw Sir William Thomson, who professed at Glasgow: known to some of us by name, well known to students who had come to Cambridge from his classes at Glasgow. (In my day, many of the best Scots students came on to Cambridge from Glasgow, from Edinburgh, from Aberdeen, after a distinguished home-career.) I happened to know about Thomson also as the electrical engineer of the first successful Atlantic cable: for, in the mid-months of 1877 before going into residence at Trinity, I had been on the ship which was laying a cable between Marseilles and Bona; and on board that ship, at every turn, the electrical staff cited the name of Thomson. It was only years afterwards when Stokes and J J Thomson and I were the official delegates of the University of Cambridge at the Kelvin Jubilee, that I learnt an earlier incident connecting three of the great men who have been mentioned: when the very young William Thomson had been a candidate for the Glasgow chair fifty years earlier, one of his testimonials came from Mr G G Stokes and one from Mr A Cayley. Also, Thomson (with Tait) was joint author of that book on Natural Philosophy which, as "T and T ' ", was a guide to a few men in each generation of Cambridge students.
There were other names known to us, but as yet only names. Such was Sylvester, who, at the age of sixty-three and after a varied life, had just gone to the Johns Hopkins University, and who, when he was on the verge of seventy, returned to vivify Oxford disciples with his zeal for research. There was Salmon, the friend of Cayley: he had not yet completely passed from mathematics to theology where he made a second fame: he was the author of that book on Conics which, to us, was almost a mathematical Bible. We gathered that Cayley, Sylvester, Salmon, were a world-triumvirate in a dark continent of invariants: Hermite's name was mentioned occasionally: the name of Gordan must have been unknown save to the very elect. By middle life, it was my privilege to have become acquainted with all of them personally, except Hermite, and from Hermite there came letters of appreciation beyond value: all that acquaintance now is an abiding memory.
Others also there were, though not deemed of the same high rank in our youthful minds. (I am not framing an estimate of their achievements in our science: only the very youthful, and the rather omniscient, can proceed fearlessly to such a task.) There was Henry Smith of Oxford. There was Clifford, who had only recently left Cambridge for London. There was Lamb, who had only recently gone to Adelaide, and whose book on hydrodynamics (then a slight volume, being an exposition of lectures he had given at Trinity) was the first English book that revealed a use of the complex variable in mathematical physics: let me add that it was an age when the use of √-1 was suspect at Cambridge even in trigonometrical formulae. There was Greenhill, whose early papers were a development of such work revealed by Lamb. There was Glaisher of my own college, one of the best of lecturers, full of enthusiasm about differential equations and elliptic functions and the method of least squares. There was W D Niven, also of Trinity, an interpreter of Maxwell's work: his lectures gave every man as much labour as Cayley's course had given me. There were Burnside and Chrystal, of a then recent year: Burnside, still at Cambridge, had yet to graduate from applied mathematics into pure mathematics: Chrystal, just gone to St Andrews and soon to succeed Kelland at Edinburgh, had achieved a reputation by his Encyclopaedia article on "Electricity", and was yet to be a pioneer in pure mathematics.
And there were others: even of mathematicians, I do not pretend to cite all the names held in honour in the limited range of a student's knowledge: in ancient words, they were "men of learning, honoured in their generations, a glory in their days: some have left a name behind them: and some there be which have no memorial". In diverse ways, and in varying degrees, they were an inspiration to the students of that epoch now more than half a century ago.
Such were the Great Ones on the heights or the upland slopes of our mathematical Olympus: what of the multitude of students on the plains below? We existed in the downland, seldom raising our eyes to the topmost ridges, hardly qualified for fit worship even if there were either wish or will. Some students of that day were, in their turn, to carry on the legendary torch of learning, though, then, all was mainly promise. We had any amount of youthful confidence, and more than any amount of exuberant prophecy, as to what was sure to happen: but sometimes the confidence waned as the hour of performance drew near; and old unfulfilled prophecies are forgotten.
Yet there were some - again let me repeat that I am recalling the young men, for the most part, within our own range of study - some who, even then, seemed assured of future greatness and would never need to abide challenge. There was J J Thomson - at that time, and down to this day, known as J J, in general respect and general affection. His personality stood out: we felt that he was framed in an intellectual mould different from ours: he had our worship as completely as Alfred Lyttelton and A G Steel (who were our contemporaries) had secured adoration in the world of cricket. There was Charles Parsons, great son of a distinguished father: he was absorbed in his models of swiftly-moving machines almost in anticipation of his turbines, a genius not of the conventional type that obtains early academic recognition. There was Hobson: he was, of course, bound to be Senior Wrangler: could a mathematical undergraduate in that school conceive a nobler pinnacle of fame? There was Karl Pearson, looking a fair-haired Norseman, apparently ready for anything, trying many things in happy fact, not respectful to conventional thought, perhaps not always too respectful to conventional persons. There was Micaiah Hill, who might go far, in our view, though whither was beyond our prescience: he did much for our science, and more for the University of London. There was Larmor, an outstanding representative of the Irish genius, silently noted for coming greatness, an expectation amply realised in his scientific life. One other name may fitly be mentioned here: he then was merely one of the horde of mathematical students, not more noticeable than scores of others. Later, by judgment, and thought, and no little calculation, he solved the indeterminate problem of feeding a whole nation in the sternest stress of war. The name of David Thomas, Lord Rhondda, has its place of honour on the beadroll of the benefactors of his country at an epoch of danger. There were younger men too: G B Mathews and Whitehead in one year: William Bragg and W H Young in the next. But on these I do not dwell: partly because, in the year after my own graduation, there came a change in the whole system, which (though not so recognised at the time) really was the end of a long and ancient chapter in the history of English mathematics.
Between the great professors and our unfledged selves there was nothing in common, absolutely nothing, strange as such a declaration may seem. They did not teach us: we did not give them the chance. We did not read their work: it was asserted, and was believed, to be of no help in the Tripos. Probably many of the students did not know the professors by sight. Such all odd situation, for mathematical students in a University famed for mathematics, was due mainly, if not entirely, to the Tripos and its surroundings which, as undefined as is the British constitution, had settled into a position beyond the pale of accessible criticism.
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