In 1924 Frank Ramsey began teaching mathematics at King’s College, Cambridge. He had just returned from a trip to Vienna where he spent a fortnight discussing the Tractatus with Ludwig Wittgenstein and also began psychoanalysis. He died at the age of 26 in 1930, having made major contributions to the fields of philosophy, mathematics, and economics. This essay is an extract from Frank Ramsey: A Sheer Excess of Powers, by Cheryl Misak, published by Oxford University Press.
One thing different in Frank’s new life was the mountainous amount of teaching that was now expected of him. Unlike his father, who wanted extra pupils and the revenue that came with them, and who loved College and Faculty administrative work, Frank found himself desperate to preserve more time for his own writing. His teaching duties quickly built up to a staggering sixteen hours of supervisions and lectures a week. Frank wrote a nervous letter to Keynes on 11 December 1925, asking if he might arrange to have fewer undergraduate supervisions:
I hope you won’t mind my writing to you about this, but I am worried and want your advice.
It now seems to me clear that if I go on doing as much lecturing and teaching as at present, I shall never do any important original work, which I think I might do otherwise . . . In John’s for instance, they do 9 hours a week each including lectures . . . and at Trinity they do even less . . . I have had 16 hours this term, and there seems no prospect of having less, but probably more. This does not sound much but it compares very unfavourably with . . . John’s . . .[S]ince I have been in King’s I have hardly done anything else, except write out things I thought of before . . . It is not only that I don’t get on with research, but I don’t read enough useful literature. As I am mainly interested in philosophical questions nearly the whole of my teaching is quite disconnected from my own work, and does not involve my reading or thinking of anything useful for it…. It is not that I dislike teaching, but that doing so much seems to interfere much too seriously with what I mainly want to do.
He asked if he might take a reduction in pay for a reduction in the number of hours. He didn’t want to seem ungrateful, but he also didn’t want to become “dulled in brain and personality.” He ended the letter by saying: “I haven’t said anything about this to anyone, except I.A. Richards, because if nothing can be done it is obviously better for me not to appear discontented.”
Keynes had himself found teaching exhausting and by this time had farmed it all out to Gerald Shove. Nonetheless, he told Frank that he was asking for the impossible and advised him to simply knuckle down and get on with it. That’s exactly what Frank did. And for the most part, he was very good at it.
Braithwaite remembered that one student, Jacob Bronowski (later of Ascent of Man fame), said Frank wasn’t a good teacher, and Braithwaite himself said it was hard to imagine Frank identifying with the “stupider” students and not breezing through explanations at incomprehensible speed. Tom Stonborough, Wittgenstein’s nephew, had this experience. He had arrived from Vienna to study mathematics at Trinity in 1923and in 1925 his supervisor sent him to Frank, as things were “getting hot” for him – he was predicted to fail. By his own account, he was not up to the Mathematical Tripos and, anyway, was only interested in sport. Decades later, Tommy said it was like a beginner in tennis being sent to Björn Borg to learn how to play. Frank couldn’t understand how Tommy couldn’t understand the simplest things. Tommy said that mathematics, for Frank, was like a part of his body. He used it like his hands, without thinking. Despite the extra lessons, Tommy never got the hang of, or interest in, the subject, saying that he was unteachable and that he “flunked Cambridge”. He later burned through his part of the Wittgenstein fortune, selling the Klimt portrait of his mother and the house that Wittgenstein designed. Frank agreed with Tom’s self-assessment. He told Keynes that Tommy was “nice but stupid.”
The more mathematically inclined students, on the other hand, thought Frank was a great teacher. Patrick Du Val, who went on to become a respected geometer, wrote of Frank’s “quiet voice, explaining, satisfying.” Richard Kahn, whom Frank supervised for the Mathematical Tripos Part I, said, well into his illustrious career as an economist, that it was an education from which he was still benefitting: “Here was a great man who took me all alone one hour a week. . . I regarded it as an enormous privilege.” Frank taught others who would also go on to success – Philip Hall in mathematics; Llewellyn Thomas in physics; Freddie Harmer in economics and the civil service; Henry Lintott in diplomacy. The brilliant geometer and inspirer of M.C. Escher’s geometrical drawings, Donald Coxeter, who was in effect Senior Wrangler in 1928, learnt differential geometry from Frank.
Ramsey had worried, before he started his teaching at King’s, that Berry would be “horrified” at how little applied mathematics he knew. But it turned out he could do it on his feet. Kahn said that all Frank knew of applied mathematics were Newton’s three laws of motion, and that when he had to work out an applied problem, he did so by working it out from those first principles. Kahn’s remarks were echoed by others:
I remember his saying that he didn’t know any applied maths, but he never failed to solve every applied question, & then laughed uproariously at what he said was a miracle. We got along famously, a very refreshing change from my previous five terms.
His students found him very easy to know. They liked his style – that of “a large, untidy, shy & charming man with a wide and winning smile.” It was unusual and attractive to them. Some of them felt perfectly comfortable calling him by his first name. In an era in which the mathematics dons wore suits and formal manners “rather like bankers,” Frank was a standout.
He held his supervisions in his sparsely furnished and untidy study room, books and papers piled on the floor and on cupboard tops. The reports of his students gel into a coherent picture: “One day an almighty crash behind me signalled that the law of gravity had cleared the top of the cupboard;” “My visual memory of the supervisions is of his enormous frame sprawling in an armchair, laughing a great deal of the time;” he used a thick-nibbed fountain pen, “making stabs at the ink bottle which often had the cork in it;” his mathematical illustrations were accompanied by doodles and were a mess. His supervisions sometimes wandered off into talk of music and philosophy. That might have not been good preparation for the Tripos, but his supervisees felt it more profitable in other ways. And when he turned his attention to the maths and cleared up a student’s confusion, he “was awfully good at it,” scribbling precisely understandable, analytic explanations.
His students were also consistent in reporting that, although they were awed by him, they were not frightened of him. One said this was because he had no interest whatsoever in dominating or embarrassing them. A South African undergraduate who had been made to feel like a “low colonial fellow” by his previous supervisors, wished that he had been assigned earlier to the “large, plump cheerful young man,” who was so approachable and kind. Another said: “He was always very friendly and human,” “not at all the “academic type.’” Another said that he might have been a paradigm of “intellectual elitism,” in the sense that he knew that he knew better than others about the right way to proceed mathematically, but he wasn’t an elitist about people. He always “took trouble” for his students, writing testimonials and letters of reference in a timely fashion, and taking pains to clear up their confusions. This was contrasted with Littlewood, who was singled out by some as not taking his supervisory duties “at all seriously.” His friendliness was a contrast also with his severe and unemotional father’s style of teaching.
In addition to his undergraduate supervisions, of which he had some experience at Girton, Frank was for the first time preparing and delivering lectures. He was unhappy with his initial assignments, as his favourite subjects had already been “bagged.” So he taught some of the standard courses for the Mathematical Tripos: Theory of Equations, Solid Geometry, and Functions of a Complex Variable. Later he would teach other bread and butter courses, such as Differential Geometry, Functions of a Real Variable, Algebra, and Differential Calculus. Sometimes these were taught with others. Eventually those others included his old friend Max Newman, who in 1923 had been elected a Fellow of St. John’s College, and in 1927 was made a lecturer in the Mathematics Faculty.
He was really happy when he bagged The Foundations of Mathematics, Russell’s old course. The Tractatus scholar and eminent analytic philosopher Max Black was a student at Queens’ College, Cambridge from 1927-29 and took it. His specialed subject in Schedule B of the Tripos was Mathematical Logic, which, as he put it, was “then hardly pursued in England, although abroad actively researched in Europe.” Indeed, Black claimed “there was no mathematical logic taught in England except in [my] third year when Ramsey began to be a strong influence.” Russell was not teaching. Whitehead had moved to Harvard in 1924, and had anyway left mathematical logic. Wittgenstein didn’t count, as far as Black was concerned. He thought that although Wittgenstein was interested in the philosophy of mathematics, he didn’t know much about the nuts and bolts of mathematics and logic.
Black found Frank “a poor lecturer . . . but . . . a very, very intelligent, extraordinary man.” He took the Foundations of Mathematics course in the autumn of 1929, when Frank was ill – fatally ill, as it turned out. Perhaps that explains his verdict on his lecturing style. For others had a very different account. One student remembered:
Chalk getting into his hair, all over his gown and suit, smudged over his glasses and face, and broken bits of chalk flying at all angles off the blackboard. . . He generally had his hair in tufts all over the place. I remember him in a brown tweed suit, much more countrified than the conventional grey suits normally worn by other lecturers…. Shining through all this was a round cheerful face, and his style of lecturing was also cheerful; he imparted an enjoyment of his subject and spiced a clear exposition with little touches of humour. . . Ramsey exuded some sort of personal charm into his lectures. It was like going into a friend’s house, to go into his lecture room.
Others said that his lectures were aimed at the appropriate level of difficulty and that he was “quiet, logical, and lucid.” He lectured by thinking on his feet, not by reading from notes, and had a habit of walking up and down in between the rows of students, smiling and talking. His audience was afraid to interrupt him, not because they thought he would react brusquely, but because he was “superior” and they wanted to soak up his train of thought. Llewellyn Thomas took careful notes on the Foundations of Mathematics course in Lent term 1925. The notes still exist, and show that Frank’s lectures were beautifully clear.
Thomas’s notes also show that Frank’s syllabus that year was ambitious beyond belief. On the reading list was the work of the French logician Jean Nicod; Frege’s Grundlagen der Arithmetik (The Foundations of Arithmetic) and Grundgesetze der Arithmetik (The Basic Laws of Arithmetic); and Introduction to Mathematical Philosophy and Principia Mathematica by Russell. He must have chosen selections from these mammoth tomes, especially the Frege books, as they used an unfamiliar logical notation and weren’t translated into English at the time. The lectures themselves featured a little Frege, and much Russell, Wittgenstein, Hilbert, Brouwer, and Weyl.