Department of Mathematics and Statistics

A Necessary Balance: Alec and Harry Aitken 1920-1935
P.C. Fenton


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18.   Edge

In 1932 William Leonard Edge, at the time a fellow of Trinity College, Cambridge, joined the Mathematics Department. He remained until his retirement in 1975.

Edge shared Aitken’s delight in walking, and like Aitken was a fine musician. With Walter Ledermann and Schlapp they were ‘The Mathematical Quartet’, and frequently performed at meetings of the Edinburgh Mathematical Society. He had strong opinions, a store of anecdote, and held court in the Research Room in what has been described as a Johnsonian manner. According to his obituarist,

It would be fair to say that “W.L.E.” was not a creature of the twentieth century. His role models and his interests derived from an earlier period. He disliked change, particularly in colleges, universities and the Catholic Church.134

Margaret wrote to me:

One had to be in the mood to talk to Edge – to feel robust enough, one could say. In his heyday, which was a considerable span, he was a known & sized-up character and phenomenon, & therefore influenced other people less; he was what he was and that was it. I don’t think ACA was put off by Edge’s ingrained attitudes. He would often enough recount this or that amusing anecdote about him. – Though one time, in ACA’s early days before the war, Edge was holding forth at length in the Research Room about how he had lifted out a copy of Cayley (collected papers on algebra, probably) & found the pages uncut! The disgrace, etc. Well, ACA crept into the department that evening & cut all the pages. Many years later, ACA recounted this in the Research Room – not in the presence of Edge, of course! – as an example of Edge’s dominance & views, I suppose. But I wonder what ACA felt at the time, as a much younger man & not what you would call established. Did he do it to please Edge, or for the honour of the Maths Dept, or both?135

Edge could be equally assertive as a musician.

Mother liked Edge’s voice; she used to ask him to sing. At one evening party at 74 Trinity Road, Edge, on being asked to play/sing, sat down at the piano & played a whole Schubert sonata, including repeats, which took three-quarters of an hour! George page-turned for him, & tried to turn the page over to avoid a repeat, but Edge very crossly turned the page back & insisted on all the repeats.136

When I met him in 1996 he was frail but in perfect control of his mind. His last (as it turned out) mathematical paper had been published in 1994 when he was 90, and the latest issue of the Bulletin of the London Mathematical Society lay by his bedside. His conversation was precise and waspish.137 Much of what I asked he ignored, deflected with anecdote or replaced with an opinion on another subject, yet the opinions he gave ranged widely and some might be considered indiscreet. What follows is an unconnected summary.

Aitken and Ledermann, he said, in talking about the First World War, realised that their fathers had been at the Somme together, though on opposite sides; an Irish mathematician once gulled Aitken, saying that New Zealand soldiers were the ‘finest chaps in the war’, and Aitken had swallowed it and too warmly agreed; Winifred resented Aitken’s research students for keeping him from his own work; Aitken and Winifred disagreed over the choice of a lampshade and, an artist being in the house and asked his opinion by Winifred, he pointed to the lampshade Aitken favoured and said ‘I wouldn’t choose that!’, to which Winifred responded by looking hard at Aitken and saying ‘See!’; when Aitken had visitors to the house, he asked Winifred, ‘Shall I take them into the kitchen?’ and she replied loudly, ‘No!’; Aitken’s violin playing was amateurish; in Edge’s opinion, Aitken was an amateur in mathematics, like Abel and Ramanujan; Aitken applied for a chair at Cambridge but his testimonials were not requested; Edge tried to persuade Aitken to take fewer lectures during his breakdowns but he resisted; between 1961 and 1965 Aitken did no work (although he tried for a couple of weeks in 1962); Winifred sent for Edge during Aitken’s 1941 breakdown (and, Edge had told me earlier by mail, Aitken entrusted him with the manuscript of Gallipoli to the Somme); Aitken had an illiberal side, disapproving at one time of a research student who made a woman pregnant; Aitken once said to Edge (who was Catholic) on the subject of some religious question, ‘You know that Edge! You’re part of the clergy’; Aitken was a superb lecturer but dullards could not keep up; once Aitken went to London to show off his memory and mental calculation but found that he had forgotten to bring the cards with the first thousand digits of $\pi$, necessary for his recitation to be checked by the audience. He went to a typing shop and asked ‘Can you type me a number, please?’ ‘Certainly, Sir.’ ‘Give me five copies of this by this afternoon.’ When he left the shop he turned round and found them staring after him; when Aitken had to stop teaching, he quoted a verse from Housman to describe his state: Ah, past the plunge of plummet,/ In seas I cannot sound,/ My heart and soul and senses,/ World without end, are drowned.138

Evidently Edge disapproved of Winifred’s influence over Aitken and was content to be seen to do so, and his story about Aitken and Cambridge (which was flatly rejected by Margaret139) is strange in so brief an interview, and suggests a doubtful attitude to Aitken’s reputation. Friendship with Edge may have been, so to speak, a two-edged affair.

In the correspondence between Aitken and Edge – at least Aitken’s contribution to it, which is all I have and possibly all that existed – mathematics was the main subject, overwhelmingly, but the letters have a dramatic quality that comes from Aitken’s seeming to imagine Edge before him as he writes. It is as though he were taking notes on his own conversation.

Halfway through a heavy $H(\: )H^{{-1}}$ reduction (involving a matrix which in full is 400 rows and columns – the matrix I wish to isolate in it has 225 rows and columns) I pause to justify myself, in a semi-soliloquy, which will take better form if imagined as being overheard by you. So, overhear.140

The letters are variously persuasive, critical and didactic, and depart into autobiography and such things as walking in the hills, university life, music and landscape. The first is dated 15 August 1936, four years into Edge’s time at Edinburgh, addressed to ‘Dear Edge’ and signed ‘A.C. Aitken’. The last (14 November 1958) is addressed to ‘My Dear Edge’ and signed ‘A.C.A.’ (George Aitken said that for years he was unaware that Edge had other names; he was simply Edge.)

Three examples convey the tone of the letters. The first was written from the Aitkens’ wartime retreat at Eskdalemuir.

I don’t know whether you are still at Buttermere, but I am presuming you are. As for myself, I am still here, except that on Fridays I go to Edinburgh and do “watch and ward” during the evening and all night at Drummond Street, returning to Eskdale on Saturdays. The cyclometer now shows 2450 miles, and that on George’s bicycle, formerly my own, 2030. We shall soon have done 5,000 between us.
I have come to think of Nat. Phil., where I put up on Friday nights, as “The Hotel Barkla”. Its severe scheme of interior decoration, based on motifs of bell-jars, beakers and Bunsen burners, has conduced to the austerity which may be presumed suitable to an algebraist; at any rate, since frequenting the Hotel in the double rôle of guest and concierge, I have got out the whole theory of substituants, all by elementary reasoning and with no leaning on group theory or substitutional analysis. In between times I have climbed White Coomb, Lochcraig Head, Moll’s Clench Dod and other Moffat Water hills of 2500-2700 feet, and have cycled up the Liddel to Hermitage castle and thereabouts. There is a great view from White Coomb, though walled off somewhat to the south by the ramparts of Bodesbeck, Ettrick Pen and Loch Fell; to the north Broad Law and Cramalt Craig show up well, with Culter Fell northwest and Tinto further on, as usual seeming to be 500 feet higher than its height according to Ordnance.
The main features of substituants are […]

The second is the concluding section of a letter dated 27 December 1942:

And now no more mathematics. It is ten to five, and the sun has left gold and pink cirrus clouds on a sky of “eau de Nil”, but blue in the zenith. The western view is surpassingly beautiful, the tops of the Eaglescarnie woods being suffused with the dying red. Lammerlaw is almost mauve, its fine outline sharply silhouetted, but its slopes a luminous mist. So now to draw the blinds and curtains and pile on the resinous logs, and later play Bach.

Finally an extract from the first of the ‘My Dear Edge’ letters:141

Had tea and a chat on Thursday at Randa [Royal and Ancient], St Andrews, and partly because of consulting a June time-table instead of a July one, found the 4.5 train leaving the station as I descended the steps. Herbert [Turnbull] was concerned at this, but I said I would simply take a walk by the sea and catch the next train – Herbert himself had an engagement at 5.15. So I sat not far from the R.& A. clubhouse, overlooking the bay, and proceeded to reduce $A^{{[2]}} \times A^{{[3]}}$, where $A =$ [a certain $2 \times 2$ matrix].

(The result was a $12 \times 12$ matrix with integer entries, most of four or five digits.)

One suspects that letters gave Aitken a milieu in which mathematics was more obviously art and he was more completely human. They are reminiscent of Plato’s method of philosophy-as-drama, except that Aitken was writing for an audience of two. Even then one wonders whether Edge was quite necessary; an imagined figure might have done just as well. Edge appears to have existed in the letters mainly as a means of elucidating Aitken. As he says after six pages of mathematics (beginning: ‘I have written to Young, who will be gratified by my change of ground. What convinced me was […]’):

Well, anyhow, there it is; and I am much enlightened by a new point of view.142

No doubt so was Edge, but that seems somehow beside the point.


134  Pages 631-2 in David Monk, Obituary: Professor W.L. Edge, Proceedings of the Edinburgh Mathematical Society (1998) 41, 631-641.
135  23 Jan 1998.
136  23 Jan 1998.
137  Alastair Gillespie, who took me to see Edge, told me a story on the way. Thomas More was up for canonisation in the early thirties (it was conferred in 1935) but his candidature was considered deficient in miracles. After some time Edge reported, ‘He’s getting an exemption from miracles’.
138  From A Shropshire Lad (XIV). Aitken also quoted these lines in the Memoir in relation to his breakdown of 1927: ‘Gosford Bay on a Sunday afternoon, with picnickers on every low grassy cape – “There pass the careless people,” I thought – while the knobs of the Lomonds of Fife marked the skyline across the blue Firth, looking like the ungrown horns of a mythological calf.’ (p.93)
139  ‘I have no knowledge of ACA putting in for a post at Cambridge. If it was pre-war, & it can hardly have been during the war or afterwards, I hardly think ACA, who took very ill to upheavals, would think of moving from Edinburgh, where he was by then really settled, with a particular love of the country round about; or that he would relish or even contemplate removal to flat Cambridge & a totally different life. And once talking with Mother when I was grown up about earlier days, Mother said: Everything was for you children. I thought this excessive & felt embarrassed & awkward at the time; but I know this was essentially the case. Therefore I do not think ACA would have considered taking George and me away from schools where we were settled & happy. And then there was ACA’s mental health & psychological well-being, always after the two dreadful breakdowns in my very early childhood a matter for concern. The years of George’s and my “latency” – so called by psychologists: the years between 5 & 12 or so – were probably ACA’s steadiest & most happy time.’ MM to me, 23 Jan 1998.
140  Aitken to Edge, 5 Jan 1943.
141  Aitken to Edge, 6 July 1947.
142  Aitken to Edge, 21 July 1939.
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