Regrets of a Cantab

“Cantab” = short for a mathematician from Cambridge (= a Cantabridgarian)

Here is a very long screed all the way from 1825… It looks like a work of fiction, though not written as a story as much as a reflection of a very old-sounding young mathematician (he says he’s 2I years old…) over his (brief) career as he looks back. I had a distinct sense of it being a one-player drama full of pathos, introspection, self-flagellation, regrets, and some poetic thoughts along the lines of G. H. Hardy’s essay, “A Personal Apology”, though the current story predates Hardy by more than a century. A very moving, deeply self-reflective pouring-out of the heart…

The account is written as a 30-page letter to the Editor, complete with a Post Script, reiteration and re-clarification of thoughts and personal anguish. Remarkably, the mathematician – a Senior Wrangler from Cambridge - does not focus on his own achievements, or lack thereof, but writes down a harangue against life choices themselves as related to a career, the character of mathematics, its usefulness, a lamentation about how little he has to show for all the labors over the past five years, and so on… I do hasten to add that while the letter plays on a very heavy stereotype of mathematicians, it is still a very deep thought and applicable to many areas of monomaniacal pursuits.

It seemed an odd choice to me to make the mathematician full of diatribe and resentment at so young an age. But perhaps that is also a stage of disillusionment which someone entering academia, full of dreamy thoughts, might feel after the initial foray of few years, even if the years turn out to be professionally very successful…

Perhaps the best way to convey this one-act drama of self-analysis is to show a few passages on various aspects of the mathematician’s regrets. There is far, far more in it.

A Starting Lament:

“But when my conviction tells me that I am now at length a man— that I have obtained the important age of twenty-one—that almost the last recollection of myself was as a boy of sixteen : then it is that. I ask myself, where are my five years, what have I been doing, what have I gained, what happiness have I enjoyed, in what way have I qualified myself for the duties which are now forced upon me ? I look backward, and still I look backward, and I attempt to recollect what I have been doing—how those years passed—what pleasures they brought—what ideas I have gained—what instructions secured. I try my mind in all directions— I attempt to lay hold of the past time —to measure its intervals by acquisitions of knowledge, by successions of events, by successions of feelings, of opinions, by pleasures, by changes of my views—but my attempts are vain. I find no record of time in it ; for I find no successions of events or feelings…”

On the Effects of Pursuing Mathematics:

“A single idea measures the whole of this long interval; and forever labouring in vain to expand it, the sad conviction is forever forced on me that its extremities meet, that I had fallen asleep at its commencement, and awakened at its termination. And that one idea consists in Mathematics. Mathematics! The word haunts me; I attempt to dilate it, to vary it, to specify, to analyze in what it consists —of what ideas, what parts it is composed ; to ascertain what it is that I do know, what is the knowledge that I have gained. And still the word mathematics, mathematics, recurs to me; it whirls in my head, and when I attempt to investigate what it means, a confused succession of angles, and curves, and equations, and fluxions, chases itself up and down, as it seems, in my brain, and still it cuds in the conclusion that I am n Mathematician. This is the dream of the last five years; but, even in this dream, when I attempt to trace my own progress from the first proposition in Euclid and the addition of algebraic quantities, to the very last of our Senate-house problems, to the day which saw me at the summit of honours, that day, which was the mark of my long ambition, which was to reward me for all my privations and toils, I cannot recall even the terms which called me hack to renewed exertions, far less the months and weeks which found me for ever a student over my daily and nightly task. Thus have I sat now, for months, plunged in a dark melancholy, sometimes buried in regrets, and now and then rousing myself by recollections of my reputation and honours; while, in brighter moments, I attempt to persuade myself that I have laid in a stock of useful information, that I am grounded in AII the sciences, and that I am fitted to carry on, with more brilliant success than my fellows, the profession which has fallen to my lot.”

On disillusionment with Mathematics:

“I had been told that mathematics formed the only logic; and I believed it, because every body seemed to believe it, as they believed that one book of Euclid was worth the whole of Aristotle. I fear at last that we have all been in a mistake; for I find that this is a logic which has no concern with the conduct of life, with morals, law, politics, with any thing in short of all that which forms the great mass of human action and human reasoning. I have indeed lived to find that, the logic of triangles is the logic of triangles and nothing more; that moral magnitudes cannot be measured or compared by mathematical rules, and that where nothing is definite, nothing rigidly proportional, nothing positive, and where a thousand jarring quantities are concerned in one question, it is in vain to expect aid from the rigidity of mathematical laws, or the accuracy of mathematical investigation. The human soul is assuredly not a triangle”

On loss of mathematical powers:

“And if I have, too late, unwillingly admitted this conviction, it is not, I grieve much more to confess, without finding that my mind is not the powerful engine which I had imagined while triumphing in the victories gained over those refractory problems in the differential calculus, to which I owed all my fame and fancied I was to owe my happiness and my success in the world. I feel as if all my other powers had been extinguished by the cultivation and growth of this sole one; that, like Aaron’s rod, it had swallowed up all its competitors. I cannot feel, appreciate, comprehend, what is going around me. I strive to understand what seems understood by all hut myself; to feel what others seem to feel; to infer as they infer; and to calculate on events as they calculate. But all seems a maze and a mystery; as if my mind was of a different constitution from that of mankind in general”

On Socializing:

“Wherever I go, whatever I attempt to do, my mathematics slip from beneath me ; and again I find that I am, among men and in the world, the very boy that St. John’s saw me five years ago. In society, in conversation, it matters not what society, what conversation, I must sit silent, having but just now discovered that men do not converse about equations or curves. All the world except myself, seems to abound in ideas; and I possess but one. by chance, I can partake for a moment in some diversion, I am immediately left behind, since it departs to subjects of which I know nothing, and to arguments, the force of which I cannot feel. And it often happens”

On Disconnect with other areas of scholarship:

“Every thing is new to me —all is unknown. The world of science and of morals, the whole encyclopedia of knowledge, except mathematics, is to rue as to the child just horn. If I open upon history, it is to find that I must retreat, and retreat again ; and terrified nt the magnitude as at the novelty of the undertaking, I abandon it in despair. In policy, legislation, ethics, all is darkness, for I have no principles to guide my search ; and here too I am alarmed at the obscurity, as well as at the extents of subject, of which I had never even suspected the magnitude, number, or importance, scarcely the existence. Accidentally thrown for a few months into a circle engaged in discussing matters of commerce and public economy, I retreated from it with a sense of shameful ignorance, and with the hope of mastering those subjects in private. But I labour and despair, and I see no light: I am confounded with new views, I am puzzled with reasons which seem unsatisfactory, and I am referred to facts which I know not where to seek. The whole seems a turbulent ocean where there is no rest, a chaos where I cannot yet find those principles which I am now sensible I ought long ago to have mastered, and which I cannot now exert myself to search for and establish.”

On Female Companionship:

“It is a trifle, in my present state of feelings, that female society is to me a blank, and that I am even shunned by those to whose amusement I can contribute nothing, and to whom my gravity and habits of attraction arc repulsive; but I can easily see that it will not always he a trifle, since I find myself beginning to envy the liveliness of manners of the sex, and the mutual delight or cheerfulness of those around me, where f sit meditating on some past problem, or rather, attempting to drive from my mind ideas that will ever intrude.”

Review extracted from Alice Jenkins, BSHM Bulletin, Vol 25, 2010

In 1825, a pseudonymous article appeared in the London Magazine, titled ‘Regrets of a Cantab’. The author was probably John Cowling, who had been senior wrangler in 1824, and had come first in the more advanced Smith’s Prize examination (Alex Craik disagrees, considering the article to have been ‘probably’ by Solomon Atkinson, another Senior Wrangler of the period. But a handwritten note on the first page of a copy of the article held in Cambridge University Library attributes authorship to ‘J. Cowling (St. John’s)’.)

At the time of writing the article, he was studying for the bar, and, according to ‘Regrets’, suffering severely from mental and emotional problems which he traced directly to his Cambridge mathematical training. The article painstakingly describes a lonely condition of social incapacitation, low self-esteem, disillusionment and emotional numbness. Similarities are readily apparent with Mme de Stae¨ l’s critique of mathematics as producing a failure in empathy and an aversion to problems involving uncertain data. The author’s education had inculcated ‘a habit, a permanent feeling of dissatisfaction, or doubt, respecting all truths which are not capable of strict demonstration’. This habit now runs very deep; he finds that even in post-University life, he can only think like a mathematician: and he interprets this as meaning that he has lost the ability to think like other people. Consequently, he can no longer enter into other people’s feelings. It would be fascinating to know what relationship this writer perceived between thinking and feeling, but perhaps because he experiences extreme isolation in both, his discussion jumps freely between the two almost as if they were the same thing. Miserably he attempts to mimic in his own emotions what he imagines to be the emotions of others, but fails:

“I strive to understand what seems understood by all but myself; to feel what others seem to feel; to infer as they infer; and to calculate on events as they calculate. But all seems a maze and a mystery; as if my mind was of a different constitution from that of mankind in general; as if I had not even the feelings of my species.”

The careful self-analysis offered here is both a symptom and an expression of the loneliness resulting from loss of empathy. In each of the neatly paralleled clauses of these sentences, such as ‘to infer as they infer’, the writer groups himself with others, and at the same time separates himself from them. The phrase ‘a maze and a mystery’ suggests in its alliteration and rhythm a widely-used formula, but it is almost untraceable in writing before this date, although it is used very occasionally in later texts. The phrase enacts in miniature the writer’s solitary condition, appearing to be part of a shared culture, but in fact an isolated anomaly. Above all, the writer is bitterly disillusioned by the contrast between the cultural prestige of mathematics and the real effects that his work has produced in him.

The prestige of the discipline is so great as to be almost hegemonic: ‘I had been told,’ he writes, ‘that mathematics formed the only logic, and I believed it, because every body seemed to believe it’. But on leaving the University he has found, rapidly and sickeningly, that ‘we have all been in a mistake’: mathematics has not taught him to reason effectively. It cannot do so, since it is a self-referential system based on perfect knowledge of perfect data. It is impossible to apply mathematical approaches to the messy, incomplete uncertainties of real life. As a consequence, the writer has great difficulty making ordinary decisions, afraid of doing wrong because he cannot fully predict the consequences of his actions.