Lady Lovelace had adored and revered Mary Somerville, but De Morgan’s mischievous wit lent an unexpected bonus to her lessons. ‘I don’t quite hear you, but I beg to differ entirely with you,’ was one of De Morgan’s celebrated dry asides; another was that ‘it is easier to square the circle than to get round a mathematician’.
He meant it. Sophia, writing a tribute to her brilliant husband in the 1880s, described how little sympathy De Morgan had for Ada’s impulse to race towards any new goal, as soon as it was first glimpsed. ‘Show me,’ he would command wherever an error had occurred. Caution was De Morgan’s creed: no progress was permitted until he was shown the exact progress of thought from which the fault had risen, in order that all confusion could be resolved.
The correspondence between pupil and tutor, at its most intense during the period 1840–1, offers evidence of Ada’s potential to become a remarkable mathematician. What it also reveals is how – carefully coached towards this end by Mrs Somerville and held to that same course by De Morgan – Ada became willing to persist with a single point until her mastery of it was certain. What De Morgan evidently admired in her was the energy and perseverance with which, even during periods of the grave sickness that had periodically begun to afflict her, his sweet-natured pupil bound herself to the task of her own mathematical improvement. Anything that she did not understand was instantly acknowledged. Writing to Mrs Somerville about her new telescope back in 1836, Ada had shown no qualms about admitting her absolute ignorance of how to use the instrument. So it was now when, writing to De Morgan on 13 September 1840, she freely admitted that she had no idea what was meant by an equation to a curve. Cock-a-hoop two months later when she thought she had spotted errors in George Peacock’s text-book on algebra, she readily accepted (10 November) that Peacock’s mistakes were in fact those arising from her own beginner’s mind, one ‘which long experience & practices are requisite to do away with’. Always eager to plunge into the mysteries of differential calculus, Lady Lovelace was beginning, nevertheless, to grasp (writing in this same letter) ‘the importance of not being in a hurry’.
Ada’s lessons with De Morgan took place approximately every fortnight. Frustratingly, no account survives of what was said during these sessions. Did Ada ever actually hear her teacher pronounce his well-known maxim, ‘The moving force of mathematical invention is not reasoning but imagination’? Or had Ada’s own faith in the power of imagination inspired De Morgan’s pronouncement? The connection is intriguing because, on 5 January 1841, during the time that Ada was closest to De Morgan, she wrote an essay about the potentially fruitful collaboration between the scientific faculties and the inventive aspects of the mind.
Imagination is the Discovering faculty, pre-eminently. It is that which penetrates into the unseen worlds around us, the world of Science. It is that which feels & discovers what is, the real which we see not . . .
Mathematical Science shows what is. It is the language of unseen relations between things. But to use & apply that language we must be able fully to appreciate, to feel, to seize, the unseen, the unconscious. Imagination too shows what is, the is that is beyond the senses. Hence she is or should be especially cultivated by the truly Scientific, – those who wish to enter into the worlds around us.
Writing the essay in which this intriguing passage appears, Ada laid particular emphasis upon what she described as ‘the Combining Faculty’: an ability to seize upon points in common, ‘between subjects having no very apparent connexion, & hence seldom or never brought into juxtaposition’. That analogical capacity was precisely the quick-witted, insightful approach that would glow out of the one piece of work for which Ada would later become famous.
It’s apparent that De Morgan respected what he recognised, more than any of his contemporaries, to be an extraordinary mind. Writing a long letter to Lady Byron in 1844 about the way it might develop, the logician expressed no doubt about what Ada had the potential to achieve. The worry – one upon which Annabella now sought his opinion – was the danger presented to a delicate constitution by an excess of mental strain. Caution was required. Nevertheless:
I feel bound to tell you that the power that Lady L[ovelace]’s thinking has always shewn, from the beginning of my correspondence with her, has been so utterly out of the common way for any beginner, man, or woman, that this power must be duly considered by her friends, with reference to the question whether they should urge or check her obvious determination to try not only to reach, but to get beyond the present bounds of knowledge.
If you or Lord L[ovelace] think it is a fancy for that particular kind of knowledge which, though unusual in its object, may compare in intensity with the usual interests of a young lady, you do not know the whole . . . Mrs Somerville’s mind never led her into any other than the details of mathematical work. Lady Lovelace will take quite a different route.
De Morgan liked Lady Byron, regarding her (according to his wife’s memoir), as ‘impulsive and affectionate almost to a fault’. But his was not a letter that set out to flatter or please. He was simply stating what seemed to him to be the obvious fact. Ada Lovelace was a one-off, like no other, neither in her ambitions nor her abilities. She might go beyond them all. The question – one
