Babbage pinned very high hopes upon the Turin conference. Writing to an Italian colleague, he explained why.
The discovery of the Analytical Engine is so much in advance of my own country, and I fear even of the age, that it is very important for its success that it should not rest upon my unsupported testimony. I therefore selected the meeting at Turin as the time of its publication, partly from the celebrity of its academy, and partly from my high estimate of Plana.
Babbage’s reasonable supposition was that his official host, Count di Plana, would write up a full and positive report before submitting his personal appreciation of the Analytical Engine to Britain’s Royal Society. Armed with this impartial endorsement, the inventor stood a far better chance of gaining the support from the British government that he required. Unfortunately, di Plana himself had grown too old and infirm for the demanding task of describing such a complex – and still unbuilt – machine. In 1841, encouraged by Mary Somerville and in the hope of further developments, Babbage again travelled out to Italy – this time for a conference at Florence. His reception was as enthusiastic as before but, apart from the pleasure of seeing the Somervilles, his hopes were once more crushed. Di Plana had done nothing.
By the summer of 1842, almost two years after the Turin conference, no report had yet been published upon Babbage’s wondrous invention.
In the autumn of 1840, as Babbage set off for Italy with such high hopes, his future interpreter embarked upon the most significant phase of her mathematical education. Following the recommendation of Babbage (and bowing to the unyielding persistence of Lady Lovelace herself), Augustus De Morgan had taken over the role of mathematics coach to a strong-willed young woman whose intelligence and determination still greatly outstripped her mathematical skills.
The challenge of tutoring Ada was considerable. Aged just under twenty-four, and still equipped with only a modest understanding of either algebra or trigonometry, Lady Lovelace wanted to launch straight into differential calculus. Mrs Somerville’s counsel about cautious progress was forgotten in Ada’s habitual impatience to rush ahead. ‘Festina lente,’ De Morgan reproved her on 15 September 1840: ‘ . . . it is no use trying to catch the horizon.’ A few days later, he was again obliged to rein back his ambitious pupil. Lady Lovelace might wish to bestride Parnassus, but the problems of calculus must wait until attention had been paid to the more basic skills which, as De Morgan bluntly stated, ‘you have left behind’.
It was not immediately pleasing to an impetuous young woman to be compelled to follow the sage advice that she herself, aping Mrs Somerville, had once been keen to dish out to Mary Gosford’s little daughter. ‘I work on very slowly,’ Ada sighed to her mother on 21 November 1840. ‘This Mr De Morgan does not wish otherwise.’ A month later, however, she was beginning to get the point. ‘I have materially altered my mind on this subject,’ she confessed to her tutor. ‘I often gain more from the discovery of a mistake of this sort [a simple oversight caused by hasty reading] than from 10 acquisitions made at once without any kind of difficulty . . .’ Ada’s impulse to swagger about her own cleverness remained strong, but how could De Morgan not be disarmed by the frankness with which his pupil expressed her gratitude? (‘I can only end by repeating what I have often said before,’ she wrote: ‘that I am very troublesome, & only wish I could do you any such service as you are doing me.’)
Ada was lucky. Thanks to Babbage and possibly to Mrs Somerville (still advising from afar), she had acquired her ideal teacher. Only ten years older than his pupil, De Morgan himself had been just fourteen when his gift for mathematics was first noticed. Educated at Trinity at the same time as Woronzow Greig and William King, he was soon moving at the same intellectual level as their brilliant tutors. One, William Whewell, became a lifelong friend. Another, George Peacock (who had helped his own fellow student, Charles Babbage, to found the Cambridge Analytical Society back in 1815), had written the study of differential and integral calculus from which Ada would first begin to learn about algebra. In 1828, De Morgan – still aged only twenty-two – became the new University of London’s first professor of mathematics. He taught there – with one gap of five years (due to a personal dispute) – for the next thirty years. Unremittingly industrious, he filled his spare time (when not composing his own celebrated study of differential calculus) with writing over 700 articles on mathematics for the general reader.
De Morgan’s readiness to help Ada was based in part upon a close family connection. His wife, Sophia Frend, was the daughter of Lady Byron’s own first tutor. In 1838, while Annabella visited Germany with the newly-wed Noels, the De Morgans were allowed to honeymoon for free at Fordhook for ten happy weeks. Early in 1841, they moved into the book-crammed house where Sophia’s late father had lived in Gower Street, near the British Museum. Here, more often than not, Ada went to a quick informal supper that was followed by a session of coaching by De Morgan. When his pupil
