Fordhook, Ealing
February 1834

All through the autumn and winter last year, I waited; through Brighton balls and sojourns at spa towns and cathedral concerts; smiling upon unsuitable young men with that particular gleam in their eye, and other young men, more suitable, whom I should instantly forget... and other young men still, who perhaps wanted to dance with me only so that they could relate the encounter at a later date – young men who would never in a hundred years truly wish to associate themselves with the most vulgar woman in all England... yes: through all of this, I waited for the teacher to appear. The one that I was sure would come, if only I were patient enough.

At night, I crept out onto the terrace and stared up at the stars – in the heart of London, the smog would mask them almost completely, but out in Ealing they were jewel-distinct, mapped across the heavens, twinkling with secrets – as though they contained in their constellations codes which only the brightest minds could discern. Caroline Herschel was much talked-about at gatherings – a few years ago she became the first woman to be awarded a Gold Medal by the Royal Astronomical Society – and I was longing to acquaint myself better with astronomy. Ever since my correspondence with William Frend about the stars, I’d been deeply fascinated by the heavens. But I could see that I needed more than a telescope and a casual interest to improve my understanding.

In the end, I wrote to Dr King, whom Mamma had appointed as my moral guardian. Far better Dr King than the Furies, any day, but even so it irked me that Mamma should continue to appeal to her friends to watch over me – as though I might turn into a ravening demon at a moment’s notice! I supposed the James Hopkins Affair would be brought up – not in so many words, of course; merely with the sad slanting of a knowing brow, an I-told-you-so expression – as evidence, for ever, of my potential to transgress. But there were notable benefits to a correspondence with Dr King – he might have been concerned with my morals, but the substance of our discussions was mathematical. Indeed, that was entirely the point: by focusing my mind on arithmetic, said Dr King, I would keep my more passionate, poetical tendencies at bay.

I wasn’t sure that I agreed.

‘I need a solid foundation upon which to build,’ I wrote to him. ‘My aim is to understand astronomy, but there are places where my knowledge of mathematics is weak.’

Dr King wrote back immediately, prescribing a course of Euclid. I was pleased to take up those propositions again, but even so, there was something missing.

I was still waiting.

One miserable, wet afternoon – the rain scissoring down so heavily that the view of London is nearly blotted out by it – Mrs Mary Somerville, a friend of Mamma’s who has very recently returned to England from Paris, comes to take tea with us and Mary Montgomery.

Mary Somerville is older than Mamma by perhaps a decade or so, but I can see that she was once (and still is) very pretty, with dark curls all over her head, and an unusual, even eccentric, way of dressing. There’s a bird-like delicacy to her that reminds me of Mamma, and – like my mother – she is a mathematician. She has recently published a book entitled On the Connexion of the Physical Sciences. Mamma has read it, and – after no longer than five minutes in the company of Mary Somerville – I am resolved to read it too. In her gentle Scottish accent, she talks about her work, and her self-deprecating tone cannot disguise the magnificence of her mind.

She says: ‘I have not one jot of originality or genius. Not one.I am the first to admit it. We women simply don’t possess such things.’

‘But, Mary,’ counters Mamma, ‘you were the translator of Laplace’s Mécanique Celeste! Without your contribution, no one who was unable to read French would have been able to immerse themselves in that immense set of books. It was an exceptional undertaking.’

‘Oh, there is nothing so special about the act of translation,’ says Mary Somerville.

‘I don’t agree,’ says Mary Montgomery. ‘You added to Laplace’s work your preliminary dissertation. Laplace himself said the book was unreadable – and not because it was in French. You clarified his writing; your introduction served to make the mathematics in the book more understandable to the reader. That was without doubt an act of originality.’

Mary Somerville only smiles. Is she falsely modest, I wonder, or genuinely so? She says: ‘What do you think, Ada? Are women capable of originality?’

Answering truthfully, I say: ‘I see absolutely no reason why women should not be capable of such a thing; why should a woman not think with as much originality as a man, if not more? Yes: we might not be able, for example, to lift a heavy weight, or to ride into battle. Those are physical distinctions. But there should be no such distinctions as far as the mind is concerned.’

Silence falls on our little gathering, and I am more aware than ever of the rain, and the three women in their different positions... Mary Montgomery’s smiling unspoken approval of what I have just said... Mamma’s perfectly-poised figure, on the edge of her chair, wanting me to impress the visitor, and not to say the wrong thing, even if she doesn’t know what the ‘wrong thing’ might be in this context.

And then there is Mary Somerville, whose cheeks have the bloom of a young girl. She leans forward. A little tea spills unnoticed from her cup. ‘Do you like puzzles, Ada?’ she says.

‘I love puzzles,’ I say.

‘Euclid?’

‘Yes, indeed; I might do three or four Euclidian propositions a day. I love other kinds of puzzle too.’

‘Tell me more,’ says Mary Somerville.

I pause, wanting to explain myself clearly. ‘I love anything that isn’t clear-cut,’ I say. ‘A problem you have to work at, perhaps look at in a different way in order to understand. I love anything that doesn’t seem to have an obvious answer. Take rainbows, for example. Why does a rainbow always appear in an arc of a circle? Why a circle, rather than another kind of curve? And why is it curved in the first place?’

‘Is that the sort of thing that you think about often?’

‘It’s the sort of thing that I always think about,’ I reply.

Mamma says: ‘Ada’s mind, for all its capabilities, flits from one thing to another rather too quickly, like a butterfly.’

‘Butterflies,’ says Mrs Somerville, ‘are utterly enchanting creatures.’

So now there is another Mary in my life, and I will grow just as attached to Mrs Somerville as I have long been to Miss Montgomery. I hadn’t realised that my long-anticipated teacher would be a woman, but I am so pleased that she is a woman; Miss Stamp was, after all, one of my most fondly-remembered instructors.

Mary Somerville is like no one I have ever met before. I visit her at her home at the Royal Hospital in Chelsea, where the army pensioners live and where her husband is a physician, and I stay for perhaps two nights each time. Mary has a son named Woronzow Greig, a young man of nearly thirty, from her first marriage. Theirs is a damp though prettily-furnished house; we often sit in the parlour, books and papers spread about us, and talk for hours, sometimes only stopping when Dr Somerville comes home, whistling under his breath as he enters the house.

The first few sessions are shy ones, in which we – teacher and student – get to know one another. I tell Mary a little about the regime of my early studies – the governesses who came and went with clockwork regularity; the tickets and punishments; the subjects I studied; the things I enjoyed, and the things I didn’t.

‘Mamma hopes – has always hoped – to... trammel my mind somewhat,’ I say carefully.

‘What does that mean, Ada?’

‘It means that she thinks I lack rigour and organisation,’ I say. I am not trying to complain about Mamma (well, perhaps I am complaining very slightly); I do, however, want to give Mary a clear picture of how Mamma feels about my abilities. ‘She thinks my interests are too many, and too varied. That I am too passionate. I can’t help it, though; truly, I can’t.’

Mary says nothing, encouraging me to continue.

I go on, emboldened and warming to my theory: ‘It is because we are not so very alike, Mamma and I. I was learning some Latin verbs a few months ago, and I realised the fundamental difference between me and Mamma. The right verb for Mamma is cogitare – “to think”. If I had to choose only one, I mean.’

‘And for you?’ says Mrs Somerville.

‘Sentire,’ I reply without hesitation. ‘ “To feel”.’

‘I see,’ says Mary Somerville, and I think that perhaps she does.

She tells me about her life, different to mine in many ways – her early love of nature and the outdoors, and watching things grow; her study of Latin and Greek and mathematics; the uncle that took an interest in her education. I have met the Queen, but I do not think that I have ever known a more impressive person than this woman. Astronomy, chemistry, geography, trigonometry... is there nothing to which she cannot turn her hand? She has published books; her translation of Laplace – known in English as The Mechanism of the Heavens – made her rightly famous. I have begun reading On the Connexion of the Physical Sciences and find myself bewitched by both its breadth and depth: there is more information contained within its covers than I could absorb in a lifetime. Lunar theory; light and sound; tides, crystals, volcanoes and electricity...

I am reminded of the way that Miss Stamp, with her enthusiasm and detailed knowledge, would talk to me about the world, for the book speaks to me in the warm, engaging tones of a born educator. More than anything else, I like the way in which Mrs Somerville seeks to trace the links between physical and scientific phenomena. It is as though I have discovered another kind of governess – one whose knowledge is unsurpassed. But in spite of all this, Mary Somerville is – as she showed when she first came to tea with us – as modest as she is accomplished.

‘You must understand, Ada,’ she says, ‘that whatever my achievements are – if we can call them that – they rely wholly on the achievements of others.’

She talks to me about William and Caroline Herschel, who discovered so much about the stars; about Michael Faraday, about Joseph Banks, botanist and explorer, and Humphry Davy, inventor of the safety lamp. I ask if she believes that we are living in a Mechanical Age.

‘I’ve heard it called that, certainly,’ says Mrs Somerville. ‘And certainly, we are seeing changes the likes of which we have never seen before in this country. Why, every factory in Britain – more or less – now possesses a rotary steam engine. Industries are undergoing vast transformations; new discoveries are made every day. But it’s more than mechanical, in my view. It’s an age of—’

‘Ideas,’ I say.

She looks at me delightedly. ‘Yes, Ada. Yes. Ideas.’

‘Mrs Somerville,’ I say. ‘Do you know Mr Babbage?’

‘Why, Ada, certainly I do.’