Posted by ** No maths professors were harmed in the making of this blogpost. **
On a sunny Saturday in September last year (2023), I went with my teenage daughters and husband to a public lecture at the Mathematical Institute, Oxford University, given by Andrew Wiles in the Andrew Wiles Building.
For the first two years of our marriage, my husband and I lived in Summertown, Oxford, not far from J.R.R Tolkien’s house and round the corner from Iris Murdoch’s. But after we moved to London, what with one thing and another, we’d rarely been back so, it was nice to have a reason to wander down memory lane, attend a lecture and have some drinkies afterwards.
The lecture was part of a weekend celebration to mark the 10-year anniversary of the Andrew Wiles building. Sadly, as is often the case with these academically organised events, not many people had signed up for it, so as organisers often do, they did a last minute call on many mailing lists which is how we came to be there.
Guess Who?
Our youngest daughter who really enjoys maths and was curious about the man who is famous for solving Fermat’s last theorem, kept saying: I wonder what he looks like.
At that point we were sitting outside The Royal Oak on the Woodstock Road opposite the Andrew Wiles Building. I said that he was knocking on 70 now and he was a white man probably with white hair. We began observing everyone around us only to see that there were an extraordinary large percentage of passers-by who fit that description:
That might be him now on his bike peddling up to the town centre to get himself a sandwich.
Is that him there at the bus stop nipping home to get his lecture notes?
That could be him just going into the building after having a quick pint.
And, so began our very own Where’s Wiley?
We got to the building after admiring the Penrose tiling out the front, named after physicist Roger Penrose who, whilst investigating black holes, discovered that a set of two tiles could be arranged in a non-repeating pattern which you still can’t buy down at Homebase, though I think they would be a best seller.
Then, we queued up outside the lecture theatre amongst sets of two types of white men with white hair arranged in a non-repeating pattern. However, we still couldn’t decide which one was Wiley, as there were so many to choose from.
Once seated inside the lecture theatre, another white man with a bald white head got up, and we gasped in surprise – a third variation. This one was Sam Howison who explained how, as head of the department 12-years earlier, he had burnt said bald head in the sunshine the day he went to watch them dig the foundations of what would become the Andrew Wiles Building. He also told us that the Penrose tiles were first lain incorrectly and Roger had to come round himself and reorganise them. I guess he must be a dab-hand at tiling by now and I was wondering if I could hire him for our bathroom, as there’s a bit of a black hole behind the toilet.
I recognised Sam from my hubby’s PhD committee. However, neither one of them seemed to remember that, nor did they recognise each other after the talk. I put this down to being archetypal white male middle-class English mathematicians who blend into the background and go through life trying not to be noticed. This could have been why we couldn’t find Wiley.
Deciphering Langlands: Unified theory v Piers Plowman
Finally, Andrew Wiles got up to give his talk in front of the sea of bald and frondy white heads and we agreed that we never would have spotted him as he had been at the front the whole time and was so very translucent white as to be almost invisible. I guess this is from a combination of blending in and also, according to Simon Singh’s Fermat’s Last Theorem, sitting in his attic for seven years working away until he cracked it.
I thought that his talk would be about how he cracked it but alas, it was not. Andrew Wiles would definitely fail GCSE mathematics and all those presentation classes which are on the KS4 curriculum nowadays as his talk didn’t have: a beginning, a middle or, an ending and, it definitely did not show his working out, something which infuriated my mathmo girl.
Instead Wiles talked about the Langlands program, an idea by Robert Langlands in the 70s to unify mathematics as a field. Wiles jumped about in time through a potted history of related mathematics from Babylonia to the 1970s that led to Langland being able to come up with this idea. Something our Wiley didn’t say, but said when he received the Abel Prize for Maths in 2016, is that he believes that by proving Fermat’s Last Theorem he pushes number theory towards Langlands’s idea of a unified field of mathematics. I assume this is why he decided to choose this as the topic for this lecture.
Disappointingly, the Langlands program was nothing to do with the Middle English allegorical narrative poem Piers Plowman by William Langland. Though our man Wiley did mention Italian mathematician Nicolo Tartaglia’s poem about cubic curves, the generalised form of cubic equations. Apparently, they didn’t have geometric notation back then, so proofs were often written as poetry.
This got me wondering, if I had been taught mathematics with all the intrigue and poetry that went on between mathematicians like Tartaglia and his arch-nemesis Cardono, would I have enjoyed it more?
AI before drinkies
We clapped very loudly at the end as we thought that then we would be allowed to go upstairs for drinkies. Huzzah! However, there then followed a panel of mathematicians from the Department who presented their latest work with the theme that everyone was going to use machine learning and ‘AI’. I’ve put that in quotation marks as when someone just says AI I lose patience, especially when I can’t get to the drinkies. What AI in particular are you using and how? Let’s keep it simple, there’s no need to mystify AI.
And, this put me in mind of me years ago when the then head of the department, Hilary Ockendon, invited me to give a series of lectures on human-computer interaction (HCI). She had received some EPSRC funding for the Maths Institute to get more with it in terms of technology and since she knew of me: Could I help get everyone up to speed?
Her husband, another baldy white haired white man who worked in the same department, made a point of telling me that he considered HCI to be the null set though it was well known that he never used a computer. Like many male professors of his age at that time, he got his wife/secretary to print out his emails so that he could read them and dictate answers back. Though that didn’t stop him that day sneerily dissing HCI whilst standing in front of a picture of himself on his door, all baldy and white haired, pointing a gun. I remember wondering if he found that as exciting as his research project at that time – how to get more air into the ice-cream of a Mr Whippy.
Years later, the Maths Institute is still getting more with it and working on the trajectory of the squirting cucumber, whilst I regretfully observed the continuity.
Getting chattyGPT with it (aka the boring section about AI)
A couple of people on the panel said that with the help of machine learning they will discover the meaning of mathematics. This seems to be a trend amongst mathematicians to find the underlying patterns, including Stephen Wolfram, who claimed that if we feed a large language model (LLM), such as ChatGPT, with enough data then the LLM will be able to explain how language works. And, this in turn, reminds me of how discovering the underlying organising principle of how the universe works was the desire of many mathematicians for centuries, just think of Gottfried Liebniz and Charles Babbage both subscribing to the belief of Uniformitarianism, spending their time looking for the metaphysical principles which they believed underpinned the universe. I don’t believe that mathematicians crowding around an LLM like it is the Oracle of Delphi will find a unifying theory nor the mysteries of life. They are more likely to find it staring at cucumbers, William Blake-style: To see a World in a Grain of Sand, or by holding a cucumber in the palm of my hand. And, whilst they are embracing these technologies, I can only advise them to fully embrace HCI so that they can understand what the AI is actually doing.
Instead, I believe another Oxbridge mathematics prof Ursula Martin who said that when mathematicians use technology to work together, mathematics becomes a social machine. And, that is when the results happen. Reading between the lines, it would seems that Wiles holds this view too. When concluding his lecture, he said that there are problems to work on for another 100 years before Langland’s idea could be realised. I presume he meant introverted mathmos uniting alone, together in their separate attics.
Back to it: Where’s Wiley?
Finally the talk ended and we made our way upstairs to yet another queue and that is where ta daa…. we found Wiley, patiently waiting for a vol-au-vent in a line of other white-haired wonders. We quietly said hello and our mathmo daughter got his autograph. The others were not so shy and kept coming over for a closer look and saying things. I don’t think they had seen teenage girls before in the maths department and even me being female, friendly and northern wasn’t enough to see them off. My favourite white-haired fella was the C++ guy whom we remembered from him organising the ACCU conferences.
I did find Wiley again later on when I was looking for somewhere to powder my nose as the drinks party was still in full swing but we had a train to catch. The toilets were hard to find in a building in which the walls and doors are very light grey – perfect for mathematicians – and I spotted our man Wiley standing outside his office just before he activated blend mode and disappeared. I didn’t ask him for directions even though I could still see his outline and instead did another lap of that floor on my new search.
I wondered how wild it must be to be Andrew Wiles who gets up each day to go to go work in an office with Andrew Wiles written on the door (no silly picture, thankfully) in the Andrew Wiles building. It is the mathematicians’ equivalent of the Matryoshka doll. I made a mental note of where his office is (and the toilets) to constrain my search space in case I ever find myself again in Oxford playing: Where’s Wiley.
My top tip: Check for outlines against the walls to be a Where’s Wiley winner!
