Mathematics trek: the next generation

I had an experience yesterday that helped me to anchor my own purpose better

As I stormed down the street towards the college entrance I said to myself “I am not f*****g doing this ever again, I f*****g hate this, it’s a total f*****g nightmare!”. This is the story of how I relented and repented, and realised it wasn’t about me after all, and I undoubtedly will be back.

I spent 6 hours yesterday driving down from my home in County Durham to Oxford, with a long diversion via Yorkshire villages due to the A1(M) motorway being closed for unknown reasons. The roads were busy all the way, so it took a lot of concentration to stay safe among the speeding goods vehicles. I knew I would make it there in time despite the journey being considerably longer than anticipated, but it was tiresome knowing I had an intense social engagement to follow from my extended imprisonment behind the wheel. I mused on the sunk cost fallacy, and how I had committed myself to an alumni dinner at my college, and the “insanity” of the effort involved for a single meal.

The central Oxford public car park had me driving around in futile loops, being almost completely full, luring me towards EV parking I couldn’t use, past disabled spaces I couldn’t use, and bypassing those mother and child spaces that I couldn’t use. There are red/greed LED lights above each space, with sensors detecting where there might be free parking spots; several were faulty, giving me false hope that the luminous glow denoted the end of my journey. I eventually located an available space tight against a wall, and leapt into the back of my borrowed van to get changed into my penguin suit while unseen.

Then I realised there was a problem — I seemed locked in.

The rear door wasn’t completely shut, but the catch prevented me opening the back doors. Bystanders had stopped as they could see and hear the struggle; I eventually located the interior handle that is confusingly beside the hinge, not near the lock. Rather embarrassed, I popped out in my formal suit and explained to them how I had gotten in to change my clothes and accidentally shut myself in. On top of being tired from driving, and getting late to arrive, it was a stress too many. I have put on weight, too — my formal trousers barely fitted me, and as always it’s a moral struggle to put on any tie, as my soul rejects the strangulation device.

I didn’t study mathematics or take to computers due to a love of rowdy social occasions. So the din of people milling for drinks before dinner had me waiting aloofly. It was like an echo of the past when the confident and popular students were busy doing their thing together, and I was a bit of an outsider hanging out in the computer room with a few other misfits until 5am. Why would I want to misdirect my energies into a dull old mathematics degree at age 18 when there was the early Internet to play with instead! Anyhow, it was just about time for my mood to bottom out, and for something of surprising value to happen.

Three college fellows did brief introductions for their subjects — mathematics, physics, and computer science. The last of these made a remark that really caught my attention, that there is a traditional realm of formal logic, and a new focus on data science. The former is rigour personified, whereas the latter is probabilistic. While the manipulation of those data sets can be (and is) hard science, the data points typically come from the noisy world around us. There is a jarring clash of cultures with the search for ultimately beauty and truth in nature as found in philosophy, for instance.

The academy ought be a place where we “think purely about pure thinking”; it’s not an outsourced R&D unit delivering artificial intelligence agents for industrial and military users. These talks set up an encounter that has prompted me to write about the evening. Opposite me at dinner was a brilliant young computer scientist, half my age, whose identity is private as such conversations ought to be. By the end of the evening, I had realised there was a genuine purpose for me having endured the troublesome trip down. I had fresh insight into my own role and what I wanted to achieve.

Being old enough to be my interlocutor’s father really brought home to me that there is a turnover of generations; some of the oldest present were the same age as my own parents. As it happens, he is from a noteworthy family, which also brings the generational transition into focus. His study is into “category theory”, which for the layman could be described as a “mathematical meta-theory of mathematical theories”. That’s about as hardcore purist as you can get, and ideologically contrary to munging around large data sets in the hope that some pattern emerges. He is also an amateur painter, and the resonance with my own rebalancing of the intellectual and intuitive was felt.

He described how he studies the “equals sign” (actually isomorphism with the ≅ symbol), and “not all equalities are equal” — there is a hidden deeper structure that intuition alone fails to reveal. I learned from him that the only way of making progress in some areas of deeper inquiry is to become a refugee and hide out in other departments — anything that’s too challenging to the orthodoxy isn’t welcomed. There are areas of mathematics where people rely on the “feeling of knowing” over actual proofs, or “social proofs” of who does or doesn’t believe what. He was able to deeply reflect upon where his own beliefs came from; a humble scholar being the most impressive kind, as they can unlearn, too.

I was able to share some of my experience and learning, from telecoms and as a public prognosticator, who has been persecuted for heresy. My work in packet networking was also about the “too trivial to think about” — computing the “identity function” — and the hidden structure inside of that. By coincidence, my former tutorial partner (sat beside me last night) has his own story of seeking unappreciated essential simplicity in economics. He too has faced down hardship in his professional life for refusing to compromise his principles. That you might have to endure losses in the material world in order to preserve your integrity was a message the young man could hear.

There is a lot of detail from what we went into that doesn’t belong here. The point of me writing is that there are limited venues where you can sit down for a meal, say “homotopy type theory” out loud, and not be looked at in a strange way by your companions. The perspective we older alumni could bring to the younger one was how we had struggled with the social and relational aspects of the search for truth. The greatest laughter was for the statement that it is “almost as if academia isn’t wholly committed to the search for fundamental truth”, being the understated British way of denouncing its pursuit of money, status, and privilege.

In my heart I know the historic significance of my own work, even if the world at large has yet to catch up. Last night was a chance to begin a new chapter in my relationship to the learned institution, focused on how I might assist those who follow behind. My fuming frustration at the journey mellowed as I realised it wasn’t about me at all; the purpose of me being there was to pass on what we have learned to help others. If I were a philanthropist I would have endowed this young man with “f*** you” money so he would never be swayed by the threat of loss of his tenure track or pension rights. Sadly I am not, and by an uncountably infinite margin!

I gave my old university friend a lift home after, and tried using my phone with Apple Carplay for navigation. There were two independent automated voices talking over each other, and the display had nothing to do with the route, and the satnav was determined to send us to Birmingham rather than Reading. Perhaps someday these computers will advance to the point where they do something useful and aren’t just curiosities! I did wonder if we have lost some essential human quality due to technology — like how email has displaced pigeon holes at Oxford colleges. I was the last generation raised before the Internet; this new college fellow was the first who knew nothing else. An analogue culture is dying out.

If all I did yesterday was utter the words “spiritual” and “divinity” to an upcoming computer science genius, with the heart to hear why they matter, then it was a raging success. I believe he sensed that I was offering him a shortcut to wisdom that could save him a lot of problems. He faces a world that is often more cruel and confusing that we have been led to believe. I am acutely aware that being intellectually gifted can paradoxically be exceptionally lonely and painful, with few role models you can turn to. These are real people with their own turmoils, disappointments, and struggles. I have suffered quite considerably at times, and wish there had been someone kind to mentor me.

As I sign off, I am sat in my childhood bedroom at my parents’ house near London, back in my “native” hoodie. I sense that the world is about to change in profound ways, and I have appointments and duties elsewhere, so I have to go. It is a melancholy moment as I head back out of the door and drive north again, almost tearful. I love my mother and father: it is a joy to see them and be at peace after the turmoil of the last few years. There was a contrite moment last year when it was announced that “I and your father sometimes discuss how Martin was right” — that settled it all.

They know I didn’t kick up such a huge fuss for no good reason. We are all just men and women having experiences all the time, some of which are pleasant, others are rough. My university continues to provide learning opportunities, but of a different nature to when an undergraduate. This event was preparing me to be able to support the institution and its present inhabitants as storms envelop the academic world. My parents gave me the solid values that have led me to have to stand in a very lonely place at the front line of a covert information war.

Now the hurt of my own can be transmuted into healing for all. The academics are groping around in the back of their dimly-lit “intellectual vans”, and will soon be trying to find their way around in the context of Covid war crimes trials, a financial restart, and collapsed trust in authority. A little bit of awareness of where the door handles are can save you a lot of aggro! Each setback we endure typically has a purpose that we only discover later, as it has prepared us for a higher calling. To be of service to the next generation is the destiny of my “mathematics trek”.

The campus of Durham University on the River Tees