A tribute to outstanding thinkers. From another.

“In Our Time” is back on air on BBC Radio 4, after the summer break. I particularly enjoyed the fact that the season opened with a programme on Leonhard Euler, probably the most prolific scientist and mathematician who has ever lived. 

Leonhard Euler: prolific mathematician

He just couldn’t stop himself working and publishing on any subject that caught his interest, so ended up contributing in a huge number of areas: on the flow of fluids, on the capability of columns to support weight, on pure number theory (he’s the only man to have two numbers named after him), on mathematical methods for physics and much more.

I came to know a little about Euler a third of a century ago, in my misspent youth, part of which I devoted to studying an obscure eighteenth-century French scientist, Maupertuis, made only infinitesimally less obscure by my efforts. It was thanks to Maupertuis that I came to know what has become a favourite city of mine, Basel in Switzerland, and it was thanks to a visit there that I find myself over thirty years on the husband of a Frenchwoman and the father of three Frenchmen (well, they’re Brits too, but that doesn’t make as good a cadence).

Maupertuis went to Basel because, though it’s a relatively small city, it had an extraordinary flowering of scientific brilliance in the eighteenth century. Euler was its most prestigious expression, but it was perhaps even more striking that three generations of a single family, the Bernoullis, produced eight major scientists and mathematicians. Maupertuis travelled to Basel to study with one of them, Johann, and to live with another, also and confusingly called Johann (the son of the former and, though they presumably didn’t realise it at the time, also the man in whose house Maupertuis would eventually die some thirty years later).

The Bernoulli family: eight major scientists in three generations

It was one of the Bernoullis who sprang to mind when I heard Melvyn Bragg and his guests talking about Euler on “In Our Time” the other day. Daniel Bernoulli was one of the more important mathematicians from his family, not quite the equal of Euler but a close collaborator of his for a great many years, in St Petersburg and the Russian Imperial Academy of Sciences. 

In later life, Bernoulli said that there were two incidents in his career of which he would be proud until his dying day.

Daniel Bernoulli: two incidents game him particular pride

The first was a dinner during which Euler posed a mathematical problem that had defeated him and on which he’d been working for several days. It gave Bernoulli enormous satisfaction to have solved it before they left the table.

The second didn’t concern Euler directly. Bernoulli tells that he was once on a long journey by coach and fell into conversation with a fellow passenger. Eventually they came to introduce themselves to each other.

“I’m Daniel Bernoulli,” said Daniel Bernoulli.

“Oh, sure,” replied his companion, “in that case I’m Isaac Newton.”

I like both stories, not just because of their wit, but principally because they are both at first sight boasts but, when looked at more carefully, they turn out to be tributes to other greater thinkers.

Euler and Newton: who could deserve such tributes more?

The best of friends

Being made redundant is, I’ll admit, a pretty depressing experience (particularly when it happens for the third time – why, I may soon have to start wondering whether I’ve been doing something wrong in my career, a thought that had never previously occurred to me). However, there are benefits too.

First of all, there’s the time for reflection offered by what I hope will turn out to be a brief period of unemployment. Then there’s the redundancy itself which can be quite a learning experience.

In my case this has led to my giving some thought to the nature of friendship.

My reflections were helped by listening to a discussion on the theme in an old episode of In Our Time. The participants started their review way back in classical antiquity.

Now I should say that I don’t always go along with the unquestioning admiration of all things Greek. For instance, Plato’s Lysis which I learned is devoted to the subject of friendship, rules out the attraction of opposites as a possible basis. This is because it would imply the good being attracted to the bad. This strikes me as a painfully formalistic and limited view of good: two people of opposite temperament can still both be good – there are many ways to be good. My way of being good may be the best way, but I’m tolerant and broad-minded enough to admit that yours may not be entirely without merit.

What really interested me was when they got onto the subject of Aristotle. He, it seems, distinguished three categories of friendship on the basis of utility, enjoyment or excellence. The problem with the first two is that as soon as the utility or enjoyment ends, so does the friendship – only the third endures.

Now this I can go along with. Utility friendship is clearly the kind of thing that exists in general between colleagues. At the lowest end of the scale, it’s forced – you oblige yourself to get on with people you’d probably go out of your way to avoid, left to your own devices. I confess I’m not good at that kind of artificial friendliness as people read my real feelings much too easily. I like to think that I have no patience with fools, but lots of people link to think that: after all, it’s a neatly disguised boast wrapped in contempt for others. Clearly, I think numerous people around me are fools, while thinking that I’m not a fool myself. Ironically, I’m probably at my most foolish when I get impatient with others who disagree me with me (and class themselves by that token with the fools).

Then there are the colleagues with whom one can have a real friendship. These are people one admires or who do outstanding work or with whom it’s just fun to work. Sadly, however, once we part company there’s little basis for the friendship to continue. It’s a pity, but I suspect before long all I’ll have of these utility friends is some pleasant memories and a sense of pride over some of our of things we achieved together.

This is the same as what happens with friends of enjoyment. Drinking friends or friends with whom one plays football are great until one realises that hangovers really aren’t much fun and running up and down the same pitch several dozen times is no way to spend an hour or two. When you go off to do something a bit more rational – which means more or less anything – you tend to lose touch with the old friends, some of them getting very old, who are still trying to cling on to the image of their youth and its pastimes.

Then there are the friends of excellence. These are the ones to whom you’re bound by an affection that’s mutual and unconditional: they’re your friends not because they’re cleverer or more skilful or more amusing than others but because they are who they are. No-one summarised that better than Michel de Montaigne, the sixteenth-century French writer. After his friend the poet Etienne de la Boétie died, he wrote if people pressed him to say why he loved la Boétie, he could find no better of way of replying than to say ‘because he was Etienne de la Boétie and I was Michel de Montaigne’.

Now that’s the kind of friendship that’s worth having. And I’m glad that I leave my former company with a few friendships of that strength and they won’t be broken by a mere inconvenience like redundancy.