In my discussions so far, I haven’t really brought up humanistic mathematics. It’s time to do that, so let me introduce it here, from a personal point of view.
When I wrote to Colleges during the spring about tentative questions I was interested in discussing, I worried that the idea of mathematics as a humanism would sound strange. I had arrived upon the idea in connection with a book-writing project with my colleague Mats Desaix, but curiously enough, during all that time the very phrase ”humanistic mathematics” never crossed our lines. It was really just a play with Sartre. But the phrase “Mathematics is a Humanism” read well and I hoped it was a little provocative.
So I wasn’t aware of the fact that the term humanistic mathematics is fairly well established in the US. It actually came as a pleasant surprise when Paul Campbell at Beloit College directed my attention to the Journal of Humanistic Mathematics. But wouldn’t it have been more strange if no-one had thought along these lines before?
Anyway, such was the extent of my ignorance just a few months ago. I didn’t even think about googling the term. Of course doing that brings up a lot a interesting links. Googling the corresponding Swedish words bring up some interesting stuff too, but not the same amount and not so diverse.
To view mathematics as part of the human culture is of course not new. I think most people with an interest in mathematics, sooner or later, come across the humanistic aspects of mathematics. So I asked myself when I first came into contact with this view of mathematics. I thought about reading Davis’ and Hersch’s The Mathematical Experience. I found this book in Camden Market in London in 1986 when I worked at Queen Mary College as a post-doc research fellow. We used to go there on Sundays as it was within convenient walking distance from Kentishtown where we lived.
The question struck me while reading a PhD dissertation Matematik och Bildning by Lars Mouwitz, a Swedish mathematics teacher and philosopher. The word ”Bildning” – which is the same word as the German ”Bildung” has no direct translation in English as far as I know. But it has the same connotations as ”Liberal Arts”. In Swedish, ”bildning” is something you could have. Perhaps the word ”wisdom” conveys part of the meaning. Could one say that whereas ”bildung” is an object, ”liberal arts” is more of a process?
It then occurred to me that my first encounter with cultural aspects of mathematics must have been in high school in the early seventies when I read all popular science books in physics and mathematics that I could find at the local library. There were many of them. It seems that the fifties must have been a golden age of popular science writing in the UK and the US, and then, in the sixties and seventies, it all became available in Swedish translations. In particular, there was the anthology Sigma in six volumes which I must have bought sometime because it is still on my bookshelf.
When I picked it out a while ago, I got hold of volume 6, and randomly it fell up on an excerpt from Oswald Spengler. My eyes fell on the sentence ”The mathematic, then, is an art.” This caught my attention and I read the full article which actually turned out to very interesting, its strange context notwithstanding. Apparently, Spengler wrote a long section on the meaning of numbers in his ”The demise of the West”. One of his quite intriguing ideas is that there are different mentalities in mathematics. He writes that the analytic geometry of Descartes (and Fermat) is conceptually different from the ancient Greek geometry. People ”saw” different things.
Sigma was published in the US in 1956 under the title ”The World of Mathematics” and it is a proof that awareness of cultural aspects of mathematics goes at least that far back. The editor, James R. Newman had been working on the project since 1944. Strangely enough, some time ago, I found the English version in an antiquarian book shop nearby. It was in good condition and almost unread, but there was a bookmark in an article by Bertrand Russel Mathematics and the metaphysicians.
More to follow!