I have been meaning to write something in response to two recent blog posts on history of mathematics and anecdote. Dennis Des Chene (aka "Scaliger") wrote "On bad anecdotes and good fun" and Peter Rowlett responded with "Mathematics: a culture of historical inaccuracy". I'm also grateful to Thony Christie of the always excellent The Renaissance Mathematicus blog, whose Twitter comment brought Scaliger's blog to my attention.
Scaliger writes about the anecdote that Euler spouted a piece of mathematical nonsense claiming to prove the existence of God, embarrassing Diderot in front of the Empress. The anecdote, as commonly told, is far from true, so why do mathematicians still tell without qualification? Rowlett wonders about the role of such anecdotes, which are arguably part of the culture of mathematics, in training mathematicians.
These are deep issues. I love anecdotes. I like serious history, too, but I am useless as a historian because I don't know enough. Whenever I have worked on historical topics, I have found that, the more I research, the less I feel able to say anything because I am increasingly aware that I do not know enough of the story. I admire both historians, who as a result of years of study are able to enlarge our understanding, and popular writers, who can so often find interesting angles on history without being intimidated as I am by the knowledge of their limitations.
Anecdotes appeal to me when they seem to tell me something, and I don;t think this is always entirely illusory. It doesn't take much thought to see that most anecdotes are constructions. As a teenager I bought a book of literary anecdotes which began with the rather rude "Switter Swatter" story about Sir Walter Ralegh (which is the subject of a contemporary round you can watch being performed here.). Is this anecdote true? It's documented at the time, but how did it get into the public domain? Only, presumably, from Sir Walter himself, and I don't take as gospel any stories by young men about their romantic successes. So despite its impeccable historical credentials I have some scepticism about this story. Most anecdotes are spread because they show someone in a good (perhaps self-depreciating) light (or because they present a negative image of someone's enemy.
Constructions may not be accurate. In his cricket report in last Saturday's Guardian, Vic Marks tells the story of the Durham wicket-keeper Chris Scott, who in 1994 dropped Brian Lara, the best batsman in the world, when he had made 18. Scott (Marks, being a good journalist, adds "it is said"!) moaned "I bet he goes on to get a hundred". Lara in fact went on to 501 not out, the highest score ever made. It's quite likely that Scott made exactly this comment at the time, and I'm not suggesting that this story is not exactly true as it stands. But even if he didn't say it at the time, he might afterwards have said something like "When I dropped him I thought that it would be just my luck if he made another hundred", and in the telling the story at some stage changed to "Scott said at the time that ...". The way memory works seems to be that we reconstruct our memories rather than retrieving them, and anecdotal memories get rewritten so that we come to "remember" what happened in the revised form. Consequently one should interpret even the most "authentic" anecdotes as a slightly idealised form of history.
What I would argue, I guess, is that anecdotes are valuable in passing on the culture of mathematics. We don;t need to express uncertainty about their "truth" because we should all know that anecdotes are not exactly true. When I first read the Euler story as a teenager I may have believed it to be literally true,.but as I became more experienced in such matters I realised that a more nuanced understanding was required. It's good that the background is now readily accessible, but we want to train young mathematicians who can read a story like this and enjoy it without necessarily believing it!
Academics apply rigour when they need to. Having been at an Oxbridge high table when World Cup football was being discussed, I can say with certainty that rigorous thinkers in one field don't necessarily bring the same quality of analysis of other matters. We all apply different standards of rigour in different parts of our lives: that's part of being human.
A final comment: I don't believe it is only mathematicians who take a cavalier approach to the history of their subject. All disciplines and professions have their cultures, built on anecdote and dubious history. Mathematics is no different in that respect.