Maths and arrogance

Earlier this week a popular-science Facebook page posted a letter apparently from a schoolteacher to a pupil's parent complaining about the pupil questioning the teacher's assertion that a kilometre is longer than a mile.  The teacher felt that even though he was wrong he should not have been questioned by a student.   This brought back memories of a similar occasion in my youth (when, on my parents' insistence, I privately asked my teacher whether she had meant "Fahrenheit" when she said the average summer temperature in Nebraska is 95 degrees Centigrade, and was roundly abused for my temerity.)   Others have reported similar experiences.  Being told "You mustn't question me - I am a teacher" is something many people seem to remember.

I find this baffling.  Teachers may say all sorts of things under stress, but in some of the cases cited there was no excuse.  I hope times are now more enlightened.  Children have to learn that everybody gets things wrong sometimes, and that when you make a mistake, it's best to admit it and learn from it.  Authority should be questioned when necessary.  The way to respond to a challenge is to show that the challenge is wrong. Someone who forbids questions should not expect to be believed.  Even in primary school, I don't think there is a good argument for saying children should not question a statement that they think is wrong.

I do remember one very distinguished mathematician responding angrily to a question in a postgraduate lecture.  We were all puzzled by a definition, so a friend of mine asked "Why have you defined that in this way?"  The lecturer's response was "Because it bloody well works, that's why!", which didn't help us much nor did it gain him our respect.

Despite this example, I sometimes like to think that one of the ways in which mathematics is good for the soul is that studying mathematics gives excellent protection against arrogance.   It's hard to take oneself too seriously when there are simple problems, like saying whether every even integer is the sum of at most two primes, which one cannot solve.  Mathematics is not a subject in which one can fool oneself into over-estimating one's abilities: there is always a reality check.  I might mistakenly believe that my poem is an unprecedented masterpiece but I know that my proof of the Twin Primes Conjecture doesn't stand up.

I'm probably wrong, but I feel that if mathematicians ruled the world, they wouldn't have the over-confidence to lead us into unnecessary wars.  Self-questioning and self-doubt should be encouraged (unless you're a sportsman!)

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On Monday 4th February I am giving the first of three free public lectures on computing and mathematics at Gresham College, London.  Readers of this blog are very welcome!