## Sunday, 27 January 2013

### 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!

1. Very good point with very deep implications. It is just not as simple as encouraging self-reflection. We are talking about a big ape here.

2. If that's so then mathematicians would never rule the world!

3. Of course, the existence of a single arrogant mathematician would demolish my argument, so I think it is in some trouble!

4. Mathematicians are unlikely ever to rule the world. We have too much faith in logic. We don't win arguments with politicians because we think that one solid counter-argument is enough to refute a proposal. It works that way in logic but not in life.

5. I agree with you that good mathematicians know when they're not great mathematicians, but bad mathematicians, the sort who send unsolicited proofs of the Goldbach conjecture to all and sundry, can persist their entire lives under the impression they're underappreciated geniuses.
There is of course a well-populated spectrum between those two extremes. Your argument is sort of a "no true Scotsman" one.

6. Marcus du sautoy?

7. The political leader who springs to mind is Eamon de Valera, who was a maths graduate. One wouldn't describe him as exactly lacking in self-regard...

I suspect that for every mathematician who is taught humility by the subject, there's at least one who's misled into thinking that knowledge in other fields can be as secure as it is in maths.

8. Anonymous- not why you mention Marcus. He's a good mathematician who certainly isn't arrogant!

Phil, and others - I think you're right. My argument doesn't convince me!

9. Thx for this, glad I'm not the only one to have suspected maths to have anti-arrogance properties. I'll do my best to take my maths courses as a work on myself, on my faults, from this moment on.

10. Be realistic- math sucks and everyone really hates it.

Most math teachers have no personality, which seems to be a requirement to be one.

11. Wasn't Gauss a rather arrogant and cantankerous man, Newton, Nash...