I found your blog via the entry on women and mathematics.
I know that this is not exactly what you are searching for with your demand for stories, but I have to comment on the “intrinsic competitiveness” of mathematics.
In mathematics olympiads and in professional mathematics, competitiveness is ritualized and contained by ethical rules. In my olympiad training session, you were expected to explain things to newer participants even though they might well be better than you at the competition. In olympiads and real life, I have found that this kind of ethics almost always corresponded to mathematical capability.
So here is my anecdote on competitiveness:
In primary school (age 6-10), I had about half the running speed of any other child. On the other hand, I understood everything in maths immediately and was very quick with mental calculations. In sports, we had weekly running competitions of groups by four, where my group never had a chance at all. In maths, we had weekly speed calculating competitions where each pair of students were posed a question and the quicker one would remain standing until one student was left and got a little prize. I won every time and was only allowed to participate every other week.
The lesson that good performance in math is bad for your social standing with your peers could not have been more evident.
More anecdotes on learning:
languages involved: German
Brother aged 5
My brother and I had learned (presumably from our parents) how counting goes on and on without an end. We understood the construction but we were left with some doubt that you could *really* count to high numbers, so we decided to count up to a million by dividing the work and doing it in the obligatory nap time in kindergarten in our heads. After a couple of days, we had to admit that it took too long, so we debated whether it was ok to count in steps of thousands or ten-thousands, now that we had counted to thousand many times. We ended up being convinced that it is possible to count to a million but slightly unhappy that we could not *really* do so ourselves.
languages involved: German
I participated in a mathematical competition where an inequality had to be proven by induction. I adhered strictly to a ”one-line-format” where you start with the left-hand-side of the desired inequality, apply induction hypothesis etc until you arrive at the right-hand-side.
When I afterwards saw someone at some step adding the desired right-hand-side and manipulating the unproven inequality, I understood the advantage immediately and felt stupid for not considering this possibility, but I could never have asked a question about this because I was not aware of any restriction in my thinking. My teachers also could not notice any problems because my proofs were correct.
Posted by: Alexandre Borovik | November 13, 2009
Childhood stories from TE
Posted in Uncategorized