Proof style guide
Sunday, January 25, 2009 2:29Clear mathematical writing often leads to clearer thinking. Of course, in Olympiad problems, it also reduces the risk of losing marks for small errors!
If you want to work on your exposition, I heartily recommend this style guide for writing up solutions to mathematical problems, by John M. Lee. It’s aimed mainly at people writing university mathematics assignments, with lots of time to spare, so some of the details in the last section are more pedantic than Olympiad contestants will need to bother with. But the general instructions in the first half are excellent.
One sometimes-helpful trick (Lee mentions it at the start of the second page) is to try to break down your solution to a question into several sub-arguments. In long complicated questions, clarity, and keeping track of small details, seem to arise much more easily out of a nice sequence of Propositions and Lemmas — each stated clearly, then proved before going on to the next — than out of a single essay-style answer.
Michael says:
January 26th, 2009 at 7:59 am
If you read nothing else from this article (though you should), read the first sentence of the first bullet point: “First and foremost, remember always that a mathematical
proof is designed to communicate the truth of a mathematical statement to a human reader.”
Alex HOANG says:
July 9th, 2009 at 3:51 pm
It is equivalent to the sense of giving a mathematical formulae in its appropriate position. It does not matter how we understand a problem, but we concern about how we demonstrate our problems in its best possible.