Whoever has less math anxiety wins [View all]
Modern mathematics doesn't make complete sense. The unfortunate consequences include difficulty in deciding what to teach and how to teach it, many papers that are logically flawed, the challenge of recruiting young people to the subject, and an unfortunate teetering on the brink of irrelevance.
If mathematics made complete sense it would be a lot easier to teach, and a lot easier to learn. Using flawed and ambiguous concepts, hiding confusions and circular reasoning, pulling theorems out of thin air to be justified `later' (i.e. never) and relying on appeals to authority don't help young people, they make things more difficult for them.
If mathematics made complete sense there would be higher standards of rigour, with fewer but better books and papers published. That might make it easier for ordinary researchers to be confident of a small but meaningful contribution. If mathematics made complete sense then the physicists wouldn't have to thrash around quite so wildly for the right mathematical theories for quantum field theory and string theory. Mathematics that makes complete sense tends to parallel the real world and be highly relevant to it, while mathematics that doesn't make complete sense rarely ever hits the nail right on the head, although it can still be very useful.
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Most of the problems (...) arise from mathematicians' erroneous belief that they properly understand the content of public school and high school mathematics, and that further clarification and codification is largely unnecessary.
Boojatta's question:
Is it possible for people who don't properly understand the content of public school and high school mathematics, and who know that they don't understand it, to stand up for themselves and organize a reform movement? Alternatively, like the people in the story of the Emperor's New Clothes, are they afraid to admit that they don't see the clothes?
The above excerpt was written by N. J. Wildberger
Link:
http://web.maths.unsw.edu.au/~norman/views2.htm
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