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I don't know whether the actual history of mathematics is useful for understanding mathematics. However, I do believe that a plausible story of how somebody ca
by nhaehnle 12y ago
I don't know whether the actual history of mathematics is useful for understanding mathematics.
However, I do believe that a plausible story of how somebody came up with concepts is very important. It can be tempting to structure a mathematics lecture in a very sober/bland style of definitions followed by theorems with proof. However, definitions usually arose because somebody was trying to solve a particular problem, and this should be part of mathematics teaching.
It is usually said that "mathematics is not a spectator sport". To fully learn it, you have to put yourself into the shoes of somebody who invents certain definitions and seeks out certain theorems because they have some ulterior question that motivates them.
I would go beyond what you wrote by saying that this applies to advanced mathematics as well. The truly great papers tend to lucidly lay out the thought processes that explain why definitions and proof steps are chosen to be of a certain form.
- omegant 12y agoFor me it is. For example, I read "Fermat´s last theorem". The great thing is that the author tells in a vivid way, how different mathematicians attacked different parts of the theorem, starting with Fermat, up to the present . He also explains how the tools developed along the time found real world applications. I can not say that I understand the concepts explained at the book, but now I feel that I could even start learning Number theory (well maybe this is a stretch, but you get the idea) On a side note please for give my parent comment. I was writing from the Iphone seated at a plane, so I had to hurry and didn't have time for corrections.