Games and Mathematics by Wells David

Author:Wells, David [Wells, David]
Language: eng
Format: epub
ISBN: 9781139553629
Publisher: Cambridge University Press
Published: 2012-08-30T20:00:00+00:00

Geometry is that part of mathematics in which visual thought is dominant whereas algebra is that part in which sequential thought is dominant. This dichotomy is perhaps better conveyed by the words “insight” versus “rigour” and both play an essential role in real mathematical problems.

[Atiyah 2003: 29]

It is no accident that Atiyah turned in his later years to problems of theoretical physics. We could say that MacLane thinks of mathematics from the start as game-like – and can afford to do so because of the kind of hard-edged mathematics that he does – whereas Atiyah, as MacLane notes, is more like a physicist, who is exploring a mathematical landscape that is much less clear cut, and so he hesitates and explores further as he attempts to achieve the precision and clarity which MacLane has to begin with.

Andrew Wiles expressed very well his own sense of doing mathematics as exploring in the dark:

Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. You enter the first room of the mansion and it's completely dark. You stumble around bumping into furniture, but generally you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of – and couldn't exist without – the many months of stumbling around in the dark, that precede them.

[Griffiths 2000]

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