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Letting research come naturally. (English) Zbl 0617.00022

The purpose of this paper is to show that creative mathematical work is not just the privilege of a few geniuses; it can be a natural activity of any of us with sufficient desire and freedom. Our preschool exploration of our surroundings is later hampered by the growing pressures and loss of freedom, not by loss of ability.
Some general principles of mathematical research are given, and relevance to the teaching problem is considered briefly. The main body of the paper (condensed in this version) gives examples of rediscovery of mathematical methods, some of which have played an important role in the development of modern mathematics. These examples are designed to help the reader rediscover, rather than just learn, further mathematical methods, and thus move towards new discoveries, when he/she has the freedom and desire.

MSC:

00A30 Philosophy of mathematics
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