Book contents
- Frontmatter
- Contents
- Acknowledgements
- Part I Mathematical Recreations and Abstract Games
- Part II Mathematics: game-like, scientific and perceptual
- 6 Game-like mathematics
- 7 Euclid and the rules of his geometrical game
- 8 New concepts and new objects
- 9 Convergent and divergent series
- 10 Mathematics becomes game-like
- 11 Mathematics as science
- 12 Numbers and sequences
- 13 Computers and mathematics
- 14 Mathematics and the sciences
- 15 Minimum paths: elegant simplicity
- 16 The foundations: perception, imagination, insight
- 17 Structure
- 18 Hidden structure, common structure
- 19 Mathematics and beauty
- 20 Origins: formality in the everyday world
- References
- Index
Book contents
- Frontmatter
- Contents
- Acknowledgements
- Part I Mathematical Recreations and Abstract Games
- Part II Mathematics: game-like, scientific and perceptual
- 6 Game-like mathematics
- 7 Euclid and the rules of his geometrical game
- 8 New concepts and new objects
- 9 Convergent and divergent series
- 10 Mathematics becomes game-like
- 11 Mathematics as science
- 12 Numbers and sequences
- 13 Computers and mathematics
- 14 Mathematics and the sciences
- 15 Minimum paths: elegant simplicity
- 16 The foundations: perception, imagination, insight
- 17 Structure
- 18 Hidden structure, common structure
- 19 Mathematics and beauty
- 20 Origins: formality in the everyday world
- References
- Index
Summary
Mathematics is the art of giving the same name to different things.
Henri Poincaré [Poincaré 1914]Mathematicians are always and everywhere looking for patterns. If they can't see patterns on the surface, they look underneath the surface. If they cannot spot a pattern in some isolated object they try to put it in a broader context.
Patterns in everyday life can be superficial – mere decoration – but in mathematics they are more significant. Rather than surface decoration, they resemble internal skeletons. They are the structure upon which mathematics is constructed and if you understand the skeleton, then you understand a lot about the object itself.
Patterns have another use: the same patterns — or skeletons — turn up again and again in different situations, allowing insight to be spread from one to the other, so mathematicians are also, like the best scientists, obsessed with analogies:
For above all I love analogies, my most faithful teachers, acquainted with all the secrets of nature.
Kepler [Rigaud 1841]Information
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- Games and MathematicsSubtle Connections, pp. 184 - 196Publisher: Cambridge University PressPrint publication year: 2012
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