Mathematics Made Difficult
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| Author | Carl E. Linderholm |
|---|---|
| Subject | Mathematics, Satire |
| Publisher | World Publishing |
Publication date | 1972 |
| Pages | 207 |
| ISBN | ISBN:978-0-529-04552-2 |
| OCLC | 279066 |
| 510 | |
Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical,[1][2] it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers. Linderholm discusses these seemingly-obvious ideas using concepts like categories and monoids.[3]
As an example, the proof that 2 is a prime number starts:
It is easily seen that the only numbers between 0 and 2, including 0 but excluding 2, are 0 and 1. Thus the remainder left by any number on division by 2 is either 0 or 1. Hence the quotient ring Z/2Z, where 2Z is the ideal in Z generated by 2, has only the elements [0] and [1], where these are the images of 0 and 1 under the canonical quotient map. Since [1] must be the unit of this ring, every element of this ring except [0] is a unit, and the ring is a field ...[4]
References
- ↑ Knuth, D.E. and Larrabee, T. and Roberts, P.M. (1989). Mathematical writing. Mathematical Assn of Amer. ISBN 0-88385-063-X. https://archive.org/details/mathematicalwrit0000knut., page 6.
- ↑ Howson, A. G. (March 1972). "Mathematical Fantasia" (in en). Nature 236 (5341): 83–84. doi:10.1038/236083b0. ISSN 1476-4687. Bibcode: 1972Natur.236...83H.
- ↑ Quadling, D. A. (October 1972). "Mathematics Made Difficult. By Carl E. Linderholm. Pp. 207. £2·75. 1971. (Wolfe.)" (in en). The Mathematical Gazette 56 (397): 255–256. doi:10.2307/3617023. ISSN 0025-5572. https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematics-made-difficult-by-carl-e-linderholm-pp-207-275-1971-wolfe/92B202F1AB0A4019D797D0F0BDA20589.
- ↑ Linderholm, Page 76.
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