 | |
| Author | Carl E. Linderholm |
|---|---|
| Subject | Mathematics, Satire |
| Publisher | World Publishing |
Publication date | 1972 |
| Pages | 207 |
| 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]