Author Carl E. Linderholm Mathematics, Satire World Publishing 1972 207 978-0-529-04552-2 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] it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers.

As an example, the proof that two 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 ...[2]

References

1. ^ Knuth, D.E. and Larrabee, T. and Roberts, P.M. (1989). Mathematical writing. Mathematical Assn of Amer. ISBN 0-88385-063-X., page 6.
2. ^ Linderholm, Page 76.