Mathematics Made Difficult

{{Short description|Book by Carl E. Linderholm}}

{{Infobox book

| name = Mathematics Made Difficult

| image = Mathematics Made Difficult.jpg

| image_caption =

| author = Carl E. Linderholm

| country =

| subject = Mathematics, Satire

| publisher = World Publishing

| pub_date = 1972

| media_type =

| pages = 207

| isbn = 978-0-529-04552-2

| oclc = 279066

| dewey = 510

| congress =

}}

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,{{cite book

|title=Mathematical writing

|author=Knuth, D.E. and Larrabee, T. and Roberts, P.M.

|isbn=0-88385-063-X

|year=1989

|publisher=Mathematical Assn of Amer

|url-access=registration

|url=https://archive.org/details/mathematicalwrit0000knut

}}, page 6.{{Cite journal|last=Howson|first=A. G.|date=March 1972|title=Mathematical Fantasia|journal=Nature|language=en|volume=236|issue=5341|pages=83–84|doi=10.1038/236083b0|bibcode=1972Natur.236...83H |issn=1476-4687|doi-access=free}} 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.{{Cite journal|last=Quadling|first=D. A.|date=October 1972|title=Mathematics Made Difficult. By Carl E. Linderholm. Pp. 207. £2·75. 1971. (Wolfe.)|url=https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/mathematics-made-difficult-by-carl-e-linderholm-pp-207-275-1971-wolfe/92B202F1AB0A4019D797D0F0BDA20589|journal=The Mathematical Gazette|language=en|volume=56|issue=397|pages=255–256|doi=10.2307/3617023|jstor=3617023 |issn=0025-5572}}

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 ...Linderholm, Page 76.