17 lines
1.2 KiB
Markdown
17 lines
1.2 KiB
Markdown
---
|
|
title: "Mathematics Made Difficult"
|
|
chunk: 1/1
|
|
source: "https://en.wikipedia.org/wiki/Mathematics_Made_Difficult"
|
|
category: "reference"
|
|
tags: "science, encyclopedia"
|
|
date_saved: "2026-05-05T08:45:44.083466+00:00"
|
|
instance: "kb-cron"
|
|
---
|
|
|
|
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, 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.
|
|
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 ...
|
|
|
|
|
|
== References == |