Erroll Morris ran a series of essays on the New York Times a couple of years ago, on the topic of incommesurability. The whole series is highly recommended. You may particularly enjoy reading Part III, on Hippassus of Metapontum, the mythical Pythagorean who proved the irrationality of square root of two, and was killed by the other followers of the cult as a result.
The legend is told in many places; Morris lists a few in his essay. I first found it as an appendix to Carl Sagan‘s book version of Cosmos.
A kind of library 
[…] 16. Sections 3.1-3.3. Hypassus of Metapontum. Homework 3 is due today. Homework: 3.1: 3, 4, 6. 3.2: 3-5, 8, 10. 3.3: 2, 4, 5. [Suggested […]
[…] 28. Completeness. Countable and uncountable sets. I recommend you read Errol Morris‘s essay on Hypassus of Metapontum, the apparent discoverer of the irrationality of […]