Assignment 2 - Dany Waller

In Chapter 2, section 3 of "A Primer of Mathematical Writing", Steven Krantz details how to write a rigorous proof of a mathematical theorem. He claims that a proof should not be a hasty beeline for the result, but a well-written journey that keeps the reader on a defined path. Krantz outlines two useful devices to aid in this journey, the "claim" and the well-placed technical lemma. Each has its own place in a paper, according to Krantz, but both encourage the reader's trust in the proof and serve as guides in logical progression towards the theorem.

Arguing that a paper should be written in a slow descent from easily accessible explanation to technical details, Krantz states that the reader should always know where they are in the proof and should feel that any further step is approaching the conclusion of the proof. He warns strongly against skipping technical descriptions of lemmas and corollaries but stresses that they should be explained thoroughly and at the right time, otherwise the proof will confuse the reader about your theorem.

Krantz then gives several horrifying examples of poor communication on behalf of the author, noting that the author should feel an obligation to explain on behalf of their proof, not unlike a defense attorney presenting stark evidence in favor of their client's innocence. A well-constructed mathematical proof should share the feeling of handing the reader a beautifully wrapped present, a theorem nestled beneath meticulously folded paper and ribbon.