flexibeast.space - gemlog - 2020-11-29
Some annoyances in maths papers
Andrej and Elena Cherkaev's maths jokes collection - in particular, section “Seminar semantics”, subsection “How to prove it” - describes a number of, er, ‘problematic’ phenomena in mathematical literature.
Here are some other annoyances i've encountered “in the wild” over the years:
- Guess how to verbalise the symbol! Fictional example: “If X, then Y 😃 Z. In all cases where Y 😃 Z, we also have A 😃 B, though C 😃 D is not necessarily the case.” Suggested remedy: Tell your readers how the symbol should be verbalised. “Y 😃 Z, which should be read as ‘Y is a friendly opponent of Z’, ...”
- Opposites day! Fictional example: “In this paper, we use X < Y to indicate that X is of greater cardinality than Y.” Suggested remedy: There are lots of symbols available. How about picking one that doesn't have existing meanings almost entirely unlike the meaning you want to convey?
- Unmotivated terminology choices! Fictional example: “We refer to any sets with exactly 3 members as ‘fluffy’. Fluffy sets are the linchpin of this paper ...” Suggested remedy: Explain the motivation behind the chosen terminology.
- Styling for semantics! Fictional example: “Let A be [etc]. Let 𝐀 be [etc]. Let 𝐴 be [etc]. Let 𝑨 be [etc]. It is critically important to distinguish these four things ...” Suggested remedy: Um, use different graphemes for different things rather than stylistic variants of the same grapheme?
- Excruciating detail combined with significant lack of detail! Fictional example. “Theorem 1. 1 + 1 = 2. Proof: [Three pages of proof]. Theorem 2. The Riemann Hypothesis is true. Proof: Follows trivially from theorem 1.” Suggested remedy: Rank the statements in your writing from “least likely” to “most likely” to be surprising to your intended audience, and focus on elaborating statements towards the latter end of the scale.
Providing further examples left as an exercise for the reader. ;-)
☙