# Where to put proofs in a thesis?

When writing mathematically oriented thesis, e.g., math, cs, engineering, I am wondering where would be the most appropriate place to put your proofs.

There are several ideas:

1. put them right after the theorems/propositions
2. put them separately in each chapter's appendix (i.e., a new section at the end of chapter)
3. put them all in an appendix

Can someone chime in which practice is superior than the others?

• There's proofs in engineering theses? Apr 7, 2022 at 3:02
• This really depends on how mathematically oriented - whether the proofs themselves are actually important or not. Ask your advisor. Apr 7, 2022 at 3:18
• @AzorAhai-him- definitely. Lookup theses on signal processing or control theory. Apr 7, 2022 at 3:45
• I've seen #1 and #3. For #1 I would sketch a proof if I require the reader to have some intuition about a lemma/theorem that I will then use in my solutions. This is a judgement call based on whether a statement is easily understood, and whether you require a reader to go thru' a proof to understand the next bit of your thesis. Apr 7, 2022 at 3:47
• How long are these proofs? I would never want to see a short proof (say one page) banished to an appendix. Twenty pages is another matter. Apr 7, 2022 at 15:03

This typically depends on whether the technique of proof assists in elucidating the topic under discussion or not. If the details of the proof contributes substantially to ellucidating the topic under discussion then you would keep it in the body; otherwise it is useful to relegate them to an Appendix.

The ultimate goal is for the paper to flow smoothly. Therefore, my favorite style is to place some proofs right after the propostion, while some others in an appendix, depending on how much insight the reader gets from reading the proof.

If only the result of the proposition is important and the reader is better off reading the next paragrah and skipping the proof on the first read, then place the proof in the appendix. The reader can jump to the appendix now, but you're giving a hint that it's better done later.

But if the proof elicidates the material and you do want the reader to read it before going on to the next paragraph, then place it right after the proposition. A good practice I wish I saw more of is to have an outline of the proof after the proposition and the detailed version of the proof in the appendix.