Proof methods from a tired STEM undergraduate

For use in textbooks

Proof by intimidation: Trivial!

Proof by inspection: Clear!

Proof by cumbersome notation: The theorem follows immediately from a formula containing 4 different alphabets, 7 different types of brackets and an emoji.

Proof by inaccessible literature: The theorem is an easy corollary of a result which is to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.

Proof by ghost reference: The proof may be found on page 478 in a textbook which turns out to have 396 pages.

Proof by circular argument: Proposition 5.18 in [BL] is an easy corollary of Theorem 7.18 in [C], which is again based on Corollary 2.14 in [K]. This, on the other hand, is derived with reference to Proposition 5.18 in [BL].

Proof by internet reference: For those interested, the result is shown on the web page of this book. Which unfortunately doesn't exist anymore.

Proof by importance: A large body of useful consequences all follow from this theorem.

Proof by semantic shift: The rest of the course will follow much more easily after changing standard definitions to include this result.

Proof by meta-proof: We present the following method to construct the desired proof.

Proof by obviousness: The proof is so clear that it need not be stated.

Proof by intuition: From studying similar concepts, you will already know this theorem to be true.

Proof by picture: Hours of effort were put into creating this diagram in TikZ, so it must be relevant.

Proof by lack of interest: I fear that including the proof would bore the majority of students.

Proof by calculus: This proof requires multivariate calculus, so we'll skip it.

Proof by avoidance: Chapter 3: The proof of this is delayed until Chapter 7 when we have developed the theory even further.
                                   Chapter 7: To make things easy, we only prove it for the case z = 0, but the general case is handled in Appendix C.
                                   Appendix C: The formal proof is beyond the scope of this book, but of course, our intuition knows it to to be true.

For use in lectures

Proof by vigorous circling: The board is unintelligible after five minutes.

Proof by vigorous hand-waving: The board remains blank after twenty minutes.

Proof by running out of time: I could prove this on the board but we'd be here until lunch.

Proof by flashy graphics: Only a really powerful result could underlie such an awesome sound and light show.

Proof by elimination of the counterexample: Assume for the moment that the hypothesis is true. Now, let's suppose we find a counterexample. So what?

Proof by repetition: The theorem holds. The theorem holds. The theorem holds.

Proof by authority: My good colleague Timothy said he thought he might have come up with a proof of this a few years ago...

Proof by eminent authority: I saw Wiles in the elevator and he said it was tried in the 70s and didn't work.

Proof by convenience: It would be very nice if this theorem were true, and in fact, it is.

Proof by accident: Hey, what have we here?!

Proof by slippery slope: If [proposal] was false, then that would invalidate [slightly modified proposal], and eventually we would have to accept [a radically different and clearly objectionable proposal].

Proof by vehement assertion: This result is stated in the lecture notes, which were written by a very senior professor.

Proof by insignificance: Understanding this result is not so important, but you will still be tested on it in two years' time.

Proof by tessellation: This proof is the same as the last.

Proof by necessity: If the theorem weren't true, then the entire structure of modern mathematics would crumble to the ground.

For use in papers

Proof by exhaustion: I have devoted a journal issue to the proof.

Proof by plausibility: The theorem sounds sensible.

Proof by example: We demonstrate the proof in the case that n = 2. It contains most of the ideas of the general proof.

Proof by omission: The other 253 cases are, mutatis mutandis, analogous.

Proof by accumulated evidence: A long computer search over the space gave no counterexample.

Proof by design: This motivates us to develop a new branch of mathematics in which this result is true.

Proof by general agreement: According to polls, most mathematicians believe that the theorem holds.

Proof by democracy: More than 50% of published papers on the topic assert that the result holds.

Proof by funding: How could three different government agencies be wrong?

Proof by physics: This theorem is the only one amongst competitors that makes sense with what we observe more generally.

Proof by statistics: Almost any curve can be made to look like the desired result by suitable transformation of the variables and manipulation of the axis scales.

Proof by a bad apple: Amongst the many critics of the theory, we found one who has been discredited from the academic community. Thus all the naysayers are incorrect.

Proof by running out of paper: I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.

For use in exams

Proof by supplication: We hope that this is true.

Proof by tautology: Assuming the theorem is true, we see that the theorem holds.

Proof by divinity: This was once revealed to me in a dream.

Proof by obfuscation: Thus follows a long plotless sequence of statements with an entailment graph that would make Dijkstra cry.

Proof by reduction to wrong problem: To see that P is decidable, we reduce it to the halting problem.

Proof by kitchen sink: Thus follows every theorem and result known to mankind, within which all key facts for the desired proof are contained.

Proof by delegation: // TODO.

Proof by approximation: Raising x to the third power yields the first 8 digits of π.

Proof by overkill: Supposing the opposite is true contradicts Fermat's Last Theorem.

Proof by simplification: The proof of this theorem reduces to the statement 1 + 1 = 2.

Proof by clever variable choice: Let n be the number such that the result holds.

Proof by fudging: Having already memorised the final result, thus follows a chain of statements that looks about right.


As Prof. Margaret Fleck (University of Illinois, Urbana-Champaign) writes:
"Similar lists have been circulating around the net for decades. The original was written by Dan Angluin and publisted in SIGACT News, Winter-Spring 1983, Volume 15 #1".
This is an amalgamation of all I could find, some rephrased, and a few of my own.
---404dcd, 2026, created without use of LLMs.