21
$\begingroup$

As a sidetrack in this question it came up that it is important to have students read texts (in particular proofs) critically. As examples it is nice to have correct proofs at hand (presumably in the textbook/lecture notes), but also a variety of others:

  • Proofs that are just plain wrong, like the nice "proof by induction" that all integers are larger than 10, just by omitting the base case
  • Proofs that are wrong, but the result is actually right (missing cases, hidden assumptions, ...)
  • Proofs that are right, but could be tightened up/simplified

This is in part motivated by the classic by Kernighan and Plaugher "The Elements of Programming Style", where the authors show bad program snippets culled from textbooks and other published sources, dissect them and show how they should be written right, and why. I'm aware of Edward Barbeau's "Mathematical Fallacies, Flaws, and Flimflam" (MAA, 2000), but that targets more bad computation than bad proving.

It it helps narrowing down, I'm mostly interested in combinatorics and discrete math. But approachable proofs, accessible to the relative layman (think students with Calculus I under their belt, often just taking Calculus II) in any area are quite welcome.

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Great question. There's a legend at my faculty that one of the professors used to give a wrong proof on the exam, and the students had to find the error. ;) $\endgroup$
    – mbork
    Commented May 6, 2014 at 21:04
  • $\begingroup$ @MichaelE2, sounds interesting, thanks! Will take a peek. $\endgroup$
    – vonbrand
    Commented May 6, 2014 at 21:49

2 Answers 2

Reset to default
14
$\begingroup$

Students are, of course, the best source of "bad proofs". And while one can pull from assignments/homework, I find the best "bad proofs" are the ones students give on competition style problems. To that end, I usually photocopy our students' MAA Team Contest and Putnam responses before mailing them in. Then I can type up those responses and use them in our Intro to Proofs course.

Improve this answer
$\endgroup$
9
$\begingroup$

It may not be as thorough as you're looking for, but there's a brief section in my Intro to Proofs book about spoofs in Chapter 1 B with some examples/problems.

Improve this answer
$\endgroup$
5
  • $\begingroup$ Thanks, I'll take a look. $\endgroup$
    – vonbrand
    Commented May 7, 2014 at 0:34
  • 1
    $\begingroup$ Welcome to MESE! $\endgroup$
    – Mark Fantini
    Commented May 7, 2014 at 3:10
  • $\begingroup$ Ooooh I like those notes. $\endgroup$
    – JP McCarthy
    Commented May 7, 2014 at 12:43
  • 3
    $\begingroup$ Do you have an updated link by any chance? $\endgroup$
    – hb20007
    Commented Jan 6, 2022 at 20:58
  • $\begingroup$ Here's the link at the web archive: web.archive.org/web/20141023044558/http://www.math.vt.edu/… $\endgroup$
    – Vince Vatter
    Commented Apr 29, 2023 at 18:03

Not the answer you're looking for? Browse other questions tagged or ask your own question.