Math Students Hunt For Errors in False Proofs!

Communicating mathematics is a crucial part of a developing mathematician’s career. Really, any mathematician’s career. In the classroom, with peers, and at conferences, math students organize their learning and research in order to effectively question and convey concepts that require significant math background. Of course, mastery of the many levels of communication spans everything from talking through word problems with curious elementary schoolers to defending one’s thesis.

In the spirit of celebrating the importance of effective communication, we decided to play a game with some PhD students at the University of Michigan! To test their math communication skills, we selected several “proofs” from around the internet (thanks, reddit) which have subtle errors leading to an ultimately false conclusion. For example, many math students have seen at one point a “proof” that 1 = 0. The volunteers then had to spot the error(s) in the reasoning and do their best to explain it to a broad audience.

Note: only proofs that appeal to a wide audience were selected so that more students can enjoy. There are certainly examples of error spotting in more “high tech” math (see here).

It’s fun to try it yourself! Pause the video before each section and see if you can spot the error(s).


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About Ethan Zell

I am a graduate student at the University of Michigan interested in probability. I have a background in vocal performance and in my spare time I enjoy music of all kinds.
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