{"id":33202,"date":"2020-06-27T16:18:54","date_gmt":"2020-06-27T21:18:54","guid":{"rendered":"http:\/\/blogs.ams.org\/mathgradblog\/?p=33202"},"modified":"2020-06-27T16:18:54","modified_gmt":"2020-06-27T21:18:54","slug":"math-students-hunt-for-errors-in-false-proofs","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2020\/06\/27\/math-students-hunt-for-errors-in-false-proofs\/","title":{"rendered":"Math Students Hunt For Errors in False Proofs!"},"content":{"rendered":"
<\/div>

Communicating mathematics is a crucial part of a developing mathematician\u2019s career. Really, any mathematician\u2019s 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\u2019s thesis.<\/p>\n

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 \u201cproofs\u201d 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 \u201cproof\u201d 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.<\/p>\n

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 \u201chigh tech\u201d math (see here<\/a>).<\/p>\n

It\u2019s fun to try it yourself! Pause the video before each section and see if you can spot the error(s).<\/p>\n