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I don't know if this question is best suited to this stack exchange. If it isn't, feel free to migrate it or close it. This question was inspired by a mistake I saw in a math class. I corrected the professor, and he acknowledged it. I then said, "Some students think professors never make mistakes". And he said, "Yes, and those students are mistaken". So, what are some famous or at least semi-famous examples of math professors making errors in the classroom? Note, the mistake has to have taken place in a classroom, not in a journal or book or paper.

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  • $\begingroup$ See also literature.stackexchange.com/q/22969 , although it's about "obvious" statements, not necessarily mistakes. $\endgroup$ Sep 3, 2022 at 22:44
  • $\begingroup$ Are you talking about mistakes which a professor would readily realize if they thought about it (e.g., the Grothendieck answer) or something they seriously believed and wasn't generally known to be false (e.g., the Aristotle and Wiles answers)? $\endgroup$
    – Kimball
    Sep 4, 2022 at 11:58

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Grothendieck is famous for having chosen $57$ as a prime number example, when answering a question from a student.

And actually the same mistake had been made before, by Weyl, in a paper, as can be read here. https://hsm.stackexchange.com/questions/6358/story-of-grothendiecks-prime-number

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Aristotle famously taught that the only regular solids that tiled space were the cube and the tetrahedron when, in fact, only the cube does so.

It took 1800 years for the mistake to be corrected.

Mysteries in Packing Regular Tetrahedra

Note: It is generally accepted that most of Aristotle's surving writings were, in fact, lecture notes. So the tetrahedron error is an error which he would have made in a class lecture.

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Wiles initial proof of Fermat's Last Theorem contained an error, and in some documentary he said he was about to give up on it, but tried to understand one last time what the exact problem was, and then was able to fix it (he also had the help of Richard Taylor his previous graduate student)

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    $\begingroup$ @bof Plausibly true, but it seems somewhat unfair to me. Making an analytical error when you are the first Mathematician to walk down a new path is different than if you are following in someone else's footsteps. Personally, on MathSE, I have (more than once) composed inaccurate answers to Combinatorics problems that I thought were correct. The only thing that stopped my posting the mistakes was that I recognized the danger and Java-sanity-checked first. Then, I found/corrected my errors and then posted. $\endgroup$ Sep 4, 2022 at 0:11
  • $\begingroup$ @user2661923 Speaking of errors, my comment was supposed to be a comment on the question but I accidentally posted it as a comment on an answer. $\endgroup$
    – bof
    Sep 4, 2022 at 0:44

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