The most groundbreaking moment in this sense for me was when I was writing course notes for an introductory course (level 300 on my specialty, I was ready). On a small topic, I had my references lined up, until a colleague shared that the obvious, well-known, widely referenced result had been disproven a couple of years prior. The new proof is far from simple, does not belong in a level 300 class and made me scrap the whole section.
For the interested: the course was Introduction to Numerical Analysis, the topic was the order of convergence of the bisection method. Widely known but wrong result Ironically, I can’t quickly find the paper disproving it.
The most groundbreaking moment in this sense for me was when I was writing course notes for an introductory course (level 300 on my specialty, I was ready). On a small topic, I had my references lined up, until a colleague shared that the obvious, well-known, widely referenced result had been disproven a couple of years prior. The new proof is far from simple, does not belong in a level 300 class and made me scrap the whole section.
For the interested: the course was Introduction to Numerical Analysis, the topic was the order of convergence of the bisection method. Widely known but wrong result Ironically, I can’t quickly find the paper disproving it.