I am giving a presentation on mathematical results that were widely accepted for a period of time and then later proven wrong, or vice versa. This talk is geared towards undergraduates who are likely to have not taken calculus. I have a few examples already, but I was wondering if anyone knew of others.
So far, I have the initial proofs of the 4-color problem, and "a continuous function is differentiable almost everywhere." These are both problems that can be explained simply, and their counter examples can be explained relatively simply. The problem I keep running into is that either the question is too advanced, or the counter example is too advanced. I was wondering if any of you kind people knew of examples or resources I could look into.
Any input would be appreciated. Thank you!