A previous teacher of mine had a book that had proofs to well known mathematical formulas/ideas but they were either proved incorrectly or were proved to be something else (i.e. if $x=y$ but we prove $x=2y$ using false assumptions that cleverly look right).
I would like to know books that deal with such kinds of problems. Thanks.
Well, I had this book called “Magnificient Mistakes in Mathematics” written by Posamentier and Lehmann and I should say that I absolutely loved it. Gave a great insight into the mistakes that even famous mathematicians did in their work. A book review is given here.
Why go so far? Take our own MSE collection of fake proofs!
Enjoy!