I hope I am asking my question in the right forum.
I am trying to introduce some mathematical problems (Better to be famous in the math community) to a group of senior high school students with a typical background in high school mathematics like (differentiation and applications - basic probability- basic plane geometry- little combinatorics, and graph theory and basic number theory and introductory linear algebra which are common to solve a system of linear equations.)
Actually, my friends and I are trying to introduce mathematics to senior high school students; in between, we would like to present them with some famous math problems in which there were some unsuccessful attempts to solve them, but at last, they've been solved. Or famous wrong conjectures which were thought to be correct. Through this, we wanted to emphasize that even mathematicians at a high level can get wrong, and guessing wrong or failing an attempt shouldn't worry you in studying mathematics
Thank you for helping me. I am also very grateful for other suggestions for our work, besides these.