How Do We Solve Difficult Problems in Mathematics?

#SoME3 In this video, we discuss how we tackle difficult problems in mathematics, and look at historical examples of groundbreaking new discoveries in mathematics that emerged from trying to solve a difficult problems. I made a follow up video to address an error in the video:    • Number Systems Invented to Solve the Harde...   Chapters: 00:00 Intro 01:09 Main Problem 10:51 FLT and Algebraic Number Theory 14:42 Quintic Equation and Group Theory 22:06 PDE and Fourier Analysis 27:36 Outro Corrections: 11:48 It is true that Euler provided the first proof and invented Z[√-3], but first algebraic proof using Z[ω] was by Gauss 27:03 I forgot to write the coefficients c_n for the series