Proof of Fermat's Last Theorem Intro #4.2 - Group Law for Elliptic Curves over Rational Numbers

Here we explore the basics of Elliptic Curves. I have split this topic into three parts. This video is part 2, on the Group Law for Elliptic Curves over Rational Numbers, in particular proving that if two points on the curve are rational, then their sum is rational as well. Part 1: Elliptic Curves over Real Numbers, and the Group Law Part 2: The Group Law for Elliptic Curves over Rational Numbers Part 3: Elliptic Curves over Complex Numbers Please leave any questions, comments, or suggestions in the comments below! The next videos after this will be: #4.3 Elliptic Curves over Complex Numbers #5. Then a very basic overview of Modular Forms, so he have a basic comprehension of what they are as well. #6. With a basic understanding of Elliptic Curves and Modular Forms, I will give you a brief history of the proof, then my basic understanding of Wiles' proof--how does Taniyama-Shimura (every Elliptic Curve is a Modular Form) imply Fermat's Last Theorem. (This will be the culmination of these first five videos. I think this video will already do a better job of explaining Wiles' proof in basic terms than any currently on youtube.) Please subscribe and support these videos on patreon:   / greg55666