Abstract: In this talk, I'll go over a sketch of the original proof of Adams and Atiyah of the Hopf invariant one problem and the machinery needed to tackle it. Hurwitz theorem states that there are only 4 division algebras, Adams showed this in an 80-page long article, and then with Atiyah, they were able to shorten the proof to 4 pages (densely packed ones but still). Having background in vector bundles (or being enrolled in the current 6823) is recommended.