I will present the original path that led Milnor to the existence of the famous exotic 7 sphere. We will see its relation to generalized Poincare conjecture and how to use of characteristic class to distinguish differential structures.

If time permits, I will show how we actually can count the number of differential structures on 7-sphere up to orientation preserving diffeomorphism as you may know the answer is 28. This should be regarded as a milestone in the golden age of topology in the 50-60s as it dependence on almost all other important results like h-cobordism theorem, Bott periodicity and so on.