But the 100-page proof relied on extensive computer calculations.

The proof relies on basic properties of the Gromov norm.

The proof relies heavily on what is today called side-angle-side, the previous proposition in the Elements.

The proof also relies on the following theorem proven in p. 185:

The proof relies on infinite descent, and is only briefly sketched in the letter.

The proof relies heavily on the assumption that the external potential can be expanded in a Taylor series about the initial time.

This was more difficult since the proofs relied on discarding terms that were proportional to the surface.

The proof relies on the classification of finite simple groups.

The proof relies essentially on the existence of a Lyapunov functional.

The proof relies on the use of the full separation axiom.