Terms like "impractical" and "unfeasible" are used to say the Robertson, Sanders, Seymour, and Thomas proof of the four color theorem needs computer assistance. Obviously no precise measure is possible, for many reasons.
But is there an informed rough estimate what a graph theorist would need to verify the 633 reducible configurations in that proof? $10^4$ hours? $10^8$ years?
I am not asking if other proofs are known. I want to know if graph theorists have an idea what scale of practicality we are talking about when we say the Robertson, Sanders, Seymour, and Thomas proof is impractical without machine assistance.
Best Answer
To answer the question it is important to disentangle the proof as follows.
Theorem 1. Every minimum counterexample to the 4CT is an internally 6-connected triangulation.
Theorem 2. If $T$ is a minimum counterexample to the 4CT, then no good configuration appears in $T$.
Theorem 3. For every internally 6-connected triangulation $T$, some good configuration appears in $T$.
See the actual paper for the definitions of these terms. Theorem 1 does not require computer assistance, while Theorem 2 and Theorem 3 both do require computer assistance. According to this version of the paper, Theorem 3 can in principle be checked by hand. Indeed it is explicitly mentioned that
I quote more on Theorem 3:
Theorem 2, on the other hand really requires a computer. From the same paper,
Thus, given that it took a computer 9 times longer to verify Theorem 2 than Theorem 3, and Theorem 3 apparently can be verified by hand in a few months (let us define few=3), then under some very dubious assumptions we have the ballpark answer of
Ballpark Answer. 30 months.