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.



Can one measure the infeasibility of four color proofs?
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](http://people.math.gatech.edu/~thomas/PAP/fc.pdf) 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](http://people.math.gatech.edu/~thomas/PAP/npfc.pdf), Theorem 3 can in principle be checked by hand. Indeed it is explicitly mentioned that 



> 
> It can be checked by hand *in a few months*, or a few minutes by computer (this was about 15 years ago though). 
> 
> 
> 


I quote more on Theorem 3:



> 
> For each of these five cases we have a proof. Unfortunately, they are very long (altogether about 13000 lines, and a large proportion of the lines take some thought to verify), and so cannot be included in a journal article. 
> 
> 
> 


Theorem 2, on the other hand *really* requires a computer. From the same paper, 



> 
> The proof of Theorem 2 takes about 3 hours on a Sun Sparc 20 workstation and the proof of Theorem 3 takes about 20 minutes. 
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> 
> 


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. 


