Kempe–Heawood’s Five-Color Theorem and Tait’s Equivalence

I am compelled to present here Alfred Bray Kempe’s attempted proof of the four-color conjecture (4CC). As you recall from Chap. 20 , that proof contained an oversight, found a “mere” 11 years later by Percy John Heawood. Why then do I choose to present the unsuccessful attempt here? First of all because of the beautiful ideas Kempe invented. Second, because it is not easy to notice a flaw right away. Third, because P.J. Heawood did not have to do much to salvage Kempe’s ideas to show that, in fact, they (i.e., Kempe’s ideas!) prove the five-color theorem. Finally, because just like their contemporaries underestimated the work of Heawood, my contemporaries often underestimate the contributions of Kempe.