What If We Had No Choice?

On the pages of this book, we have seen a variety of approaches used in attempts to settle the chromatic number of the plane problem (CNP). Tools from graph theory (Chap. 17 ), topology (Chaps. 8 and 26 ), measure theory (Chap. 9 ), abstract algebra (Chap. 11 ), and discrete and combinatorial geometry (Chaps. 4 , 6 , and 7 ) have been tried – and only recently an improvement has been attained in the general case. The range for CNP still remains (too) wide: χ = 5, 6, or 7.