How the Monochromatic AP Theorem Became Classic: Khinchin and Lukomskaya

Is it possible to find a needle in a haystack? Yes, it is, with good fortune and great perseverance. We discussed the birth of this monochromatic AP theorem earlier in the book, so by now, it should be “old news” to you. In fact, it has taken 20 years and a Russian aid for this theorem to become classic. As you recall, its 1927 publication [Wae1] in a small-circulation Dutch journal hardly helped its popularity. Only two Japanese mathematicians [KM] and Issai Schur with his two students Alfred Brauer and Richard Rado realized its importance and improved upon Van der Waerden’s result almost immediately; and later, in 1936, Paul Erdős and Paul Turán commenced density considerations related to Van der Waerden’s result [ET].