The story revolves around an ancient stone artifact found near Cairo which has engraved markings of slanted lines. In an incredible non-sequitor, one of the characters in the story guesses that the numbers must represent a gigantic "Godel number", factorizable in the form (2^k2)*(3^k3)*(5^k5)*…(pn^kn) with non-zero exponents kj. The string of k’s is then supposed to be holding a secret message.
The author mentions that the number system used is base-12 but then ends up reverting to base 10 while counting the number of lines on the stones. The inscribed "Godel number" is conjectured to be 17^19 + 39^(27^45) + 12^[41^(37^43)] (not sure if this IS a Godel number. Quite doubtful). The decoded message shows the geographical location of an alien/ancient civilizations library of knowledge, also encoded in Godel numberings on thousands of stone artifacts. Indeed, part of the knowledge base includes information on curing lymphosarcoma….Godel’s incompleteness theorems play no part in the story but the author has taken a brief stab at explaining it. There is some Russian espionage thrown in as well but that story thread is left dangling and incomplete.
The story assumes that in 1968, we had the capability of factoring such large numbers easily, which we don’t even now. The story really should have been set in the future and some made-up theorem used to get around this difficulty of factoring. Further, since the message is designed to survive "millions of years", it would have been a nice touch to have a much older artifact, show that the date of its creation was obtained based on encoded information about relative star positions and then have the physical location of the library obtained by correcting for continental drift. Having the artifact dated at 3000 BC is anachronistic if the originator were an earth civilization. In any case, the author has done a nice job of explaining the deciphering of the map.
Overall, a very good idea for math sci fi. Would have worked well in a Dan-Brown-type novel.