Uncle Petros and Goldbach's Conjecture

I interrupted the main book I’ve been reading lately (Cryptonomicon) to read “Uncle Petros and Goldbach’s Conjecture”. It is by Apostolos Doxiadis, translated from Greek by the author. The author is a mathematician and the subject matter is the struggle of a mathematician, Uncle Petros, to prove an unproven proposition – Goldbach’s Conjecture – viz. according to the author, every even number greater than 2 is the sum of two prime numbers. It seems though that the real Goldbach conjecture, written in 1742 states "that every number that is greater than 2 is the sum of three primes". Maybe something got lost in Doxiadis’ translation, or he just included this as part of this fiction? It was a delightful light read, most interesting, and a wonderful diversion. Ok, I have to admit too that the fact the author was Greek (a major part of my ethnic heritage) and the subject matter was mathematics (my original post-secondary academic love) drew me to this book. I was also intrigued by the staircase design on the cover which was drawn in a depiction of what I’ve normally seen fractals represented as. There are two levels to the story.

First, there is the mathematics. Not the number crunching, calculation type of math. It’s described in the book as grocery bill math. Neither is it the equational type of math you think of in algebra or calculus. Rather it is about types of math, whether it be logic, universal algebra, number theory, etc. being used as tools to solve complex mathematical hypotheses. So in a sense it is what I would describe as meta-math – math about math. It really is looking at it from a different level. That really stretched my mind because my studies never got to that level. I was still back at the learning the tools stage: calculus, logic, set theory, modern geometry, universal algebra, etc. Would have been fun to get to that next stage!

The second level is the human story of the quest of Uncle Petros. He works hard. He makes the mistake of not sharing his intermediate results which would have been considered ground breaking and worthy of notable publication. He seems on the verge of solving it. But then he gets negative feedback from well placed colleagues. He retires to the family property in Greece, shunning the scientific world. He interacts with a nephew who Uncle Petros tries to dissuade from becoming a mathematician. That eventually succeeds and the nephew studies business, after doing an initial degree in math. Later he draws out his uncle, who we are lead to believe discovers the solution, but dies of a stroke before the proof is documented. Tragic. Some side stories of family relations. I really felt the Greek family celebrations. Touching stories too of two brothers of Uncle Petros who run the family business and support Uncle Petros financially. Should one pursue one’s dreams? Should one be practical and support one-self? Should he have given up on the basis that the Conjecture was unproveable, or persevered?