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Every Even Number Greater than 2 is the Sum of Two Primes

Posted by C Moon on November 23, 2007

Every even number greater than 2 is the sum of two primes.


The above proposition is notorious Goldbach’s Conjecture, which remained unsolved for two hundred and fifty years. We can check empirically that the proposition holds for small even numbers.

and so on.

But unless we prove it for all even numbers, we cannot call it a theorem. There are always possibilities that it holds for small even numbers and fails to hold for extremely large even numbers. Then, can we prove it definitely?

Uncle Petros and Goldbach’s Conjecture is a mathematics novel. But it does not require mathematical knowledge in enjoying it. The plot evolves around Goldbach’s Conjecture and a mathematician, who devoted his whole life in trying to prove it. Through Uncle Petros’ life-long devotion to this seemingly simple proposition, the novel reveals the passion, tolerance, and efforts that mathematicians pour into their studies. Uncle Petros, a key figure in the novel, is in some sense a tragic hero who is hubristic. He thinks that mathematics is only for the “talented,” and deters his nephew from becoming a mathematician. He is bewitched by the Conjecture and continues to search for a solution, but he does not cooperate or share his byproducts with other mathematicians, believing he alone will be the one to prove it. In his early 20s he was praised as a genius, but in later years his pride made him an isolated mathematician with no tangible mathematical exploit. He became exhausted and died with his works unpublished.

The following is part of a short posting that I’ve found on the internet, reflecting the book’s charm.

Name a book you own that you think no one else on your friends list does: Uncle Petros and the Goldbach Conjecture(Apostolos Doxiadis). I’m hoping this will change, though. Cool Math novel!

The author himself is a mathematician, but he does not talk about details on Goldbach’s Conjecture. Rather, he hints that the proof on Goldbach’s Conjecture may not be possible by introducing into the story Kurt Godel’s Incompleteness Theorems that some mathematical problems can never be resolved. Difficulties in seemingly simple propositions are the charm of mathematics. I am especially moved by the sentence, “Every person has the right to expose himself to whatever disappointment he chooses.” As far as I understand, the author asks us to aim high rather than take an easy path.
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Photo Credits: front cover of Uncle Petros and Goldbach’s Conjecture, taken by myself

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