[Apostolos Doxiadis is the author of the bestselling novel of mathematics and obsession, “Uncle Petros and Goldbach’s Conjecture” (and, more recently, “Logicomix”). I’ve been to his house. It’s very nice. ]
OB: First things first: what is Goldbach’s conjecture? And why is it important?
AD: Goldbach’s Conjecture is the hypothesis that every even number greater than 2 (like 4, 6, 8 etc. ) can be written as the sum of two primes, i.e. two whole numbers whose sole divisors are the number 1 and themselves (like 2,3,5,7,11,13, etc.) This was first conjectured in 1742 by the German mathematician Christian Goldbach and, although it has now been checked to be true up to truly enormous numbers (at least up to 1014), no one has been able to find a general proof. And, the even numbers being infinite, we definitely need a general proof to call it a theorem, to be sure that it is a full mathematical truth. As to its importance: it seems to reflect (if true) a very basic insight about the way the primes (the building blocks of the number system, through multiplication) are distributed. Although Goldbach’s Conjecture sounds so ridiculously elementary it is so notoriously difficult — this certainly gives us the feeling that a truth of enormous importance lies concealed somewhere behind it. Read the rest of this entry »