edited by Yuan Wang (Academia Sinica, China)

This book provides a detailed description of a most important unsolved mathematical problem — the Goldbach conjecture. Raised in 1742 in a letter from Goldbach to Euler, this conjecture attracted the attention of many mathematical geniuses. Several great achievements were made, but only until the 1920's. The book gives an exposition of these results and their impact on mathematics, particularly, number theory. It also presents (partly or wholly) selections from important literature, so that readers can get a full picture of the conjecture.

• Representation of an Odd Number as the Sum of Three Primes:
  • A New Proof of the Goldbach–Vinogradov Theorem (J V Linnik)
  • A New Proof on the Three Primes Theorem (C B Pan)
  • An Elementary Method in Prime Number Theory (R C Vaughan)
  • A Complete Vinogradov 3- Primes Theorem under the Riemann Hypothesis (J M Deshouillers et al.)
• Representation of an Even Number as the Sum of Two Almost Primes (Elementary Approach):
  • New Improvements in the Method of the Sieve of Eratosthenes (A A Buchstab)
  • On Prime Divisors of Polynomials (P Kuhn)
  • On an Elementary Method in the Theory of Primes (A Selberg)
  • Lectures on Sieves (A Selberg)
• Representation of an Even Number as the Sum of a Prime and an Almost Prime:
  • On the Representation of large Integer as a Sum of a Prime and an Almost Prime (Y Wang)
  • The Density Hypothesis for Dirichlet L-Series (A I Vinogradov)
  • On the Large Sieve (E Bombieri)
  • and other articles