Timeline of Number Theory - 20th Century

20th Century

• 1903 - Edmund Georg Hermann Landau gives considerably simpler proof of the prime number theorem.
• 1909 - David Hilbert proves Waring's problem.
• 1912 - Josip Plemelj publishes simplified proof for the Fermat's Last Theorem for exponent n = 5.
• 1913 - Srinivasa Aaiyangar Ramanujan sends a long list of complex theorems without proofs to G. H. Hardy.
• 1914 - Srinivasa Aaiyangar Ramanujan publishes Modular Equations and Approximations to π.
• 1910s - Srinivasa Aaiyangar Ramanujan develops over 3000 theorems, including properties of highly composite numbers, the partition function and its asymptotics, and mock theta functions. He also makes major breakthroughs and discoveries in the areas of gamma functions, modular forms, divergent series, hypergeometric series and prime number theory.
• 1919 - Viggo Brun defines Brun's constant B₂ for twin primes.
• 1937 - I. M. Vinogradov proves Vinogradov's theorem that every sufficiently large odd integer is the sum of three primes, a close approach to proving Goldbach's weak conjecture.
• 1949 - Atle Selberg and Paul Erdős give the first elementary proof of the prime number theorem.
• 1966 - Chen Jingrun proves Chen's theorem, a close approach to proving the Goldbach conjecture.
• 1967 - Robert Langlands formulates the influential Langlands program of conjectures relating number theory and representation theory.
• 1983 - Gerd Faltings proves the Mordell conjecture and thereby shows that there are only finitely many whole number solutions for each exponent of Fermat's Last Theorem.
• 1994 - Andrew Wiles proves part of the Taniyama–Shimura conjecture and thereby proves Fermat's Last Theorem.
• 1999 - the full Taniyama–Shimura conjecture is proved.