Klaus Roth publishes in 1955, in Mathematika, the proof of what is now known as the Thue-Siegel-Roth theorem: for any irrational algebraic number, the number of "very good" rational approximations is finite, optimally fixing the approximation exponent at 2. The result closes a line of research begun by Axel Thue in 1909 and continued by Carl Ludwig Siegel in 1921, solving a problem Siegel himself described as one of the most eagerly awaited in number theory. Siegel remarked in a letter to Harold Davenport that the result "will be remembered as long as mankind is interested in mathematics." Roth received the Fields Medal in 1958.