Nikolai Krogius, Russian GM and sports psychologist, summarized the state of knowledge regarding chess and aging and described his own research in his 1976 book, Psychology in Chess.
First, he dismisses US research :-)
In his dissertation, P. Buttenwisser (Stanford USA, 1935) advanced the opinion that a chess player preserves his optimal strength until the age of fifty. He came to this conclusion by analyzing the games of chess amateurs who did not participate in competitions regularly. For this reason Buttenwisser's findings cannot be regarded as convincingly demonstrated.
He is more impressed by the Soviet research of Stanislav Strumilin.
More serious research on the connection between the age of a chess player and his achievements was carried out by Soviet Academician, Strumilin. In his book Problems in the Economics of Labour (Moscow 1925) he made a statistical analysis of the results of 43 matches (1863 - 1911) and of 34 international tournaments (1890-1914). The participants in these competitions were divided into several age groups. Strumilin counted the total number of games played and then wins, losses and draws, and then compared the results for different age groups. He concluded that a chess player reached the peak of success between the ages of 32 and 33, after which there was a sharp fall in results, while after the age of 60 there was a catastrophic fall in the player's mental energy.
Krogius then describes his research into the subject. He differs from Strumilin, who considered wins, loses and draws, in that he considered tournament standings as more important. He examines the records of 32 great players ranging in time from Chigorin and Tarrasch through to Bottvinnik, Bondarevsky, Kotov and Boleslavsky and 125 tournaments from 1881 to 1967.
A chess player attains his best results at about the age of 35: his period of optimal and consistent results lasts somewhat longer than 10 years; it ranges between the ages of 30 and 40; some decrease in strength is observed usually around the age of 43 and a particularly noticeable decline starts at the age of 47.