In the twentieth century work by Axel Thue, Carl Siegel, and Klaus Roth reduced the exponent in Liouville's work from "d" + ε to "d"/2 + 1 + ε, and finally, in 1955, to 2 + ε. This result, known as the Thue–Siegel–Roth theorem, is ostensibly the best possible, since if the exponent 2 + ε is replaced by just 2 then the result is no longer true. However, Serge Lang conjectured an improvement of Roth's result; in particular he conjectured that "q"2+ε in the denominator of the right-hand side could be reduced to "q"2 log("q")1+ε.