1968, and a complete proof was not given until 1984. Mordell conjecture over function fields. Manin published a proof in 1963, but found and corrected a gap in the proof. In 1973 Britton published a 282-page attempted solution of Burnside's problem. In his proof he assumed the existence of a set of parameters satisfying some inequalities, but Adian pointed out that these inequalities were inconsistent. Novikov and Adian had previously found a correct solution around 1968. Classification of finite simple groups. In 1983, Gorenstein announced that the proof of the classification had been completed, but he had been misinformed about the status of the proof of classification of quasithin groups, which had a serious gap in it. A complete proof for this case was published by Aschbacher and Smith in 2004. Kepler conjecture. Hsiang published an incomplete proof of this in 1993. In 1998 Hales published a proof depending on long computer calculations. Incorrect results In 1759 Euler claimed that there were no closed knight tours on a chess board with 3 rows, but in 1917 Ernest Bergholt found tours on 3 by 10 and 3 by 12 boards. Euler's conjecture on Graeco-Latin squares. In the 1780s Euler conjectured that no such squares exist for any oddly even number n ≡ 2 (mod 4). In 1959, R. C. Bose and S. S. Shrikhande constructed counterexamples of order 22. Then E. T. Parker found a counterexample of order 10 using a one-hour computer search. Finally Parker, Bose, and Shrikhande showed this conjecture to be false for all n ≥ 10. In 1798 A. M. Legendre claimed that 6 is not the sum of 2 rational cubes, which as Lamé pointed out in 1865 is false as 6 = (37/21)3 + (17/21)3. In 1803, Gian Francesco Malfatti claimed to prove that a certain arrangement of three circles would cover the maximum possible area inside a right triangle. However, to do so he made certain unwarranted assumptions about the configuration of the circles. It was shown in 1930 that circles in a different configuration could cover a greater area, and in 1967 that Malfatti's configuration was never optimal. See Malfatti circles. In 1806 André-Marie Ampère claimed to prove that a continuous function is differentiable at most points (though it is not entirely clear what he was claiming as he did not give a precise definition of a function). However, in 1872 Weierstrass gave