an example of a continuous function that was not differentiable anywhere: The Weierstrass function. Intersection theory. In 1848 Steiner claimed that the number of conics tangent to 5 given conics is 7776 = 65, but later realized this was wrong. The correct number 3264 was found by Berner in 1865 and by Ernest de Jonquieres around 1859 and by Chasles in 1864 using his theory of characteristics. However these results, like many others in classical intersection theory, do not seem to have been given complete proofs until the work of Fulton and Macpherson in about 1978. Dirichlet's principle. This was used by Riemann in 1851, but Weierstrass found a counterexample to one version of this principle in 1870, and Hilbert stated and proved a correct version in 1900. incorrectly claimed that there are three different groups of order 6. This mistake is strange because in an earlier 1854 paper he correctly stated that there are just two such groups. Frege's foundations of mathematics in his 1879 book Begriffsschrift turned out to be inconsistent because of Russell's paradox, found in 1901. In 1885, Evgraf Fedorov classified the convex polyhedra with congruent rhombic faces, but missed a case. Stanko Bilinski in 1960 rediscovered the Bilinski dodecahedron (forgotten after its previous 1752 publication) and proved that, with the addition of this shape, the classification was complete. Wronskians. In 1887 Mansion claimed in his textbook that if a Wronskian of some functions vanishes everywhere then the functions are linearly dependent. In 1889 Peano pointed out the counterexample x2 and x|x|. The result is correct if the functions are analytic. published a purported example of an algebraic curve in 3-dimensional projective space that could not be defined as the zeros of 3 polynomials, but in 1941 Perron found 3 equations defining Vahlen's curve. In 1961 Kneser showed that any algebraic curve in projective 3-space can be given as the zeros of 3 polynomials. In 1898 Miller published a paper incorrectly claiming to prove that the Mathieu group M24 does not exist, though in 1900 he pointed out that his proof was wrong. Little claimed in 1900 that the writhe of a reduced knot diagram is an invariant. However, in 1974 Perko discovered a counterexample called the Perko pair, a pair of knots listed as distinct in tables for many years that are in fact the same. Hilbert's twenty-first problem. In 1908 Plemelj claimed to have