shown the existence of Fuchsian differential equations with any given monodromy group, but in 1989 Bolibruch discovered a counterexample. In 1925 Ackermann published a proof that a weak system can prove the consistency of a version of analysis, but von Neumann found an explicit mistake in it a few years later. Gödel's incompleteness theorems showed that it is not possible to prove the consistency of analysis using weaker systems. Groups of order 64. In 1930 Miller published a paper claiming that there are 294 groups of order 64. Hall and Senior showed in 1964 that the correct number is 267. Church's original published attempt in 1932 to define a formal system was inconsistent, as was his correction in 1933. The consistent part of his system later became the lambda calculus. Kurt Gödel proved in 1933 that the truth of a certain class of sentences of first-order arithmetic, known in the literature as [∃*∀2∃*, all, (0)], was decidable. That is, there was a method for deciding correctly whether any statement of that form was true. In the final sentence of that paper, he asserted that the same proof would work for the decidability of the larger class [∃*∀2∃*, all, (0)]=, which also includes formulas that contain an equality predicate. However, in the mid-1960s, Stål Aanderaa showed that Gödel's proof would not go through for the larger class, and in 1982 Warren Goldfarb showed that validity of formulas from the larger class was in fact undecidable. Grunwald–Wang theorem. Wilhelm Grunwald published an incorrect proof in 1933 of an incorrect theorem, and George Whaples later published another incorrect proof. Shianghao Wang found a counterexample in 1948 and published a corrected version of the theorem in 1950. In 1934 Severi claimed that the space of rational equivalence classes of cycles on an algebraic surface is finite-dimensional, but showed that this is false for surfaces of positive geometric genus. Quine published his original description of the system Mathematical Logic in 1940, but in 1942 Rosser showed it was inconsistent. Wang found a correction in 1950; the consistency of this revised system is still unclear. One of many examples from algebraic geometry in the first half of the 20th century: claimed that a degree-n surface in 3-dimensional projective space has at most ()−4 nodes, B. Segre pointed out that this was wrong; for example, for degree 6 the maximum number of nodes is 65, achieved by