Inter-universal geometry と ABC予想 (応援スレ) 45

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 45 (1002ﾚｽ)
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841: 現代数学の系譜 雑談 ◆e.a0E5TtKE  [] 2020/05/16(土) 12:57:48.40 ID:I/5uqoYj

>>837
>だといいんだけど何だか怖いね
>初等的な証明ができないからと命題を疑いもしない感じがして

それは、一般論としては いままであったし、これからもあるでしょうね
IUTとは、ちょっと切り離した方がいいですね

（参考）
https://en.wikipedia.org/wiki/List_of_incomplete_proofs
List of incomplete proofs

・Fundamental theorem of algebra (see History). Many incomplete or incorrect attempts were made at proving this theorem in the 18th century, including by d'Alembert (1746), Euler (1749), de Foncenex (1759), Lagrange (1772), Laplace (1795), Wood (1798), and Gauss (1799). The first rigorous proof was published by Argand in 1806.

・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.

・The proofs of the Kronecker?Weber theorem by Kronecker (1853) and Weber (1886) both had gaps. The first complete proof was given by Hilbert in 1896.

・In 1905 Lebesgue tried to prove the (correct) result that a function implicitly defined by a Baire function is Baire, but his proof incorrectly assumed that the projection of a Borel set is Borel. Suslin pointed out the error and was inspired by it to define analytic sets as continuous images of Borel sets.

・ Class numbers of imaginary quadratic fields. In 1952 Heegner published a solution to this problem. His paper was not accepted as a complete proof as it contained a gap, and the first complete proofs were given in about 1967 by Baker and Stark. In 1969 Stark showed how to fill the gap in Heegner's paper.

http://rio2016.5ch.net/test/read.cgi/math/1588552720/841

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