big list - Examples of interesting false proofs - MathOverflow
2012年5月19日 · False proof: The two groups have different cardinalities, since there are $2^\kappa$ many permutations of an infinite set of size $\kappa$, and $\kappa\lt\lambda$ implies $2^\kappa\lt 2^\lambda$. QED. See the question: Can the symmetric groups on sets of differing infinite cardinalities be isomorphic? for further information and a correct proof.
ho.history overview - Widely accepted mathematical results that …
C.S. Peirce in his 1903 Harvard lectures on pragmatism says:"Mr. Alfred B. Kempe, proposed a proof of it, somewhat, though not exactly, of the kind we are supposing our imaginary inventor to be aiming at. Yet I am informed that many years later a …
Are there mistakes in the proof of FLT? - MathOverflow
2021年11月19日 · No there are not any mistakes in these papers of any interest. In the 1990s there were a bazillion study groups and seminars across the world devoted to these papers; I personally read all three of the papers you cite, back in the days when I was young and an expert in this area, and they all looked fine to me, and they all looked fine to all the people who were at the IAS with me in 1995 ...
What are some correct results discovered with incorrect (or no) …
Heegner's proof in 1952 that there is no tenth imaginary quadratic field of class number one is an interesting example. It was thought to be incorrect because of some gaps. Stark gave a correct proof in 1967 and explained how it was essentially the same as Heegner's proof. In 1969 Stark formally filled in the gap in Heegner's proof.
Why should I trust Coq when assumption-free proof of False in …
Damien Pous announced code for assumption-free proof of False in Coq which means inconsistency in Coq (without using exploits, lol). Damien is critical of "fully certified decision procedure returning wrong results"
Awfully sophisticated proof for simple facts - MathOverflow
There is a Fourier analytic proof for Sperner's theorem which is much more complicated than the combinatorial proof (and give less in certain respects). This was part pf the polymath1 project. A general point is that sometime trying to prove a Theorem X using method Y is valuable even if the proof is much more complicated than needed.
Examples of common false beliefs in mathematics
This is another very widespread false belief. It depends on personal opinion and interpretation what a proof by contradiction is and whether Euclid's proof belongs to this category. In fact, if the derivation of an absurdity or the contradiction of an assumption is a proof by contradiction, then Euclid's proof is a proof by
Consequences of the Riemann hypothesis - MathOverflow
2015年5月23日 · p) Proof of André-Oort conjecture. In 2014, Klingler and Yafaev showed GRH for zeta-functions of CM number fields implies the André-Oort conjecture. Daw and Orr gave another proof also using the same version of GRH. Update: This is now an obsolete application of GRH since the André-Oort conjecture has been proved without GRH. See here.
Theorems that are 'obvious' but hard to prove - MathOverflow
The formulation says (or at least immediately implies) that a certain 3-manifold (the trefoil complement) is not the solid torus. The proof is about as straightforward as any statement about 3-manifolds could possibly be. Moreover, the proof was found almost immediately when the techniques existed- it was never an "open problem".
Examples of conjectures that were widely believed to be true but …
Kolmogorov proved results in 1928 which seemed to suggest that Luzin's conjecture must be false but Carleson amazed the world of mathematics when he proved Luzin's long-standing conjecture in 1966. He explained how he was led to prove the theorem:-