Answer by Olaf Teschke for Widely accepted mathematical results that were...
Recently, Alberto Facchini and Jennifer Parolin A little mistake in a paper by Bob Gilmer on rngs, Zbl 07660836 noticed a minor error in R. W. Gilmer jun.'s classic paper Eleven nonequivalent...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
Very recently, Prasit Bhattacharya and Nitu Kitchloo [The stable Adams conjecture and higher associative structures on Moore spectra, Zbl 07483861] showed that Friedlander's proof of the stable Adams...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
R. V. Gurjar and M. Miyanishi [Affine surfaces with $\bar {\kappa}\leq 1$, Algebraic geometry and commutative algebra, in Honor of Masayoshi Nagata, Vol. I, 99-124 (1988) ZBL0707.14015] gave a...
View ArticleAnswer by Chandan Singh Dalawat for Widely accepted mathematical results that...
Couldn't resist quoting Conway (https://www.maths.ed.ac.uk/~v1ranick/books/dublin.pdf, p. 24) :For nearly 50 years it has been supposed that the universality problemfor quaternary integer-matrix forms...
View ArticleAnswer by Harry Altman for Widely accepted mathematical results that were...
Not sure how widely known this one is, but I've seen it mentioned on e.g. Wikipedia, so I figured I'd post it.This paper by Gagola claimed that the commutant of a Moufang loop (the subloop of elements...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
The PBW theorem of Rinehart [Rinehart, G. S., Differential forms on general commutative algebras, Trans. Am. Math. Soc. 108, 195-222 (1963). ZBL0113.26204] is not true in the claimed generality, as...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
Due to the relative obscurity of the journal (and the relatively obvious mistake), this would perhaps rarely count as "widely accepted", but it was used in later publications: E. Habil claimed in...
View ArticleAnswer by Gerry Myerson for Widely accepted mathematical results that were...
Aristotle stated as a fact that the regular tetrahedron tiles space. This was accepted and repeated in commentaries on Aristotle for 1800 years, until Regiomontanus showed it was wrong. A detailed...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
Very recently, Dobbs A minimal ring extension of a large finite local prime ring is probably ramified, ZBL 07192436. identified an error in the proof that "a separable extension of finite rings is...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
In 1892, Michel Frolov Equalities of the second and third degree, Bull. Soc. Math. Fr. 20, 69-84 (1892). JFM 24.0176.01. claimed a proof that there are no 7th-order bimagic squares, since there is no...
View ArticleAnswer by Olaf Teschke for Widely accepted mathematical results that were...
A recent example: The main theorem of [Masa-Hiko Saito, On the infinitesimal Torelli problem of elliptic surfaces, J. Math. Kyoto Univ. 23, 441-460 (1983). ZBL 0532.14019] has been shown to be...
View ArticleAnswer by Panagiotis Konstantis for Widely accepted mathematical results that...
Pontryagin made a famous mistake in A classification of continuous transformations of a complex into a sphere which led him to the false conclusion that the homotopy group $\pi_{n+2}(S^n)$ is zero....
View ArticleAnswer by Kimball for Widely accepted mathematical results that were later...
Grunwald's Theorem (1933) says that an element of a number field is an $n$-th power if and only if it is locally almost everywhere. As anyone who studied number theory now should guess, there is a...
View ArticleAnswer by none for Widely accepted mathematical results that were later shown...
This thread doesn't seem to mention Gauss's first proof of the fundamental theorem of algebra, from 1799. He claimed it as the first really rigorous proof, but it had a topological gap discovered 120...
View ArticleAnswer by Yemon Choi for Widely accepted mathematical results that were later...
The following is very far from my areas of competence, but I think it would fit the bill if the authors are correct:https://arxiv.org/abs/1801.06359L. Rempe-Gillen, D. Sixsmith, On connected preimages...
View ArticleAnswer by Timothy Chow for Widely accepted mathematical results that were...
No less a mathematician than Kurt Gödel was guilty of claiming to have proved a result that was accepted for decades, and even used by others, before being shown to be wrong. Stål Aanderaa showed that...
View ArticleAnswer by Timothy Chow for Widely accepted mathematical results that were...
I'm surprised that this one has not already been mentioned. Voevodsky wrote an article explaining that one of the main motivations for his interest in homotopy type theory and univalent foundations was...
View ArticleAnswer by Bruno for Widely accepted mathematical results that were later...
The wronskian determinant of $n$ functions which are $(n-1)$ times differentiable is$$W(f_1,\dotsc,f_n)=\det\begin{pmatrix} f_1 & f_2 & \dots & f_n\\ f_1'& f_2'& \dots & f_n'\\...
View ArticleAnswer by fretty for Widely accepted mathematical results that were later...
I guess one major example is that unique factorisation doesn't always hold in rings of integers of number fields.Classical attempts at solving Fermat's Last Theorem resulted in moving to cyclotomic...
View ArticleAnswer by KConrad for Widely accepted mathematical results that were later...
Any rational function field over a finite field has genus $0$ and class number $1$, where the class number of a function field over a finite field is the number of degree-zero elements of the divisor...
View ArticleAnswer by Alexey Ustinov for Widely accepted mathematical results that were...
Hilbert's sixteenth problem. In his speech, Hilbert presented the problems as:The upper bound of closed and separate branches of an algebraic curve of degree n was decided by Harnack (Mathematische...
View ArticleAnswer by bof for Widely accepted mathematical results that were later shown...
Lebesgue famously "proved" that the projection of a Borel set in $\mathbb R^2$ is a Borel set in $\mathbb R$. Famously disproved by Souslin a decade later. See this answer by Gerald Edgar.
View ArticleAnswer by Sean Lawton for Widely accepted mathematical results that were...
The Auslander Conjecture states: Every crystallographic subgroup $\Gamma$ of $\mathrm{Aff}(\mathbb{R}^n)$ is virtually solvable, i.e. contains a solvable subgroup of finite index.He published an...
View ArticleAnswer by C. Yang for Widely accepted mathematical results that were later...
The Steiner Ratio Gilbert–Pollak Conjecture was proved by Dingzhu Du and Frank Hwang in 1990, and published in Algorithmica in 1992. In 2001, a gap of the original proof was found by A.O. Ivanov and...
View ArticleAnswer by Vlad Niculae for Widely accepted mathematical results that were...
This blog post, the previous one (linked inside) and the addendum caused by reader response, treat exactly this question, including Euler's polyhedra formula from Micah Miller's response.
View ArticleAnswer by Alain Valette for Widely accepted mathematical results that were...
Carmichael's totient function conjecture (stating that the equation $\phi(x)=n$ never has a unique solution) was a theorem until an error was found in 1922 (apparently after the proof was left as an...
View ArticleAnswer by Alex Eskin for Widely accepted mathematical results that were later...
In 1959 Kravetz published a proof that the Teichmüller metric on Teichmüller space is negatively curved in the sense of Buseman. This was widely quoted and used until Linch found a gap in 1971.In 1974,...
View ArticleAnswer by George Jelliss for Widely accepted mathematical results that were...
Euler in his 1759 paper on knight's tours claimed that closed tours were not possible on any board with 4 or fewer ranks, though he gave no explicit proof. The claim was repeated by other influential...
View ArticleAnswer by roy smith for Widely accepted mathematical results that were later...
I heard that Bott's theorem on the periodicity of the stable homotopy of the unitary group was delayed for some time by an erroneous computation in dimension 10, possibly due to Pontryagin.
View ArticleAnswer by Gerry Myerson for Widely accepted mathematical results that were...
Another one from Grunbaum's paper:According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010,...
View ArticleAnswer by Steven Landsburg for Widely accepted mathematical results that were...
This thread on the Italian tradition in algebraic geometry contains some important examples.
View ArticleAnswer by Gerry Myerson for Widely accepted mathematical results that were...
According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010, Andreini in 1905 claimed that there are...
View ArticleAnswer by Gerry Myerson for Widely accepted mathematical results that were...
According to Branko Grunbaum, An enduring error, Elemente der Mathematik 64 (2009) 89-101, reprinted in Mircea Pitici, ed., The Best Writing On Mathematics 2010, Daublebsky in 1895 found that there are...
View ArticleAnswer by Beren Sanders for Widely accepted mathematical results that were...
The Busemann-Petty problem (posed in 1956) has an interesting history. It asks the following question: if $K$ and $L$ are two origin-symmetric convex bodies in $\mathbb{R}^n$ such that the volume of...
View ArticleAnswer by Peter Arndt for Widely accepted mathematical results that were...
Here is a list of counterexamples to once accepted theorems on Clifford algebras.Edit: The original link is broken, I now replaced it by a pointer to the wayback machine. Alternatively, here are two of...
View ArticleAnswer by Matthieu Romagny for Widely accepted mathematical results that were...
In a 1966 paper (Rational surfaces over perfect fields, Publ. Math. IHES), Manin gave examples of cubic surfaces with Brauer group of order 2. In 1996, Urabe proved a conjecture of Tate on The bilinear...
View ArticleAnswer by Marko Amnell for Widely accepted mathematical results that were...
In 1803, Gian Francesco Malfatti proposed a solution to the problem of how to cut out three circular columns of marble of maximal area from a triangular piece of stone. Malfatti's solution was three...
View ArticleAnswer by Daniel Moskovich for Widely accepted mathematical results that were...
In 1993, Pat Gilmer asserted as Theorem 1 of Classical knot and link concordance, that certain Casson-Gordon invariants vanish for all slice knots, which would be true if the kernel of the inclusion...
View ArticleAnswer by Misha Verbitsky for Widely accepted mathematical results that were...
The (in)famous Jacobian Conjecture was considered a theoremsince a 1939 publication by Keller (who claimed to prove it).Then Shafarevich found a new proof and published it in someconference proceedings...
View ArticleAnswer by Matheus for Widely accepted mathematical results that were later...
This question reminded me of the following article of A. Neeman with an appendix by P. Deligne:Neeman, Amnon, A counterexample to a 1961 “theorem” in homological algebra, Invent. Math. 148, No. 2,...
View ArticleAnswer by Adam Gal for Widely accepted mathematical results that were later...
Verma proved that the multiplicities of all simple modules in a verma module are 1 or 0.When BGG tried to repeat his proof for some other case they found an error. This led to the study of...
View ArticleAnswer by Jose Brox for Widely accepted mathematical results that were later...
In the 1960s, John Horton Conway verified the Nineteenth Century efforts of Tait and Little to tabulate all the knots through alternating 11 crossings (1). He found several omissions and one...
View ArticleAnswer by Will Jagy for Widely accepted mathematical results that were later...
EDIT: The episode I had in mind turns out to be the work of Robert Coleman repairing a gap in a paper by Manin about the Mordell conjecture over function fields. See comments by KConrad below, giving...
View ArticleAnswer by Greg Graviton for Widely accepted mathematical results that were...
(I don't have enough rep to comment on KConrad's answer, hence this additional answer.)On the matter of Cauchy's "mistaken" proof that a convergent infinite series of continuous functions is...
View ArticleAnswer by Daniel Asimov for Widely accepted mathematical results that were...
One part of Hilbert's 16th problem is to determine whether a polynomial vector field in $\mathbb R^2$,$$V(x,y) = (P(x,y),Q(x,y)),$$has at most a finite number of limit cycles.In 1923, Dulac published a...
View ArticleAnswer by Micah Miller for Widely accepted mathematical results that were...
The Euler Characteristic $V-E+F$ has an interesting history. It was initially stated that, for all polyhedra:$$V(\text{vertices})-E(\text{edges})+F(\text{faces})=2$$and its proof was widely accepted,...
View ArticleAnswer by KConrad for Widely accepted mathematical results that were later...
Mathematicians used to hold plenty of false, but intuitively reasonable, ideas in analysis that were backed up with proofs of one kind or another (understood in the context of those times). Coming to...
View ArticleAnswer by John Stillwell for Widely accepted mathematical results that were...
Hilbert's 21st problem, on the existence of linear DEs with prescribedmonodromy group, was for a long time thought to have been solved byPlemelj in 1908. In fact, Plemelj died in 1967 still believing...
View ArticleAnswer by dvitek for Widely accepted mathematical results that were later...
Kempe's "proof" of the four-color theorem springs to mind. Wikipedia says that Kempe published it in 1879 and it was proven to be incorrect by Heawood in 1890. As I recall, the flaw in the original...
View ArticleWidely accepted mathematical results that were later shown to be wrong?
Are there any examples in the history of mathematics of a mathematical proof that was initially reviewed and widely accepted as valid, only to be disproved a significant amount of time later, possibly...
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