Answer by Bananach for Examples of mathematical results discovered "late"
The Meyers Serrin theorem that $ H=W $ (see their paper with exactly this equality as title) came only decades after people had proven all kinds of things with both $ H $ and $ W $, and is so...
View ArticleAnswer by Josse van Dobben de Bruyn for Examples of mathematical results...
Various irrationality and transcendence results have already been posted, but it is interesting to see that the mere existence of transcendental numbers was not proven until the nineteenth century. Of...
View ArticleAnswer by gamma for Examples of mathematical results discovered "late"
Find an explicit bijection between $\mathbb N$ and $\mathbb Q^{+}$.The countability of $\mathbb Q^{+}$ had been known for a century, but an explicit bijection was not known until, in $1989$, Yoram...
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Answer by Rodrigo A. Pérez for Examples of mathematical results discovered...
The Perko pair:Since the first knot tables published around 1900, these two were thought to be different knots. The mistake slipped by Alexander's (1920s), Conway's (1960s), and Rolfsen's (1970s)...
View ArticleAnswer by Zhipu 'Wilson' Zhao for Examples of mathematical results discovered...
The one that bumps up in my mind is Erdos-Mordell inequality. It states that for a point $ p $ in a triangle $ ABC $, with $\alpha ,\beta,\gamma $ denoting the distance of $ P $ to the 3...
View ArticleAnswer by user3063896 for Examples of mathematical results discovered "late"
Smale's paradox: in topology, the fact a sphere in R3 can be turned completely inside out without tears or sharp creases (self-intersection is allowed) was only indirectly proved in 1957 and an actual...
View ArticleAnswer by Lenar Hoyt for Examples of mathematical results discovered "late"
James A. Garfield (20th President of the United States) found 1875 (~2175 years after Euclid) a quite simple, yet clever trapezoid proof of the Pythagorean theorem. Here is a video explaining...
View ArticleAnswer by KalEl for Examples of mathematical results discovered "late"
The Futurama Theorem: Regardless of how many mind switches between two bodies have been made, they can still all be restored to their original bodies using only two extra people, provided these two...
View ArticleAnswer by Doug Spoonwood for Examples of mathematical results discovered "late"
The Deduction Meta-Theorem for slews of logical calculi, and slews of conditional proofs in ordinary mathematics which can get said to have an interaction with it.
View ArticleAnswer by Alexander Gruber for Examples of mathematical results discovered...
Grothendieck said that he found it embarassing that it took humanity so long to define a group.
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Answer by ocg for Examples of mathematical results discovered "late"
Theorem $\big($Sylvester-Gallai$\big):$ For any $n$ points in $\mathbb{R}^2$, not all collinear, there exists a line passing through exactly two of them.$\rm{Proof}:$ Pick any $2$ points and draw a...
View ArticleAnswer by John M for Examples of mathematical results discovered "late"
The binary GCD algorithm was only discovered (re-discovered?) in 1967.
View ArticleAnswer by MJD for Examples of mathematical results discovered "late"
I'm not sure this is a real answer, but Wikipedia claims that the Möbius strip was invented in 1858, by Möbius. I find it incredible that there is any property of the strip that was still undiscovered...
View ArticleAnswer by Marco13 for Examples of mathematical results discovered "late"
Another result that seems to have appeared late is the AKS primality test ( http://en.wikipedia.org/wiki/AKS_primality_test ). Although the field of computational compexity is relatively new, one could...
View ArticleAnswer by Marco13 for Examples of mathematical results discovered "late"
Another result that was discovered late is the construction of the Heptadecagon (regular seventeen-sided polygon) by compass and unmarked straightedge, found by Gauß in 1796. Wikipedia describes it as...
View ArticleAnswer by KCd for Examples of mathematical results discovered "late"
The Mason-Stothers theorem (aka the $abc$ conjecture for polynomials): if $f(t)$, $g(t)$, and $h(t)$ are nonzero polynomials over a field satisfying $f(t) + g(t) = h(t)$ with $f(t)$ and $g(t)$ being...
View ArticleAnswer by azimut for Examples of mathematical results discovered "late"
The theorem that$$\text{PRIMES is in P}$$was proven only in 2002 (via the AKS primality test). The algorithm certainly isn't rocket science, making it quite surprising that this wasn't found way...
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Answer by azimut for Examples of mathematical results discovered "late"
Informally, the historical definition of an Archimedean solid requires that all its faces are regular polygons and that each vertex of the solid locally looks the same. Since the ancient Greeks it was...
View ArticleAnswer by D Wiggles for Examples of mathematical results discovered "late"
It took 2000 years for anyone to recognize that Euclid's Parallel Postulate didn't follow from his other four axioms. It has always been surprising to me that people tried for so long to prove the...
View ArticleAnswer by Martin Argerami for Examples of mathematical results discovered "late"
Apéry's 1975 proof of the irrationality of of $\zeta(3)=\sum_{n=1}^\infty\frac1{n^3}$ took the experts by surprise, and uses tools that had been available for a very long time. See A Proof that Euler...
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