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...
View ArticleAnswer by MvG for Examples of mathematical results discovered "late"
Pascal's theorem was discovered in 1639 or 1640, but its projective dual, Brianchon's theorem, was only discovered in 1806. So it took about 167 years despite the fact that Pascal already realized the...
View ArticleAnswer by Marco13 for Examples of mathematical results discovered "late"
The first thing that came to my mind was the Kepler conjecture. While it's not a straightforward or simple proof, the fact that fruitsellers stacked their apples optimally for thousands of years until...
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Answer by Jose Antonio for Examples of mathematical results discovered "late"
This is not a theorem but a result which was discovered "too late". The number $e$ hiding inside Pascal's triangle was found it by Harlan Brothers in 2012, in a very simple way!
View ArticleAnswer by ljfa for Examples of mathematical results discovered "late"
How about the Jordan curve theorem? It seems obvious at first sight, but it is quite complicated to prove.
View ArticleAnswer by user1729 for Examples of mathematical results discovered "late"
Generally the JSJ-decomposition of 3-manifolds is considered to be discovered "late" (by $40$ years, but that is a long time in modern maths!).From Allen Hatcher's Notes on Basic 3-Manifold...
View ArticleAnswer by Per Erik Manne for Examples of mathematical results discovered "late"
A Dandelin sphere of a conic section will touch the plane of the conic section at a focus of the conic section. This pretty and useful fact was discovered only in 1822, but there is no reason why it...
View ArticleAnswer by sicklybeans for Examples of mathematical results discovered "late"
I got three of them for you.Trisecting the angle, doubling the cube, and squaring the circle. They were three famous geometric problems from ancient Greece. They were concerned about whether or not...
View ArticleAnswer by Wonkman123 for Examples of mathematical results discovered "late"
One possible answer would be the discovery of Strassen algorithm in 1969. This is a way to multiply large matrices together in (slightly) faster than standard time. Although it may not be the fastest...
View ArticleAnswer by zyx for Examples of mathematical results discovered "late"
Brouwer's demonstrations of the difficulties with classical logic and the excluded-middle principle (tertium non datur), which had been used in mathematics and logic for more than 2000 years.The...
View ArticleAnswer by Konstantinos Gaitanas for Examples of mathematical results...
This is not a theorem but a result as you require that was discovered "late" . As Erdős mentions : "At that time,mathematicians of the seventeenth and eighteenth centuries found pairs of odd amicable...
View ArticleAnswer by Shane for Examples of mathematical results discovered "late"
I'd say the fact that zero took until sometime after the 600s before it was used in math takes the cake here.
View ArticleAnswer by user127688 for Examples of mathematical results discovered "late"
An example of this that jumps to my mind is Fermats last theorem, for which was conjectured by him in 1637 but only proved in 1995 despite many years work by countless mathematicians. But this proof...
View ArticleAnswer by Martín-Blas Pérez Pinilla for Examples of mathematical results...
An example mentioned for Martin Gardner (Martin Gardner's New Mathematical Diversions from Scientific American): Morley's trisector theorem is elementary enough to be proved two millenia ago, but...
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Answer by MJD for Examples of mathematical results discovered "late"
This proof of the irrationality of $\sqrt 2$ appears to have been discovered in 1892 by A.P. Kiselev:If $\sqrt2$ is rational, let $\triangle ABO$ be the smallest possible isosceles right triangle whose...
View ArticleExamples of mathematical results discovered "late"
What are examples of mathematical results that were discovered surprisingly late in history? Maybe the result is a straightforward corollary of an established theorem, or maybe it's just so simple that...
View ArticleAnswer by azimut for Examples of mathematical results discovered "late"
AnswerMirsky's theorem (1971) in order theory has been discovered late.BackgroundIn 1950, Robert Dilworth published what is today known as Dilworth's theorem:In any finite poset $(X,\leq)$, the size of...
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