Liouville published Galois' work a decade after the death of this singular mathematician. Are there other cases of results being rescued by the mathematical community long after their authors were gone? Please include results whose importance went unnoticed at their time. Rediscoveries may be interesting too.
Ramanujan's Lost Notebook is one such collection of mathematical results. It consists of loose and unordered sheets of paper in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life.
Its whereabouts were unknown to all but a few mathematicians until it was rediscovered by George Andrews in 1976, at the Wren Library at Trinity College, Cambridge.
According to Wikipedia:
Berndt says of the notebook's discovery: "The discovery of this 'Lost Notebook' caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world."
The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics. The mock theta functions in the notebook have been found to be useful for calculating the entropy of black holes.
Here is a copy of an answer of mine from MathOverflow:
Bernhard Bolzano .... ( interesting reading ) Much of his work was unpublished until much later (for reasons see the link), thus remaining largely unknown. For example, a theorem of Weierstrass is now known as the "Bolzano-Weierstrass theorem", acknowledging that Bolzano had proved it previously. Bolzano anticipated Cantor and Dedekind in work on doing calculus without infinitesimals. His example of a continuous nowhere-differentiable function is in a manuscript from 1830, but only published in 1930.
(See also the other answers to that MathOverflow question.)
Is the Fast Fourier Transform a mathematical result? The point might be debated but its history has been well researched (e.g. Heideman et al., (1984). Gauss and the history of the fast FFT . IEEE ASSP Magazine). In 1987 One of the modern (re)discoverers also wrote on the topic.
The method and the general idea of an FFT was popularized by a publication of Cooley and Tukey in 1965, but it was later established that they had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805, and subsequently rediscovered several times in limited forms. Backtracking leads to Gauss's unpublished work from 1805 needed to interpolate the orbit of asteroids . While Gauss's work predated even Joseph Fourier's results in 1822, he did not analyze the computation time.
[Links and refs are in the wikipedia article which has been used here]
Jean-Robert Argand published his geometrical interpretation of the complex numbers as points of the plane in 1806. It become a standard way of dealing with these numbers and now sometimes the complex plane is called the Argand plane. However, the same idea had been published in 1799 by Caspar Wessel, a norwegian surveyor, and it was forgotten. Wessel's paper was rediscovered in 1895, when Christian Juel draw attention to it. In the same year, Sophus Lie republished the paper.
Leonard James Rogers (1862 - 1933) obtained degrees in Mathematics, Classics and Music from Oxford. During 1888-1919 he was Professor of Mathematics at Yorkshire College, before returning to his Alma mater. In 1894 he published the paper 'On the expansion of some infinite products'.
This contains the Rogers-Ramanujan identities, so called because they were rediscovered, without proof, by Ramanujan before 1913. In 1917 Ramanujan chanced upon Rogers' paper and expressed great admiration. A correspondence followed, and Rogers was led to a considerable simplification of his original proof.
In 1936 Atle Selberg, published a 'generalization' of the Rogers-Ramanujan identities which turned out, in fact, to be another special case of Rogers' original result.
Bayes' Theorem, fundamental in Bayesian statistics, was considered unremarkable by Thomas Bayes and so not published.
After Bayes' death, Richard Price edited Bayes' manuscript for reading at the Royal Society for which he was elected a Fellow.