Nineteenth Century
Kepler did not have a proof of the conjecture, and the next step was taken by Carl Friedrich Gauss (1831), who proved that the Kepler conjecture is true if the spheres have to be arranged in a regular lattice.
This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one. But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove. In fact, there are irregular arrangements that are denser than the cubic close packing arrangement over a small enough volume, but any attempt to extend these arrangements to fill a larger volume always reduces their density.
After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century. In 1900 David Hilbert included it in his list of twenty three unsolved problems of mathematics—it forms part of Hilbert's eighteenth problem.
Read more about this topic: Kepler Conjecture
Famous quotes related to nineteenth century:
“American family life has never been particularly idyllic. In the nineteenth century, nearly a quarter of all children experienced the death of one of their parents.... Not until the sixties did the chief cause of separation of parents shift from death to divorce.”
—Richard Louv (20th century)
“The most revolutionary invention of the Nineteenth Century was the artificial sterilization of marriage.”
—George Bernard Shaw (1856–1950)
“Detachment is the prerogative of an elite; and as the dandy is the nineteenth century’s surrogate for the aristocrat in matters of culture, so Camp is the modern dandyism. Camp is the answer to the problem: how to be a dandy in the age of mass culture.”
—Susan Sontag (b. 1933)
“Posterity—the forlorn child of nineteenth century optimism—grows ever harder to conceive.”
—Mason Cooley (b. 1927)
“The nineteenth century planted the words which the twentieth ripened into the atrocities of Stalin and Hitler. There is hardly an atrocity committed in the twentieth century that was not foreshadowed or even advocated by some noble man of words in the nineteenth.”
—Eric Hoffer (1902–1983)