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:
“We have now traced the history of women from Paradise to the nineteenth century and have heard nothing through the long roll of the ages but the clank of their fetters.”
—Jane, Lady Wilde (1821–1896)
“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)
“Why does he not know how to select servants? The ordinary procedure of the nineteenth century is that when a powerful and noble personage encounters a man of feeling, he kills, exiles, imprisons or so humiliates him that the other, like a fool, dies of grief.”
—Stendhal [Marie Henri Beyle] (1783–1842)
“The secret point of money and power in America is neither the things that money can buy nor power for power’s sake ... but absolute personal freedom, mobility, privacy. It is the instinct which drove America to the Pacific, all through the nineteenth century, the desire to be able to find a restaurant open in case you want a sandwich, to be a free agent, live by one’s own rules.”
—Joan Didion (b. 1934)