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:
“Literature always anticipates life. It does not copy it, but moulds it to its purpose. The nineteenth century, as we know it, is largely an invention of Balzac.”
—Oscar Wilde (1854–1900)
“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)
“In the nineteenth century ... explanations of who and what women were focused primarily on reproductive events—marriage, children, the empty nest, menopause. You could explain what was happening in a woman’s life, it was believed, if you knew where she was in this reproductive cycle.”
—Grace Baruch (20th century)
“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)
“Posterity—the forlorn child of nineteenth century optimism—grows ever harder to conceive.”
—Mason Cooley (b. 1927)