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:
“In the nineteenth century the problem was that God is dead; in the twentieth century the problem is that man is dead.”
—Erich Fromm (1900–1980)
“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)
“Of the creative spirits that flourished in Concord, Massachusetts, during the middle of the nineteenth century, it might be said that Hawthorne loved men but felt estranged from them, Emerson loved ideas even more than men, and Thoreau loved himself.”
—Leon Edel (b. 1907)
“Posterity—the forlorn child of nineteenth century optimism—grows ever harder to conceive.”
—Mason Cooley (b. 1927)
“When I see that the nineteenth century has crowned the idolatry of Art with the deification of Love, so that every poet is supposed to have pierced to the holy of holies when he has announced that Love is the Supreme, or the Enough, or the All, I feel that Art was safer in the hands of the most fanatical of Cromwell’s major generals than it will be if ever it gets into mine.”
—George Bernard Shaw (1856–1950)