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)
“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)
“Well, well, Henry James is pretty good, though he is of the nineteenth century, and that glaringly.”
—Robert Louis Stevenson (1850–1894)
“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)
“There is one great fact, characteristic of this our nineteenth century, a fact which no party dares deny. On the one hand, there have started into life industrial and scientific forces which no epoch of former human history had ever suspected. On the other hand, there exist symptoms of decay, far surpassing the horrors recorded of the latter times of the Roman empire. In our days everything seems pregnant with its contrary.”
—Karl Marx (1818–1883)