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:
“The nineteenth century was completely lacking in logic, it had cosmic terms and hopes, and aspirations, and discoveries, and ideals but it had no logic.”
—Gertrude Stein (1874–1946)
“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 ... 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)
“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)
“The most revolutionary invention of the Nineteenth Century was the artificial sterilization of marriage.”
—George Bernard Shaw (1856–1950)