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:
“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)
“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 nineteenth century is a turning point in history, simply on account of the work of two men, Darwin and Renan, the one the critic of the Book of Nature, the other the critic of the books of God. Not to recognise this is to miss the meaning of one of the most important eras in the progress of the world.”
—Oscar Wilde (1854–1900)
“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)