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)
“If the nineteenth century was the age of the editorial chair, ours is the century of the psychiatrist’s couch.”
—Marshall McLuhan (1911–1980)
“Well, well, Henry James is pretty good, though he is of the nineteenth century, and that glaringly.”
—Robert Louis Stevenson (1850–1894)
“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)
“The most revolutionary invention of the Nineteenth Century was the artificial sterilization of marriage.”
—George Bernard Shaw (1856–1950)