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)
“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)
“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 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)
“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)