History and Motivation
The formula for the volume of a pyramid,
had been known to Euclid, but all proofs of it involve some form of limiting process or calculus, notably the method of exhaustion or, in more modern form, Cavalieri's principle. Similar formulas in plane geometry can be proven with more elementary means. Gauss regretted this defect in two of his letters. This was the motivation for Hilbert: is it possible to prove the equality of volume using elementary "cut-and-glue" methods? Because if not, then an elementary proof of Euclid's result is also impossible.
Read more about this topic: Hilbert's Third Problem
Famous quotes containing the words history and/or motivation:
“What is most interesting and valuable in it, however, is not the materials for the history of Pontiac, or Braddock, or the Northwest, which it furnishes; not the annals of the country, but the natural facts, or perennials, which are ever without date. When out of history the truth shall be extracted, it will have shed its dates like withered leaves.”
—Henry David Thoreau (1817–1862)
“Self-determination has to mean that the leader is your individual gut, and heart, and mind or we’re talking about power, again, and its rather well-known impurities. Who is really going to care whether you live or die and who is going to know the most intimate motivation for your laughter and your tears is the only person to be trusted to speak for you and to decide what you will or will not do.”
—June Jordan (b. 1939)