Home > Work > The Poincaré Conjecture: In Search of the Shape of the Universe
1 " The willingness to reexamine lifelong beliefs because of conflicting data takes enormous courage, and contrasts sharply with recent examples of public discourse in which our political, cultural, and religious leaders have fit data to preconceived theories. "
― , The Poincaré Conjecture: In Search of the Shape of the Universe
2 " Sadly, we know almost nothing about Euclid (c. 325-c. 265 BCE).32 We know even less about him than we do about Pythagoras, and what little we do know has been hotly contested by scholars. Euclid wrote at least ten books, only half of which have survived. A number of mutually consistent indications suggest that he lived after Aristotle and before Archimedes. He was one of the first mathematicians at the great library of Alexandria and there had gathered a group of talented mathematicians about him. Legends about him abound, many as (possibly apocryphal) insertions in other mathematicians' works. One tells that Ptolemy asked Euclid for a quick way to master geometry and received the reply, "There is no royal road to geometry." Another tells of a student who, after encountering the first proposition in the Elements, asked Euclid what practical use studying geometry could have. The mathematician allegedly turned to his slave and replied dismissively, "Slave, give this boy a threepence, since he must make gain of what he learns. "
3 " Not understanding that great circles are the shortest paths on earth has caused some bizarre arguments. Many religions have preferred directions in which to pray. For example, the ancient biblical tradition among Jews was to pray facing Jerusalem. However, this was usually taken to mean that if one were west of Jerusalem, one should face east. Baha'i tradition states that one should face to Acre to pray. And early Christian practice was to face east. However, these practices were not entirely uniform, and not binding. "
