What mathematical concept puzzled and alarmed the ancient Greek thinkers and is believed to have contributed to the decline of creative mathematical thought in the ancient world?

zbeckabee

Plato and his students understood the power of the continuum. In keeping with number worship—now brought to a new level—Plato wrote above the gates of his academy: "Let no one ignorant of geometry enter here." Plato's dialogues show that the discovery of the incommensurable magnitudes—the irrational numbers such as the square roots of two or five—stunned the Greek mathematical community and upset the religious basis of the Pythagoreans' number worship. If integers and their ratios could not describe the relationship of the diagonal of a square to one of its sides, what could one say about the perfection the sect had attributed to whole numbers? http://www.washingtonpost.com/wp-srv/style/longterm/books/chap1/mysteryaleph.htm Jun 24 09, 4:53 AM

Bronxiteone

It has been said that the students of Pythagorous killed people who publicly taught the concept of the irrationality of teh square root of two. http://www.freeessays.cc/db/1/auj117.shtml It was also said that Pythagoras himself sacrificed a hecatomb, or an ancient Greek ritual of 100 oxen, when he discovered the Pythagorean Theorem. The group was also said to have vowed to secrecy. One day the Pythagoreans discovered irrational numbers. They referred to these numbers as “algon” or unutterable. They were so shocked by these numbers they killed a member of the group that mentioned them in public. [Lower text and link added -- Zb] Jun 24 09, 5:32 AM