Via GiFS comes an interesting article:
A Prayer for Archimedes: A long-lost text by the ancient Greek mathematician shows that he had begun to discover the principles of calculus.
It seems that an old (very old) prayer book was discovered to have a faint palimpsest, which turned out to be writings of Archimedes.
Archimedes wrote his manuscript on a papyrus scroll 2,200 years ago. At an unknown later time, someone copied the text from papyrus to animal-skin parchment. Then, 700 years ago, a monk needed parchment for a new prayer book. He pulled the copy of Archimedes' book off the shelf, cut the pages in half, rotated them 90 degrees, and scraped the surface to remove the ink, creating a palimpsest—fresh writing material made by clearing away older text. Then he wrote his prayers on the nearly-clean pages.I was going to include more snippets from the article, but I ended up with most of it. Just go read it at the above link. It is awesomely cool.Of course his prayers were far more important than whatever nonsense had been preserved for 1500 years
Later,
4 people have spouted off:
Yeah, it's really cool that Archimedes was onto calculus almost two thousand years before Newton and Leibniz figured it out. Yea math! Boo covering genious with insipid pleas to an imaginary tyrant.
fascinating !
That article's summary isn't quite accurate. The article says that "Modern calculus no longer makes use of the actual infinite; it sticks with Aristotle's distinction." That's true only in a very rough sense. In actual practice mathematicians don't use the term "actual infinity" and "potential infinity." More often limiting processes ("potential infinity") are used to approximate our intuitions about "actual infinity" but one can have "actual infinity" in a calculus setting. See for example the "extended reals." Moreover,
many other areas of math such as set theory use what can only be reasonably described as actual infinity.
Spout off: