The Revival of Number Theory

Abstract

Some important results in number theory were discovered in the Middle Ages, though they failed to take root until they were rediscovered in the seventeenth-century or later. Among these were the discovery of Pascal’s triangle and the “Chinese remainder theorem” by Chinese mathematicians and formulas for permutations and combinations by Levi ben Gershon [1321]. The Chinese remainder theorem will not be discussed here, as it did not reemerge until after the period we are about to cover. A full account of its history may be found in Libbrecht [1973], Ch. 5. Pascal’s triangle, on the other hand, began to flourish in the seventeenth-century after a long dormancy, so it is of interest to see what was known of it in medieval times and what Pascal did to revive it.