ABSTRACT
Mathematics has a rich history, going back at least 5000 years. Very few subjects still make use of ideas that are as old as that, but in mathematics, important discoveries have lasting value. Most of the latest mathematical research makes use of theorems that were published last year, but it may also use results first discovered by Archimedes, or by some unknown Babylonian mathematician, astronomer, or priest. For example, ever since Archimedes proved (around 250 BC) that the volume of a sphere is what we would now write as 43pir
3, that discovery has been available to any mathematician who is aware of the result, and whose research involves spheres. Although there are revolutions in mathematics, they are usually changes of viewpoint or philosophy; earlier results do not change-although the hypotheses needed to prove them may. In fact, there is a word in mathematics for previous results that are later changed: they are called ‘mistakes’.
