It seems impossible to believe that at one point in ancient time, human beings had absolutely no formal mathematics-that from scratch, the ideas for numbers and numeration were begun, applications found, and inventions pursued, one layered upon another, creating the very foundation of everyday life. So dependent are we upon this mathematic base-wherein we can do every-thing from predict space flight to forecast the outcomes of elections to review a simple grocery bill-that to imag-ine a world with no athematical concepts is quite a difficult thought to entertain.
In this volume we encounter the humble beginnings of the ancient mathematicians and various developments over thousands of years, as well as modern intellectual battles fought today between, for example, the logicians who either support the mathematic philosophy of Platonism or promote its aptly named rival, anti-Platonism. We explore worldwide math contributions from 4000 BCE through today. Topics presented from the old world include mathe-matical astronomy, Greek trigonometry and mensuration, and the ideas of Omar Khayyam. Contemporary topics include isomorphic structures, topos theory, and comput-ers and proof.