Aside from the number of visitors to my blog, it is also the title of my latest review. I picked up book Zero, the Biography of a Dangerous Idea by Charles Seife , from the science section of the local Barnes & Nobles because it had a nifty title and very bright red cover(link?) that naturally caught my attention. The simple thesis is of the book is to follow the development of the mathematical concepts of zero and infinity. Book it self is written in a very readable style that keeps the subject interesting, but is not afraid to include graphs and formulas.
Naturally, the book starts off with the somewhat murky origins of counting and of the brutish life without the zero. The book is full fun little facts like the Egyptians lack of a zero is the likely cause of our Egyptian derived calendars lack of a zero year. We then move on to the Greeks and Babylonians who were willing to use zero as a placeholder, but rejected using it in more useful ways.
Here the book points out the fascinating fact that the for the Greeks, mathematics was not separate from geometry. To have a convincing proof for the Greeks was to draw it with shapes, not with equations. This is source of the term squaring. (take a line of length x, then x squared would be the area of a square with x sides). This was something that was never taught to me in school. For that matter, except for my Hungarian algebra II teacher, I don't recall any of my teachers going into the history of Mathematics or into the odd characters who developed the concepts that we studied. Why did we spend so much time on Conic Sections?
After the Rejection of zero and infinity by the Greeks and other westerners it moves into India where the modern number line was developed with negative numbers and zero. The Arabs picked up this mathematics developed it more and soon it spread to Europe during the High Middle Ages and was essential for the development of modern mathematics. Newton and Leibniz's based caclus on mathematics that involved dividning by zero and conviently ignored that it really ought to be impossible. I fear I'm not skilled enough in Mathematics to explain this in detail so I suggest picking up the book for better description. I will however share an entertaining quote made by George Berkley, an Irish Bishiop, in 1734 AD "he who can digest a second or third fluxion[dirivative], a second or third difference, need not, methinks, be squeamish about any point in divinity."
Questions:
The Book never mentions any Chinese contribution to mathematics, is this because China had no notable contributions, possible, since it seems the movement of ideas went east from Greece, Egypt and Babylon to India and then back west, perhaps China's location (like the Meso-American) left it out of the proverbial loop.
Conclusion:
I found the book to be very enjoyable journey into the history, uses and oddities of zero. I particularly enjoyed the comical proof from the Appendix where zero was used to prove Winston Churchill = a carrot. It's almost as funny as the "women = evil" proof.