Chapter 6, Infinity's Twin Summary and Analysis

Zero and infinity shared a lot. Multiply either by itself and you get itself. Dividing anything by one yields the other.

Zero was not the only ignored number. One number, 'i', was ignored as well. 'i' appears whenever one takes the square root of a negative number. Descartes refused to permit these 'false roots'. Over time, algebraists came to accept negative answers to equations but later they had to accept 'imaginary numbers' as well. With the introduction of imaginary numbers, every polynomial equation could be solved and the fundamental theorem of algebra was discovered.

Before imaginary numbers could be fully accepted, several developments had to occur. The first development was projective geometry, which allowed armies to use projectile weapons effectively. Kepler used projective geometry to better understand the elliptical orbits of the planets. By employing the concept...