Copernicus imagined that the sun was at the center instead, and the planets moved in simple circles. Planets would seem to zoom backward as Earth overtook them; no epicycles were needed. Though Copernicus’s system didn’t agree with the data completely—the circular orbits were wrong, though the heliocentric idea was correct—it was much simpler than

Kabbalists thought that words and phrases with the same numerical value were mystically linked. For instance, Genesis 49:10 states, “The scepter shall not depart from Judah . . . until Shiloh come.” The Hebrew phrase for “until Shiloh come” has a value of 358, exactly the same for the Hebrew word meshiach, messiah. Hence, the passage presages the

Add a number to itself and it changes. One and one is not one—it’s two. Two and two is four. But zero and zero is zero. This violates a basic principle of numbers called the axiom of Archimedes, which says that if you add something to itself enough times, it will exceed any other number in magnitude.

Archimedes figured out that 1051 grains of sand would fill the entire universe, packed full even unto the outermost sphere of fixed stars. (1051 is a really, really big number. Take 1051 molecules of water, for instance. It would take every man, woman, and child now on Earth, each drinking a ton of water a second, over 150,000 years to drink it

If you look carefully enough, you will see that people usually do start counting with zero. A stopwatch starts ticking from 0:00.00 and only reaches 0:01.00 after a second has elapsed. A car’s odometer comes from the factory set at 00000,

By rejecting zero, the Greek philosophers gave their view of the universe the durability to survive for two millennia.

The number of rabbits goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, . . .; the number of rabbits you have in any given month is the sum of the rabbits that you had in each of the two previous months. Mathematicians instantly realized the importance of this series. Take any term and divide it by its previous term. For instance, 8/5=1.6;

infinity. It is the infinite that lies at the heart of Zeno’s paradox: Zeno had taken continuous motion and divided it into an infinite number of tiny steps.

Geometric constructions and shapes were the same thing. Zero was a number that didn’t seem to make any geometric sense, so to include it, the Greeks would have had to revamp their entire way of doing mathematics. They chose not to.