The Joy of x attempts to demystify math so that "the rest of us" can gain some of the excitement that mathematicians do. The author succeeds fairly well in relating complex mathematics to the real world.
The Joy of x starts simple and takes nothing for granted. An example from Sesame Street calling for "fish fish fish" begins the introduction into numbers and counting. Subtraction begat the need for negative numbers. Square roots gave us the need for imaginary and complex numbers. Parabolas and other conic shapes have the ability to concentrate and amplify due to their structure. Geometry, calculus and algebra all help us explain real world phenomena.
"School math" often focuses on isolated equations or contrived story problem. Connecting it to the real world does a good job of making things alive. There are always the assumptions in word problems that we are asked to take to solve them. In high school, wind resistance always drove me crazy. Riding my bicycle, I knew that the wind and hills made a huge difference in speed and effort. Yet, all word problems seems to assume that all travel was done in a flat vacuum. The math to account for those details was "too complex" for the moment, but important for the real world. Even acknowledging those factors helps increase the "joy" in math.
Infinite Powers explores the evolution of calculus and the important roll that it plays in our lives. Both the concepts of "0" and "infinity" are key to the understanding of the world. However, these were not universally understood concepts in the ancient world. Many mathematicians did understand bits of it, but it wasn't until Newton and Leibniz separately put it all together.