In Chapter 3 Pythagoras is one of the main featured mathematicians who is talked about in this chapter. In the book it talks about how although the Pythagorean theorem was known for more than a thousand years before the Pythagoreans, it is generally accepted that Pythagoras independently discovered the result and may have been the first to rigorously prove it. It also goes on to talk about how the concepts of amicable, perfect, deficient, and abundant numbers all originated from the Pythagoreans. This may seem pretty bland but I found it interesting that not only was Pythagoras associated with all these discoveries but it is overlooked and often taken for granted that he created the musical scale that is used in music today.

Pythagoras was very interested in music, and so were his followers. The Pythagoreans were musicians as well as mathematicians. Pythagoras wanted to improve the music of his day, which he believed was not harmonious enough and was too hectic.

"According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."

The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras believed in something called the "harmony of the spheres." He believed that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony."

I found this on wikipedia and found this an interesting topic you guys may want to look at.