Famous Classical Theorems
There are many famous theorems in mathematics. Some are known for their importance, others for their depth, usefulness, or sheer beauty. In this chapter we discuss seven of the most remarkable classical theorems; in the next chapter, we discuss three others from more recent times. Our choices for this top ten list were motivated primarily by the nature of their proofs; we apologize if we did not choose your favorite theorem. (A more representative top 40 list can be found in Appendix D at the end of the book.) Here we included theorems that are considered to have the oldest, the most well-known, the most surprising, the most elegant, and the most unsettling proofs. Some of the theorems in our list were disappointing—even angering—to mathematicians of the time, others were celebrated instantly by most.