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The narrator explains to Donald the story of Pythagoras, who is considered by some to be the father of mathematics and music. He discusses Pythagoras' society, the Pythagoreans, and how they used mathematics to create music.

In this clip, a serial killer is choosing his victims from the Los Angeles phone book based on a system of beliefs rooted in numerology. Numerologists believe that numbers have a spiritual or mystical meaning that transcends what mathemeticians and scientists understand. Charlie is forced to learn about these beliefs, and determine what mathematical patterns the killer is using in order to predict the next victim.

In Episode 207, "Convergence," an old college rival comes to CalSci (Marshall Penfield, played by Colin Hanks,) to present new research on a gap he has found in Charlie's proof. Although Charlie does find a way to resolve the error term, it isn't clear to many people watching still what type of math Charlie really does do! What he studies falls into the area of probability and statistics involving what are called "random matrices." While the first activity has no prerequisites, the latter activities all assume some basic knowledge of linear algebra, matrices, and determinants.

In this intro scene to A Beautiful Mind, a professor gives a speech explaining how mathematics contributed to the Cold War and the national security of the United States.

In this clip, Charlie develops a mathematical model of the accident on the computer to recreate the path that the car took just before the accident. One important component of that model is the friction circle.

Bud Abbott, the landlord, collects thirteen week's worth of rent at $7 a week from his tenant, Lou Costello. Lou argues that he only owes $28. Perplexed by what Lou is saying, Bud offers to give Lou the room for free if he can prove to him why the answer is $28.

On Christmas Eve, Ms. O is surprised to learn from Santa that she is on his naughty list. Santa shows her that she has performed more naughty actions than nice actions and explains his use of the "greater than" symbol. Unless she performs more nice actions than naughty actions before Christmas, Ms. O will not receive any presents.