- This website claims that Ken Keeler, one of the writers who has a PhD in math, devised a NEW theorem for use in the show. The theorem and proof are here. I do not know if it is new but it is correct and interesting.
- Bender the robot had mind switched with Amy, so he was in a human body. In order to prove that he was really a robot he had to pass the reverse Turing Test.
- Since PURE MATH lead to a solution of a PRACTICAL PROBLEM The professor exclaimed And they say pure math has no real applications!
Both The Simpsons and Futurama have websites devoted to math refs in the show: Simpsons Math, Futurama Math.
It is not surprising that The Simpsons and Futurama have math refs since writers Jeff Westbrook, David X. Cohen, and Ken Keeler who write for these shows, are all math folk.
See these two prior posts for more on comedy and math.