Having human characters interact with living numbers is a relatively common idea in mathematical fiction. See, for example, Numberland, The Mathematician's Nightmare, Squate, Quaternia, The Cat in Numberland, and Three Days in Karlikania. Of course, Futurama's take on it is funnier than most! (For instance, you can see that "Numberland" appears in other titles, but only Futurama turns it into a punny reference to the Cumberland Gap.)

Following are some comments about the mathematical content of the episode. I warn you that they all are essentially spoilers. So, if you want to watch the episode without knowing these things in advance, I suggest you stop reading now.

• Combining the signal from a numbers station and Fry's new hobby of paint-by-numbers, Amy builds a device that opens the portal to Numberland. (Don't worry if that doesn't make much sense to you. I don't think it was intended to, but it is probably a reference to the plans for a device encoded in mathematics in Carl Sagan's Contact.)
• Towards the beginning of the episode, the Professor expresses growing distaste for the real world. The aches of his aging body have him longing for an abstract existence, and so he is happy to stay with the numbers who never age. But, he is disappointed in their response when he asks them how to prove Goldbach's Conjecture (not mentioned by name).
• Danica McKellar (actress and author of popular mathematics books) appears in this episode as a bodiless head, signing autographs and offering Bender advice.
• Bender admits to having a fear of numbers. Not all numbers. He likes one and zero. But, numbers like two and all of the others apparently terrify him. (McKellar says he has an irrational fear of numbers. He adds that he also has a fear of irrational numbers!)
• The Professor finds Georg Cantor, "discoverer of the hierarchy of infinities", trapped in Numberland. It turns out that he was the one who sent the signal that Amy used to create the device. It was his call for help.
• Cantor presents a mathematical proof in an attempt to free himself (and the Professor and Bender) from captivity. Specifically, he uses diagonalization argument to prove that there are numbers between 0 and 1 which are not fractions, and hence that not all numbers are present at their trial as required. (Of course, the diagonalization argument does much more than that...it shows that there are uncountable sets! I guess that's why they have The Professor point out to Cantor that there would be easier ways to prove that there are irrational numbers and Bender says something about sizes of infinite sets.)
• There is some discussion about what makes math beautiful/interesting/useful and Gödel's Theorems are "name dropped". Pretty heavy stuff for a cartoon!
• At one point, the Professor gives the famous "proof by contradiction" that all (natural) numbers are interesting. (Namely, that if there were any uninteresting ones, then one of those would be the smallest non-interesting number, which would be interesting.)
• In the end, the Professor decides to return to the "applied math" of physical existence, but Cantor supposedly moves on to something even more "pure" than Numberland. (He does this using a portal labeled ℵ_1/2 ; )