When working on the puzzle that revolves around two guards where one always lies and one always tells the truth, Oliva remarks that she remembers this from a movie. She's referring to the movie Labyrinth (1986) in which the character Sarah (Jennifer Connelly) had to solve the same problem.
When Galois is showing off to the young women about how every even number is the sum of 2 prime numbers, he chooses the number on the license plate of a nearby random car. But when he picks up Hilbert, he is driving this car, so of course he already knew the "solution" to this large number on his own car.
The rowboat has the name "Pitagoras" (Pythagoras in Spanish) painted on the side. Legend has it that Hippasus was a mathematician of the Pythagorean school who was drowned by being thrown out of a boat after he discovered irrational numbers.
The red wallpaper pattern and the interface of the PDA resemble the layout of the room when seen from overhead, the same as the diagram drawn on the blackboard to figure out how to put the shelves together.
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2.
Luis Piedrahita: When they're putting the bookcases on the floor and filling them with the books, you can see a green book written by the director with him on the cover.