In the mid-19th century, mathematics was rapidly blossoming into what it is today: a finely honed language for describing the conceptual relations between things. Dodgson found the radical new math illogical and lacking in intellectual rigor. In "Alice," he attacked some of the new ideas as nonsense — using a technique familiar from Euclid’s proofs, reductio ad absurdum, where the validity of an idea is tested by taking its premises to their logical extreme.
Some of Carroll's satire is simply wrong - de Morgan's discovery of complex numbers turned out to be integral to modern mathematics and, in a twist of irony, physics and even engineering. But it's still worth bearing in mind when reading Alice.