Lewis Carroll was really Charles Dodgson who wrote a pretty bazaar tale called "Alice in Wonderland". Not only are they not based on wild imagination but are in fact a commentary of sorts on the then current theories of mathematics, which would have been in the 19th century. His attack of the proposed new ideas is evident by the use of a mathematical technique where the validity is tested by taking the idea to the extreme. The first symbolic system of algebra, which was proposed by a London math professor named Augustus De Morgan, is represented when Alice has the exchange with the caterpillar. His modern approach to algebra said that any procedure
following internal logic should be valid. An example of that would be the square root of a negative number. All numbers squared give positive results so even Morgan himself thought the idea to be absurd.  He felt that eventually math would have its full meaning restored to it after the intellectuals were through with it.Hence, the caterpillar sitting on the mushroom  suggests that something has come from nowhere and is uninteresting to the followers. Alice decides to restore her larger size but ends up going quite the opposite. She came from her world of logical arithmetic to an illogical one that she can vary from tiny to enormous in size. Alice is advised to keep her temper which meant to stay in proportion which was important in Wonderland. In her former world absolute length was what mattered. Chapter six gives a look at a concept that is now used in modern topology. The idea was introduced in France in the mid-19th century. One shape can bend and stretch into another as long as it keeps the same basic properties. The Chesire cat's grin is a parabola which is the same as a circle. When Alice takes the baby outside it turns into a pig just as the chesire cat expected.  He is the voice of traditional geometric logic.  The Mad Hatter and the March Hare represent Victorian Algebra of innovator William Rowan Hamilton.
In Chapter seven the t-party meant "time" instead of tea. Hamilton thought that manipulations with numbers should be in pure time which had to do with sequence instead of time on the clock. The Hatter, Hare and Dormouse going around the table represented the number system based on four terms, called quaternion. This was the final step proposed to calculate motion during the 1860's. 
During the mad tea party, time is missing  from the table so then the third term (Hatter, Hare and Dormouse) will be forced to circle around the tea table in a plane forever.The dormouse is being stuffed into the teapot so the Hatter and Hare can exist as an independent pair of numbers. The Lory and Eaglet are Alice's sisters, Alice is Alice Pleasance Liddell who father was an Oxford Dean and Dodgson was the Dodo. Dodgson was a math tutor at Christ Church, Oxford. To me the book makes more sense and has some kind of purpose when it can be understood for what it really is. On the surface it is nonsense and craziness.

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