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What would Lewis Carroll\s \Alice\s Adventures in Wonderland\ be without the Cheshire Cat, the trial, the Duchesss baby or The Mad Hatters Tea Party? These famous characters are missing from the original story the author told Alice Liddell and her 2 sisters during a boat trip near Oxford . What inspired these later additions?

Lewis Carroll was Charles Dodgson, a stubbornly conservative mathematician at Oxford . He valued Euclids Elements as the epitome of mathematical thinking, starting with a few axioms and building complex arguments through simple, logical steps in geometry and trigonometry. But the 19^th century was a turbulent time for mathematics with new concepts like imaginary numbers, symbolic logic, projective geometry and quaternions. For Dodgson this was all semi-colloquial and therefore parodied in Alice – hence the Cheshire Cat, the Duchesss baby and the Mad Hatters Tea Party – each one a critique of the new mathematics. This is a new analysis of Alice , originated by Melanie Bayley a PhD student from Oxford.