Mathematics is a language that has helped mankind to unravel the mysteries of the universe
In Lewis Carroll’s Alice’s Adventures in Wonderland, the Mad Hatter notes that “say what you mean” is not the same as “mean what you say,” because “you might as well say that ‘I see what I eat’ is the same thing.” thing like ‘I eat what I see’!” Readers may smile in recognition at the author’s tongue-twisting, logic-twisting nonsense, but the Victorian literature expert Melanie Bayley suggested something much more interesting. Carroll was a pseudonym for Charles Dodgson, an Oxford mathematics don who satirized radical new ideas in algebra. In the passage above, he targeted the emergent form of multiplication known as noncommutativity: when “a times b” does not equal “b times a”.
Yet such controversial concepts gained wide acceptance as the new ideas proved their worth. How it laid the foundations of the modern world is part of the story told in a remarkable new book, Vector, by Robyn Arianrhoda historian of science. To fully understand her text requires an undergraduate understanding of mathematics. But her broader theme is easier to recognize: how social and technological change is intertwined with the advancement of mathematical thought.
