Robert Recorde, author the first English textbook on algebra (published in 1557), chose to give his book the metaphorical title The Whetstone of Witte to encourage people to take up the new and difficult practice of algebra. The metaphor of a whetstone, or blade-sharpener, suggests that algebra is not only useful, but also good mental exercise. In the verse that he included on its title page, he writes,
Its use is great, and more than one. Here if you lift your wits to wet, Much sharpness thereby shall you get. Dull wits hereby do greatly mend, Sharp wits are fined to their full end.
Mathematics, and algebra in particular, according to The Whetstone of Witte is like a knife-sharpener for the brain. Four hundred years later, in his book Mathematician’s Delight (1961), W.W. Sawyer takes up a similar metaphor, suggesting that “Mathematics is like a chest of tools: before studying the tools in detail, a good workman should know the object of each, when it is used, how it is used.” Whether they describe mathematics as a sharpener or other tool, these mechanical metaphors are commonly used to emphasize the practicality and versatility of mathematics, particularly when employed in engineering or science, and suggest that it should be used thoughtfully, and with precision.
An often quoted mechanical metaphor that suggests a more frantic and less precise process of mathematical creation is often attributed to Paul Erdos: “a mathematician is a machine for turning coffee into theorems.”
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*Credit for article given to dan.mackinnon*