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BIOLOGISTS can touch, smell, prod and even taste their work, and physicists can squeeze, freeze, charge, hit and irradiate. Astronomers can only stand back and stare. They have been doing this for a long, long time with rich results, and are renowned for involving other scientists.

Take mathematics. Christopher Linton’s From Eudoxus to Einstein shows how astronomers were forced to develop whole new areas of mathematics, such as trigonometry, to predict and explain the movement of the sun, moon, planets and comets. Two problems led to calculus: the gravitational perturbations that complicate the motion of the moon, and the analytically difficult solutions to Kepler’s law of…

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