text: The Handmaiden of the Sciences by Eric Temple Bell, 1937 | Online Research Library: Questia
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  MATHEMATICS has been called both the queen of the sciences and their handmaiden. Some would dispute either title and drive mathematics out, like Hagar, to the deserts of barren speculation. In the chapters following this we shall attempt only to suggest by a small handful of illuminating examples and general principles that mathematics is indeed the efficient servant of the sciences. Something could also be said for mathematics as a trustworthy scout in certain wildernesses of philosophy.
  The claim that mathematics is a powerful aid in scientific research does not pass unchallenged. In fact some uncompromising empiricists condemn the use of mathematics in the exploration of nature as a vice, and it is undeniable that scientific work of the highest excellence has been done by men who were practically illiterate mathematically. Michael Faraday is an instance.
  At the other extreme a few youthful enthusiasts halfseriously place mathematical theories of nature before experiment. These assert that while experience necessarily blunders through the fog of the senses, calculation, inspired by the creative imagination, foresees clearly what must be the outcome of any experiment. Somewhere between these extremes winds the level road of well attested historical fact.
  The Handmaiden of the Sciences *
  Chapter 1 Science and Mathematics 1
  Chapter 2 from Cyzicus to Neptune 20
  Chapter 3 Two Kinds of Picture 45
  Chapter 4 Eternal Flux 58
  Chapter 5 the Chief Instrument of Applied Mathematics 73
  Chapter 6 Pictorial Thinking 90
  Chapter 7 Arithmetized Geometry 101
  Chapter 8 Beyond Intuition 115
  Chapter 9 Permanence in Change 125
  Chapter 10 Greatest or Least 141
  Chapter 11 Waves and Vibrations 161
  Chapter 12 Return to the Discrete 180
  Chapter 13 Choice and Chance 197
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