"Einstein's Heroes - Imagining the World through the Language of Mathematics" by Robyn Arianrhod

Imagine you are fluent in a magical language of prophecy, a language so powerful it can accurately describe things you cannot see or even imagine. Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's most amazing accomplishments.

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The heart of the book illuminates how Maxwell, using the language of mathematics in a new and radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of the radio wave, something utterly unexpected, teasing it out of the mathematical language itself.