Maxwell's Mathematical Rhetoric:

Rethinking the Treatise on Electricity and Magnetism

by Thomas K. Simpson

7" x 10", 376 pages, diagrams, index and bibliography.
Publication Date: July 2010
For pricing and ordering information, see the ordering section below.

Maxwell's Mathematical Rhetoric cover Green Lion Press is delighted to issue as a fine volume Simpson's classic work, the first major study of Maxwell's Treatise to take seriously the way Maxwell's presents his arguments. It is newly edited and presented in an attractive readable layout.

After many years of circulating in typescript form, this remarkable study by Thomas K. Simpson — a work long celebrated as something of an underground classic — is at long last available in a new edition worthy of its vision and depth.

Simpson identifies the distinctively rhetorical functions of mathematics, as Maxwell employs them in the Treatise on Electricity and Magnetism. Like the tropes of classical rhetoric, mathematical rhetoric seeks intelligibility and illumination—in this respect contrasting with what Maxwell termed "the mathematics of pure quantity," which emphasizes precision and logical economy.

A striking example of this is found in the way the energy of an electrified system can be represented. Mathematically, it can be expressed either as a two-dimensional integral over one or more surfaces or as a three-dimensional integral over space. The two forms are numerically equivalent; but to Maxwell, Simpson argues, they present a rhetorical question: whether the energy of a system is to be ascribed to "charges" residing on surfaces, or to a state of strain extending throughout the space between surfaces. The choice between these and similar alternatives is consequential, not merely for the structure of electromagnetic science but for future sciences, sciences not yet conceived in either Maxwell's time or our own.

Maxwell's Mathematical Rhetoric is the book to which Simpson’s Figures of Thought (also available from Green Lion Press) serves as an introduction. Maxwell's Mathematical Rhetoric explores in greater depth and detail the themes adumbrated in Figures of Thought.


  • The complete text of this underground classic, newly edited and presented in an attractive readable layout.
  • A deep and perceptive reading of Maxwell.
  • The full version, to which Figures of Thought is an introduction.

Sample Pages

Below are links to PDF versions of the Table of Contents and Simpson's Preface.
You may need to open this PDF document in Adobe Reader or an equivalent program.

About the Author

Thomas K. Simpson photoThomas K. Simpson is Tutor Emeritus at St. John's College in Annapolis, Maryland and Santa Fe, New Mexico. He has taught at the American University at Cairo, and is a co-founder of The Key School in Annapolis, Maryland.

Simpson was educated at Rensselaer Polytechnic Institute, St. John's College, Wesleyan University, and the Johns Hopkins University, where he received his doctorate in history of science in 1968.

He has written extensively on both Michael Faraday and James Clerk Maxwell. His wide range of interests, suggestive of those of Maxwell himself, extends also to schools, museums, and in general towards broadening the role of what the Scottish philosopher George Elder Davie has called "the democratic intellect."

His books include Maxwell on the Electromagnetic Field (Rutgers, 1997) Figures of Thought (Green Lion Press, 2005), and Newton, Maxwell, Marx (Green Lion Press, 2012).

Ordering Information for Maxwell's Mathematical Rhetoric

Sewn hardcover, ISBN 978-1-888009-36-1, list price: $59.00

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