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In presenting a mathematical argument the great thing is to give the educated reader the chance to catch on at once to the momentary point and take details for granted: his successive mouthfuls should be such as can be swallowed at sight; in case of accidents, or in case he wishes for once to check in detail, he should have only a clearly circumscribed little problem to solve (e.g. to check an identity: two trivialities omitted can add up to an impasse). The unpractised writer, even after the dawn of a conscience, gives him no such chance; before he can spot the point he has to tease his way through a maze of symbols of which not the tiniest suffix can be skipped.
A Mathematician's Miscellany, Methuen Co. Ltd., 1953.
Loci: Convergence
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Equations from God: Pure Mathematics and Victorian Faith
Equations from God: Pure Mathematics and Victorian Faith. Daniel J. Cohen, 2007, x + 242 pp. $ 50.00 hardcover. ISBN 10: 0-8013-8533-1, ISBN 13: 978-0-8018-85532. Baltimore: The John Hopkins University Press. http//www.press.jhu.edu
On August 31, 1846, Urbain Le Verrier announced to the French Academy that he had used mathematics to predict the existence of a new planet. He described its mass, motion, and distance from the sun. Three weeks later in Berlin, Johann Gottfried Galle used this information to see the planet that would be called Neptune. Some ten years later the Oxford clergyman Adam S. Farrar informed his congregation that the equations of mathematics ultimately “reveal to us the infinite wisdom of God.” Daniel J. Cohen develops this mental/spiritual pairing with a thorough study of Victorian idealism, Benjamin Peirce, George Boole, and Augustus De Morgan with a coda on the secularization of mathematics.
Benjamin Peirce, “the father of pure mathematics in America,” held to a broad monotheistic faith in which the search to know God was identical with the search to know mathematical truth. After an epiphany about the number 1 or “Unity”, George Boole was convinced that the Divinity had revealed to him the idea of mathematical logic, a tool to be used to understand religious truths better. In seeking to avoid polarizing religious debate, Augustus De Morgan developed a “new logical system [that] would provide a dispassionate technique for human beings to discuss and analyze their ideas in a reasonable, considerate, and open way.” As first President of the London Mathematical Society, De Morgan strove to separate mathematics and religion. Perhaps for the first time, members of LMS faced the questions, “What is a mathematician? What does a mathematician do?” Whatever the answer to the second question, religion would have no part in it.
While there is significant mathematics in the book, there are more significant insights into the times and the thinking of the 19th century protagonists who produced the mathematics. The book is a good read.
Barnabas Hughes, O.F.M., Professor Emeritus, California State University, Northridge