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Tuesday, May 01, 2018

Seeing the Sublime in Mathematics | Books & Arts - The Weekly Standard

David Guaspari, writer in Ithaca, New York review the David Stipp’s short book, A Most Elegant Equation.

David Stipp’s short book, A Most Elegant Equation , aims to persuade the “math-averse” that “great mathematics is as provocative, beautiful, and deep as great art or literature.” His exemplar is Euler’s identity, which can be written as the gnomic formula eiπ + 1 = 0. Stipp offers to explain what it means, why it’s true, and why it is significant as science and as art. The discussion, he says, will take pains to assume no mathematical prerequisites beyond checkbook arithmetic, and he isn’t kidding. For example, every algebraic manipulation that crops up is accompanied by a verbal paraphrase (often lengthy). A 101-word footnote on page 15 is devoted to explaining why “x = −1” means the same thing as “x + 1 = 0.”

“Euler” is Leonhard Euler, the master mathematician of the 18th century and one of the greatest of all time—also the most prolific. Publication of his collected works, begun in 1911 and ongoing, will total more than 80 large volumes. He is by all accounts an appealing character—a pious family man who, according to one contemporary, could work happily with “a child on his knees, a cat on his back.” Euler was generous in his dealings with other scholars, a good teacher, and something of a polymath who, in addition to his native German, knew Latin, Russian, French, and English and published works on mathematics, science, philosophy, and music. He could recite the entire Aeneid from memory. Euler began to lose his sight at an early age but blindness seemed if anything to increase his productivity: He worked things out in his head and dictated the results.

The exotic ingredient in Euler’s identity is eiπ: π is what you think, the ratio of a circle’s circumference to its diameter; e and i need considerable explaining, as does the use of iπ as an exponent (“raising e to the power iπ”). Without rehearsing those lengthy explanations it’s possible to scan the terrain in which that intellectual adventure takes place...

The final chapter, called “The Meaning of It All,” asks what makes it beautiful. Stipp begins by noting qualities that mathematicians have attributed to beautiful results. From G. H. Hardy, for example, he gets this famous list: seriousness, generality, depth, unexpectedness, inevitability, and economy. Such reflections will help those who already sense beauty in mathematics to articulate their experience; they won’t persuade others that beauty is there to be found. But persuasion is not Stipp’s aim. His book is not a work of philosophy. 
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Additional resources
A Most Elegant Equation:
Eulers Formula and the Beauty of Mathematics

Source: The Weekly Standard