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Saturday, June 23, 2018

An Euler Bookshelf: No Ordinary Genius | Life & Arts - Wall Street Journal

Photo: Siobhan Roberts
Siobhan Roberts, Canadian author and science journalist on books about the brilliant 18th-century mathematician Leonhard Euler.

Photo: Peter and Maria Hoey

A few years ago, a mathematician and a neuroscientist led a study investigating “the experience of mathematical beauty and its neural correlates.” The methodology rolled 14 mathematicians into a functional magnetic resonance imaging machine and asked them to view and rate a collection of 60 mathematical formulas that they had previously assessed as beautiful, neutral or ugly. (Detractors of this sort of study call it “neurotrash,” but no matter.) While viewing the more aesthetically pleasing specimens, the mathematicians’ fMRI results showed activity in the “emotional brain,” specifically field A1 of the medial orbito-frontal cortex—the same area stimulated by moral, musical and visual beauty. Sometimes the mathematicians exited the machine weeping.

The equation that consistently rated the most beautiful was a famously compact specimen devised in the 18th century by the Swiss mathematician Leonhard Euler : e iπ + 1 = 0.
 
Euler’s equation links—via three basic arithmetic operations, each deployed only once—five fundamental mathematical constants: 0, 1, i (the square root of -1, aka the “unit imaginary number”), π and e (“Euler’s number”—2.71828 . . . —which is linked to exponential growth). It is sometimes called Euler’s identity, or Euler’s formula, but by whatever name it is currently having something of a moment.

Two new books pull apart the equation—deconstructing it technically and historically—and celebrate its niftiness: “A Most Elegant Equation” (Basic, 221 pages, $27) by David Stipp and “Euler’s Pioneering Equation” (Oxford, 162 pages, $19.95) by Robin Wilson. Mr. Stipp’s roving account is propelled by his folksy sense of humor, and, as the author himself admits at one point, by “giddy metaphorical overreach.” Mr. Wilson’s account is more no-nonsense, proceeds on a shorter mathematical tether and has a quieter epigrammatic levity.

Both books, by way of introduction, mention the neuroscience study, and both lean on the Stanford mathematician Keith Devlin for this pronouncement: “Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler’s equation reaches down into the very depths of existence.” Both also quote the physicist Richard Feynman, who at age 14 wrote in a notebook that Euler’s equation was “the most remarkable formula in math.”

Convinced yet? If you aren’t by all this anecdotal testimony about the formula’s pure beauty, then consider its applied incarnations.
Read more... 

Recommended Reading

A Most Elegant Equation:
Euler's Formula and the
Beauty of Mathematics
A Most Elegant Equation
Bertrand Russell wrote that mathematics can exalt "as surely as poetry." This is especially true of one equation: ei(pi) + 1 = 0, the brainchild of Leonhard Euler, the Mozart of mathematics. 


Euler's Pioneering Equation:
The most beautiful theorem
in mathematics
Euler's Pioneering Equation
In 1988 The Mathematical Intelligencer, a quarterly mathematics journal, carried out a poll to find the most beautiful theorem in mathematics.

Source: Wall Street Journal 


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