Jim Holt is the author of Why Does the World Exist? His forthcoming book, When Einstein Walked with Gödel, will be published in May. (December 2017)

IN THE REVIEW

Positive Thinking

Ludwig Wittgenstein

Exact Thinking in Demented Times: The Vienna Circle and the Epic Quest for the Foundations of Science

by Karl Sigmund
The “Vienna Circle” was the self-chosen designation for a group of philosophers, scientists, and mathematicians, some three dozen in all, who came together in the mid-1920s with the ambition of purging philosophy of metaphysics and making it into the handmaiden of science. Every other Thursday evening, its members would convene …

Something Faster Than Light? What Is It?

The Irish physicist John Stewart Bell, who in 1964 proposed a way to observe ‘spooky action’ of particles experimentally, at the Large Electron-Positron Collider at CERN, near Geneva, Switzerland, 1989

Spooky Action at a Distance: The Phenomenon That Reimagines Space and Time—and What It Means for Black Holes, the Big Bang, and Theories of Everything

by George Musser
In physics, as in politics, there is a time-honored notion that all action is ultimately local. Aptly enough, physicists call this the “principle of locality.” What the principle of locality says, in essence, is that the world consists of separately existing physical objects, and that these objects can directly affect …

In the Mountains of Mathematics

Kurt Gödel and Albert Einstein, Princeton, New Jersey, 1954

Mathematics Without Apologies: Portrait of a Problematic Vocation

by Michael Harris
“The science of pure mathematics…may claim to be the most original creation of the human spirit.” So declared the philosopher (and lapsed mathematician) Alfred North Whitehead. Strange, then, that the practitioners of this “science” still feel the need to justify their vocation—not to mention the funding that the rest of …

At the Core of Science

William Blake: Newton, 1795–circa 1805

To Explain the World: The Discovery of Modern Science

by Steven Weinberg
In 1967, Steven Weinberg, then a visiting professor at MIT, published what has become one of the most frequently cited papers in physics. In it, he presented a mathematical model that “unified” two of the four fundamental forces of nature. What he showed was that these two seemingly very different …

NYR DAILY

Charles Rosen’s Lost Masterpiece

Frédéric Chopin was “the greatest master of counterpoint since Mozart”—so claimed the late pianist and author Charles Rosen in a 1987 review in these pages. At the time I read this, it came as a double surprise to me. I had never thought of Chopin’s music as having a lot of contrapuntal interest. I had always imagined it to stress sonority over structure, to be more emotional—even sentimental—than intellectual: a sort of higher mood music.