Einstein's Genius Club (4 page)

Still, Gödel was only twenty-five when in 1931 he proved the “incompleteness” of mathematics. And the early days of quantum physics saw a procession of theorists remarkable for their youth as well as their genius: Wolfgang Pauli and Werner Heisenberg were both twenty-five, and Paul Dirac was twenty-four, when they published their landmark contributions. Newton's insights into gravity and optics came when he was twenty-three, “in the prime of my age for invention” or his “annus mirabilis.” Einstein published his special theory of relativity at the age of twenty-nine in his own annus mirabilis of 1905. In the last four centuries, only Newton and Einstein among major theorists were able to surpass their earliest work—Newton with his universal law of gravitation in 1686 and Einstein with his general theory of relativity in 1916.

But even Einstein's gifts finally failed. In the late 1920s, while in his late forties—an almost Methuselah-like age for topflight creative work in theoretical physics—Einstein began his exit.

Why such a “running down” of energy happened to him, or happens to other scientific theorists, is a puzzle, as mysterious as the initial outburst of genius that occurs early in such careers. Explanations range from the physiological (a decrease in testosterone, according to the psychologist Satoshi Kanazawa) to the sociological (math and physics reward brash, revolutionary discoveries, and thus brash, youthful thinkers) to the biohistorical (age statistics are affected by life expectancy or the relative “age” of
the field).
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Despite a mountain of studies, we know very little about why such supreme gifts appear or disappear.

“Genius” is a word that only gives a local habitation and a name to an unfathomable phenomenon: Would we call it genius otherwise? Genius eludes definition partly because it points not to a single ability, but to a web of abilities and coincidences that must hang together delicately yet powerfully to work at all. In physics and logic, mathematical prowess is obligatory; but so are audacity and courage, penetrating insight, imaginative vision, tenacity—and luck. And luck must occur not only within the arena of study—for instance, finding the right equations—but in a larger sense as well: In order to ponder gravity, Newton must first have survived the plague; in order to develop his general theory of relativity, Einstein must first have had the leisure and salary offered by the Kaiser Wilhelm Institute of Physics and must first have accepted the post in late 1913, before World War I had barred him from entering Germany. Accident not only historical, but emotional can loose creative genius. Take, for instance, Einstein's separation from his first wife, Mileva, in the year prior to general relativity, and Gödel's serendipitous marriage to a cabaret singer who kept him sane.

At some point, however, one or another of these powers—or the way they join together—changes, and “genius” departs. Perhaps insight fails, or else ambition or energy, or the theorist becomes too cautious, or is surpassed by students (as the great physicist Max Born confessed of Pauli, his onetime assistant), or can't keep up with new ideas. (Paul Ehrenfest, Einstein's cherished friend, committed suicide at fifty, an act Einstein attributed in part to the “difficulty that adaptation to new ideas inevitably imposes on a man of fifty.”
⁵
) Or perhaps the theorist simply finds physics no longer quite so important—as with Newton, who in middle age took up theology.

The “middle-aged” scientist often seems to his or her colleagues to be a flawed version of that younger, more brilliant self.
Those phenomenal gifts are still evident, but something seems “off” or amiss.

Einstein's seeming failure to produce theoretical insights after the mid-1920s is an example. In 1916, when he published his theory of general relativity, he was thirty-eight, still at the height of his powers. His last contributions, on wave theory and quantum statistics, came in 1925. By then, Einstein was launched on his quest for a unified theory—as quixotic a journey as that of any hapless knight. Many critics think that Einstein misjudged the problem of a unified theory as he would never have done before. But even so, something slowed him down. He was stymied at every step. Only his old boldness and tenacity kept him doggedly going, decade after pointless decade. Some crucial power seems to have left that marvelous mind, and Einstein eventually became resigned to it.

Something similar happened to Pauli in physics and to Russell and Gödel in logic. In his thirties, Pauli was already becoming more of a critical than a creative force within physics. In their thirties, Russell and Gödel both began to abandon logic for philosophy.

Why do physicists and mathematicians seem more susceptible to this fading of creative energy and genius than, say, artists and composers and writers? Johann Sebastian Bach, after all, kept building incomparable structures of abstract musical symbols until his death at seventy-five; Yeats wrote great poems into his seventies. Goethe's artistic maturation continued until his death at eighty-three. Picasso worked successfully into his nineties, DeKooning into his eighties, Braque until his death at eighty-one. No such example of late-stage genius and production can be found in the sciences.

This striking difference between the worlds of science and art was noted by the eminent astrophysicist S. Chandrasekhar, who, musing on artistic genius, thought of Beethoven's words: “
Now,
I know how to compose.” At forty-seven, Beethoven had already written eight symphonies, five piano concertos, eleven quartets, and twenty-five of his thirty-two piano sonatas.

Scientists do not develop this way, suggests Chandrasekhar. Their genius flowers young and does not “mature.”
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No major scientist has continued to grow through life as did Beethoven, or Shakespeare, or Rembrandt—not to mention Verdi, Titian, Picasso, or Thomas Mann. To paraphrase F. Scott Fitzgerald, there are a great many triumphant third acts in art and literature, but even second acts are rare in science.

Something systemic—peculiar to scientific endeavor—seems to be involved. Genius is an individual matter—one that varies from person to person and is expressible in a myriad of forms. But science is a collective enterprise. It progresses and builds, dependent on a process of incremental contribution. Even revolutions in science—Thomas Kuhn's paradigm shifts—require structures to build upon (or tear down).
⁷

Scientists thus often live to see their greatest work superseded, modified, or refuted. None escapes the relentless march: Immortal Newton was displaced by Einstein, and Einstein fully expected that his work would be corrected or surpassed. In 1949, he wrote to a friend:

You imagine that I look back on my life's work with calm satisfaction. But from nearby it looks quite different. There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track.
⁸

Einstein's humble reflection reveals from within what can be called “the pathos of science.” Neither artists nor philosophers are prey to this pathos: Nothing can “improve” upon Socrates'
Oedipus Rex
or Mozart's
Don Giovanni
or Plato's
Republic,
though these works are subject to the vicissitudes of changing tastes and interpretations. Indeed, poets are especially caught up in intimations of immortality, as distinct from mere fame. Milton invokes the “Heavenly Muse” to ensure that his
Paradise Lost
would “soar / Above
th' Aonian mount, while it pursues / Things unattempted yet in prose or rhyme.”

Scientists, on the other hand, create only to be superseded. The greatest scientific achievements will be scrutinized and, eventually, proven inadequate. After two thousand years, Euclid's geometry was shown to be limited and was augmented by the non-Euclidean geometry of Carl Friedrich Gauss. Within twenty years, a fellow German, Georg Friedrich Bernhard Riemann, improved on Gauss—and Riemann's geometry helped lead Einstein to his general theory of relativity.

Science is a community of interlocked, perpetual, cumulative effort. No one can be successful except by working within its common premises and rules of procedure and proof—however “revolutionary” the work. But the cumulative nature of science also means that each individual effort will be supplanted. Discoveries keep occurring—and every discovery means that some previous finding becomes modified or discarded. Thus, most productive scientists become half-forgotten figures in the public mind, existing in textbooks as abbreviations, symbols, and identifiers: Boyle's law, the joule, the fermi, Planck's constant. The incessant construction of science provides new and exalted triumphs (Einstein, after all, can build on Newton), but also ensures one's own “defeat” or limitation—sometimes within a few years.

The four men in Einstein's study provided striking examples of this “pathos of science.” Here were two aging scientists paired with upstart revisionists: Einstein and Pauli, Russell and Gödel. At stake were none other than the fundamental structures of modern physics and logic.

Wolfgang Pauli was only sixteen when Einstein's general theory of relativity turned physics upside down. Within four short years, Pauli was to write a definitive explanation of relativity for the
Encyclopädie der Mathematischen Wissenschaften
—an account so clear that forty years later, Niels Bohr lauded it as “still
one of the most valuable expositions” of Einstein's theory. Five years later, Pauli presented his “exclusion theory,” the first in a number of successive discoveries by Pauli and Werner Heisenberg that defined the nascent field of quantum mechanics.

Behind it all was Einstein, who, using Planck's concepts, “launched” quantum physics in 1905. But Einstein's quantum physics was built on classical physics. No “uncertainty” there. The new quantum mechanics, formulated by Bohr, Heisenberg, and Pauli, no longer postulated an objective reality that could be observed and measured. To Einstein's horror, physics had become a matter of statistical laws rather than certainty. “God does not play dice with the world!” he exclaimed.

Pauli and the quantum physicists had triumphed, however. At the Fifth Solvay Conference in 1927, quantum physics took on classicism from the lectern and in the corridors of discussion. Einstein, who did not present a paper, spoke against the new world of physics heralded by Niels Bohr and his young followers, among them Pauli and the German wunderkind Werner Heisenberg. Stubbornly, Einstein held out against the tidal wave of quantum physics. All indeterminacy was temporary, he insisted, a passing stage within the history of physics. Sooner or later, with more knowledge and insight, physicists would be able to lay aside uncertainty. He never gave up that belief.

But quantum physics, argued Bohr and his quantum conscripts, was here to stay. Uncertainty was not an imposition of humanity onto nature, but a fundamental state. However distressed the Solvay participants might have been by Einstein's vehement opposition, the conference shifted the ground so vigorously that, during the three years between the Fifth and the Sixth Solvay Conference, Einstein found himself in a rearguard position. He was by far the most visible and vocal critic of quantum physics. He devoted the remainder of his life to the search for a unified theory, in hopes of proving Pauli and his quantum mechanics wrong. But in the intervening years, Einstein's position had gained no ground.
Pauli and his quantum associates held sway in a world of physics that had passed Einstein by.

Russell and Gödel were also scientific rivals. Russell's pioneering
Principia Mathematica
won him fame as a logician and was the basis of his philosophic authority and later reputation. Written with Alfred Whitehead and published in three volumes beginning in 1910, the
Principia
tackled the entire domain of mathematics. Its purpose was to demonstrate that “all pure mathematics follows from purely logical premises and uses only concepts definable in logical terms.”
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The impulse to subsume mathematics into pure logic (called “logicism”) began with Gottfried Leibniz, who, in the seventeenth century, yearned for a universal language based on logic. Not until the late nineteenth century, however, did logicians develop the tools (in the form of definitions and methods) needed to place mathematics more or less within the realm of logic. In 1879, the German logician Gottlob Frege began his life's work on a system to formalize logic and to develop a logical foundation for mathematics. In their
Principia,
Russell and Whitehead solved inconsistencies that Frege and others could not. (Indeed, Russell had to solve his own “Russell's paradox,” which demonstrated inconsistencies in Frege's axioms, before he could complete his
Principia
.) In its three lengthy volumes, the
Principia
devised a comprehensive and very usable notation system; by demonstrating the power of logic, it inaugurated the field of metalogic; it placed logicism comfortably within the realm of traditional philosophy and even made it fashionable.

But the underlying premise of the
Principia
—that mathematics was a complete and thus a universal language and logical system—was thoroughly demolished by the upstart Gödel. In 1931, Gödel published his infamous proof known as the “incompleteness theorem.” In it, he demonstrates that no mathematical system that depends on axioms can be thought of as complete, for in any such system, some propositions can be neither proved nor disproved. In extinguishing the dream of a consistent mathematical
system, Gödel became, in the eyes of many, one of the two most important logicians of the twentieth century—the other being Russell himself.

Pauli and Gödel were simply following in the tracks of Einstein and Russell. Einstein built upon and upended Newton; Russell built upon and upended the pioneering mathematical logician Gottlob Frege. So science marches on.