“The greatest mind in American history”

Beinecke Rare Book and Manuscript Library, Yale University

J. Willard Gibbs (1839–1903), a Yale student and professor, was a quiet, bookish figure who left a towering legacy. View full image

Beinecke Rare Book and Manuscript Library, Yale University

J. Willard Gibbs (1839–1903), a Yale student and professor, was a quiet, bookish figure who left a towering legacy. View full image

Beinecke Rare Book and Manuscript Library, Yale University

Gibbs as a young man. View full image

Beinecke Rare Book and Manuscript Library, Yale University

Gibbs as a young man. View full image

The US Navy research vessel that was named for Gibbs. View full image

The US Navy research vessel that was named for Gibbs. View full image

The US stamp printed in his honor. View full image

The US stamp printed in his honor. View full image

Ed Hoop

The J. W. Gibbs Research Laboratories, on Science Hill, housed decades’ worth of research but have become outdated. The structure is being replaced by a new science building. View full image

Ed Hoop

The J. W. Gibbs Research Laboratories, on Science Hill, housed decades’ worth of research but have become outdated. The structure is being replaced by a new science building. View full image

Gibbs's second masterpiece, published in 1902, ushered chemistry into the quantum era. View full image

Gibbs's second masterpiece, published in 1902, ushered chemistry into the quantum era. View full image

Cavendish Laboratory, Cambridge

A plaster model based on some of Gibbs's three-dimensional equations. It was constructed by Scottish theorist James Clerk Maxwell, who sent it to Gibbs; it is still at Yale's Sloane Physics Laboratory. View full image

Cavendish Laboratory, Cambridge

A plaster model based on some of Gibbs's three-dimensional equations. It was constructed by Scottish theorist James Clerk Maxwell, who sent it to Gibbs; it is still at Yale's Sloane Physics Laboratory. View full image

When Josiah Willard Gibbs died in 1903, a European physicist described him as “the greatest synthetic philosopher since Newton.” And this was before scientists really understood the full importance of his work.

Admirers have since given Gibbs’s name to a crater on the moon, a US Navy research vessel (now retired), and an annual medal honoring the world’s most eminent chemists. Yale, the place to which Gibbs devoted his life, also honored him. In 1955 it opened the J. W. Gibbs Research Laboratories on Science Hill. But the lab became badly outdated (and leaky in wet weather). It has been demolished to make way for a new science building, with advanced labs and instruments, designed as an interdisciplinary hub for biology and the physical sciences. 

From the aesthetic point of view, Gibbs Lab isn’t considered much of a loss. (Vincent Scully ’40, ’49PhD, a Sterling Professor of Art History emeritus, has called it “banal and rather tacky late modernism.”) And Gibbs’s name will still be memorialized on campus. A plaque near Berkeley College marks the site where his house once stood. A plaque from Gibbs Lab has been preserved and will become part of a memorial in his honor. A walkway connecting Sloane Physics Laboratory and Sterling Chemistry Laboratory will be named for him. But the demolition of the lab demands a moment of reflection on Gibbs and what he accomplished—all the more necessary because most laypeople barely know his name, let alone his work.

He was born in New Haven, the child of Josiah Willard Gibbs Sr. ’09, a Yale professor of sacred languages. (The elder Gibbs is also remembered for his successful effort to find a translator for the enslaved captives of the Amistad, so that their story could be heard.) After earning Yale’s, and the country’s, first engineering doctorate in 1863, young Gibbs focused at first on practical problems in steam engine and railroad mechanics. But in about 1870, he switched to theory. Working largely in isolation, he laid out the foundations for modern chemical thermodynamics and helped found the fields of physical chemistry and statistical mechanics. Even high school math students experience his influence: the vectors they use to depict the magnitude and direction of a force come from the system of vector analysis devised by Gibbs.

Why isn’t a scientist of Gibbs’s stature more widely known? He was a quiet, bookish figure, with no interest in self-promotion. He rarely socialized and never married (though one acquaintance described him as “the happiest man” she ever knew). And he wrote in a terse mathematician’s style that tended to conceal the intellectual treasures his work contained.

Gibbs deserves to be known, and his accomplishments recognized, by Yale alumni. In the following pages, writer Richard Panek provides a short layperson’s guide to the work of a home-grown scholar whom Yale physics professor Ramamurti Shankar describes as “one of the great creative scientific geniuses of all time.”—The Editors 

Josiah Willard Gibbs was—is—a scientist’s scientist. He quietly did what he did; what he did wound up mattering a lot; and then, just as quietly, he disappeared. Unless you’re familiar with his field, you’d never hear his name.

But which field? Part of his legacy—his reputation as a foundational figure in modern thermodynamics, at least among modern thermodynamicists—is that he pioneered so many disciplines. His first masterpiece, a 300-page paper he published in the 1870s, long ago gained a reputation as the Principia of thermodynamics (the science of heat and energy), precisely because of its fecundity: like Newton’s synthesis of celestial and terrestrial physics, Gibbs’s work on thermodynamics unified myriad seemingly unrelated concepts, bequeathing to future generations the challenge of developing each into its own field of study.

Gibbs didn’t start as a theorist. As a PhD candidate in engineering at Yale in the early 1860s, he produced a thesis entitled “On the Form of the Teeth of Wheels in Spur Gearing”; he rendered the form of the teeth in geometry. After traveling to Germany and encountering the principles of the physicists Gustav Kirchhoff and Hermann von Helmholtz and the chemist Robert Bunsen, Gibbs’s focus turned to chemistry and thermodynamics.

When Gibbs, now a professor of mathematical physics at Yale, began publishing scientific papers in 1873, the first two laws of thermodynamics were only eight years old: “The energy of the universe is constant,” the German physicist Rudolf Clausius had declared in 1865. “The entropy of the universe tends to a maximum.” Gibbs added entropy to the components of a thermodynamic system and, drawing on his thesis work, created a system for describing their interrelationships through geometry—first in two dimensions, then in three: volume, entropy, energy. 

Gibbs’s use of the geometric approach to thermodynamics, rather than the traditional algebraic approach, caught the attention of James Clerk Maxwell, the Scottish theorist who had recently formulated the equations that unite electricity, magnetism, and light. Maxwell became Gibbs’s champion, even constructing plaster models of the thermodynamic surface for a fictitious water-like substance that he based on Gibbs’s three-dimensional equations. (One of these plaster models he sent to Gibbs; it remains on display at Yale’s Sloane Physics Laboratory.) “Read Gibbs,” Maxwell wrote to a fellow Scottish physicist. “He has more sense than any German”—a not insignificant compliment in an era in physics that was dominated by German scientists.

Then came On the Equilibrium of Heterogeneous Substances. In this 1878 book-length paper, Gibbs provided what amounted to a unified theory for thermodynamics. Gases, mixtures, surfaces, solids, phase changes, chemical reactions, electrochemical cells, sedimentation, osmosis: Gibbs showed how thermodynamic principles can describe each of these seemingly separate phenomena.

Beinecke Rare Book and Manuscript Library, Yale University

Gibbs's PhD thesis, now in the Beinecke Library. View full image

“In the 1870s, with the discipline of physical chemistry not yet born, Gibbs’s topics were unfamiliar and disparate,” the chemist William H. Cropper wrote in a chapter on Gibbs in his 2001 book Great Physicists, including Gibbs among a pantheon of only 30 scientists from Galileo to Stephen Hawking. “Each of these topics is now recognized, largely by physical chemists, as a major area of research.”

To this point in his career, Gibbs had focused mostly on a macroscopic view of thermodynamics. In the 1880s, and for the rest of his life, he concentrated on the microscopic view—the realm populated not by engines and candles, but by molecules and atoms.

The existence of molecules and atoms was still a matter of contention, but many theorists, including Gibbs, saw them as useful imaginative tools. Gibbs soon realized, however, that the microscopic view necessarily involves the behavior of a system that is too complex for the likes of us, with our macroscopic-evolved eyes and macroscopic-constrained brains, to follow on a molecule-by-molecule basis.

Ever since Newton, cause-and-effect relationships had ruled science. Measure the angle, mass, and force of a billiard ball that crashes into another billiard ball, and you can predict the outcome for both balls—trajectory, speed, final resting place. At the molecular level, however, systems operate as if they consist of billions of billiard balls, each seemingly behaving in a random fashion.

Gibbs had already foreseen the problem, as well as its solution, in a discussion of atoms in On the Equilibrium of Heterogeneous Substances. Expanding on the work of Maxwell and the Austrian physicist Ludwig Boltzmann, he argued that rather than a strictly deterministic approach, the study of systems of molecules requires a statistical approach. “You have to describe it as a population,” says Yale physics professor Ramamurti Shankar, who has been “a big fan of Gibbs” since discovering his work as a student in Madras, India. “But now the subject matter is not people, but molecules.” Just as an actuary can’t predict the health of any individual but can assess the death rate for a population of sufficient size, so the scientist working on the molecular level can make use of probabilities. The behavior of individual atoms is due to chance, but the outcome for the system as a whole is certain.

Or, more accurately, very, very, very nearly absolutely certain. “Impossibility,” Gibbs wrote, “seems to be reduced to improbability”—improbability of a very high order, but improbability nonetheless. He enshrined his concepts in his second masterpiece, Elementary Principles in Statistical Mechanics Developed with Special Reference to the Rational Foundation of Thermodynamics, published in 1902, a year before his death. Statistical mechanics—a term he invented—was the methodology that would allow chemistry, almost alone among sciences, to make the transition from the classical era of cause and effect to the quantum universe of all probability all the time.

Except among his immediate peers, Gibbs never attained a broader profile. After the trip to the Continent in the 1860s, he rarely left New Haven; even there his perambulations extended mostly from his home on High Street to his office in the Sloane Laboratory and back again. His breakthrough work in the early 1870s was published in The Transactions of the Connecticut Academy of Arts and Sciences, a journal that, whatever its intellectual merits, didn’t have much of a readership. 

When Maxwell died prematurely in 1879, at the age of 48, Gibbs lost his foremost advocate just as word of his work was beginning to spread. And his writing style was nearly cryptic in its economy—at least in the opinion of others. The physicist Lord Rayleigh wrote to Gibbs that On the Equilibrium was “too condensed and too dense”; Gibbs responded that the book was “too long.” Even Einstein found Gibbs’s writing inscrutable—but also admirable. “The greatest mind in American history,” Einstein called Gibbs.

Those in the know continued to praise Gibbs. In his 1910 Nobel Prize acceptance speech, the Dutch physicist J. D. van der Waals acknowledged Gibbs’s influence. Max Planck, in his own Nobel acceptance speech in 1918, declared that Gibbs “not only in America but in the whole world will ever be reckoned among the most renowned theoretical physicists of all times.”

Or not. Among his (few) biographers was the poet and political activist Muriel Rukeyser. 

Why a poet? In a 1943 review of her Willard Gibbs: American Genius, Waldemar Kaempffert, the science and engineering editor of the New York Times as well as the first director of the Museum of Science and Industry in Chicago, offered a guess: “His equations are as romantic as any lyric ever penned by an Elizabethan poet. They reveal a wildly improbable world in which a kettle of water may freeze if put on a fire or all the salt in the ocean may spontaneously pile up in one place.” Gibbs was, Kaempffert wrote, “the most distinguished creative scientist this country has ever produced, yet”—he added, crucially, prophetically—“a man whose name means nothing to the multitude.”

Gibbs’s name remains a presence in the terminology of chemistry: Gibbs free energy, Gibbs-Duhem equation, Gibbs vector. That recognition likely would have been enough for Gibbs. “He expected nothing; nothing from outside,” Rukeyser wrote. “He was sure of himself, and trusted himself.” In that respect, his instincts were as unerring as they were in his theoretical work: he was content to do his science, to know it was important, and to suspect, correctly, that it would long outlast him.