Philip Anderson, a theoretical physicist who wrote rules that dictate the strange behavior of condensed matter and lent his deep intuition to problems beyond physics, died on March 29, 2020. He was 96 years old.

“It is hard to overstate the importance of the ideas of Phil Anderson to the science of SFI and complexity in general," said Santa Fe Institute President David Krakauer. "His 'More is Different' article from Science in 1972 was the most important and rigorous refutation of the foolishness of reductionism for complex systems yet published. Not only did Phil articulate why confusing parts for the whole was a problem, but in the process, he explained why different fields of inquiry – from genetics to economics – needed to exist. This was a supreme act of intellectual modesty and generosity."

Within the physics community, Anderson was known for his crucial work on a diverse array of phenomena, from superconductivity to antiferromagnetism to electron localization—for which he shared the 1977 Nobel Prize in Physics. He was also interested in emergence, or the ways in which new properties appear as systems get more complex, a pursuit which led him to help found SFI.

In 1984, Anderson took part in the Institute’s first workshops, “Emerging Syntheses in Science,” where he discussed an exotic type of magnet called spin glass, which he believed held connections between physics, evolutionary biology, neuroscience, and computer science.

The mathematical description of spin glasses, Anderson argued, was broadly applicable and revealed that “in each case the behavior of a system is controlled by a random function of a very large number of variables.” In the brain, this mathematical function could describe neurons; in the cell, it could describe the complex, random behavior of the genome. These were no idle analogies and the ideas led to potent applications.

“You can see a direct thread all the way through from Anderson's work on spin glasses to the modern ideas of machine learning,” said Piers Coleman, a physicist at Rutgers University in New Jersey and one of Anderson’s former doctoral students.

Over the next two decades, Anderson continued to be involved with the Institute, attending workshops and engaging in sharp intellectual battles with its other leading minds. He tackled interdisciplinary problems with insight honed by decades of solving the toughest problems in physics. But he never believed physics alone could provide all the answers.

In a seminal paper, “More is Different,” Anderson wrote: “It is not true, as a recent article would have it, that we each should ‘cultivate our own valley and not attempt to build roads over the mountain ranges … between the sciences.’ Rather, we should recognize that such roads, while often the quickest shortcut to another part of our own science, are not visible from the viewpoint of one science alone.”

Philip Warren Anderson was born in Indianapolis, Indiana on December 13, 1923, to Henry Warren Anderson and Elsie Eleanor Anderson, neé Osborne. He grew up surrounded by, as he put it, “secure but impecunious Midwestern academics,” who helped nurture his love of science and nature.

A voracious reader, Anderson earned a scholarship to Harvard, where he spent three years learning physics before graduating at nineteen and shipping off to the Naval Research Laboratory to help with the war effort. Afterwards, he returned to Harvard for graduate school, where his advisor was John Van Vleck, with whom he would later share the Nobel. Anderson fondly recalled spending time with fellow graduate students, who included philosopher of science Thomas Kuhn and the satirist Tom Lehrer. In 1947, he married Joyce Gothwaite and they had a daughter, Susan.

Anderson finished his graduate thesis—in retrospect, it was a breakthrough that solved a major problem in microwave spectroscopy—but his work was unrecognized. It was only with help from Van Vleck that he landed a job at Bell Labs, where he would be employed for the next 35 years. There, Anderson learned from and worked with world-class solid-state physicists whom he frequently credited for showing him the ropes.

At Bell Labs, his first major success came in a theory explaining antiferromagnetism. In a normal magnet, magnetic moments align in the same direction; in an antiferromagnet, they alternate in opposite directions. Previous theories couldn’t figure out how the unusual magnetic state could exist—quantum fluctuations were predicted to wipe its delicate order out. But Anderson showed that in two or more dimensions, the quantum fluctuations would actually cancel out, so the antiferromagnetic order would be preserved.

”Magnetism was something on which he cut his teeth,” said Coleman. “It provided a framework which helped him greatly in his understanding of superconductivity.”

In 1957, Anderson’s contemporaries, John Bardeen, Leon Cooper, and Robert John Schrieffer, put together a theory to explain superconductivity, the strange state of matter in which electrons flow unimpeded. But BCS theory had a problem: it introduced an unaccounted-for macroscopic quantum field. Anderson spotted this problem and rescued the theory by making it gauge-invariant—a crucial property necessary for the theory’s stability.

During his career, Anderson also took on many students, two of whom later became Nobel laureates: Brian Josephson and Duncan Haldane.

“Phil was sort of like the Oracle of Delphi,” said Clare Yu, a former student and physicist at the University of California, Irvine. “He was really hard to understand. And he would know what he was talking about, but he was half talking to himself and half talking to you.”

But, Yu said, learning from him taught her to really think. Whatever his methods, Anderson’s care for his students bred loyalty. In 2014, decades after some had learned from him, students and colleagues from around the world gathered to celebrate his 90th birthday.

As a physicist, Anderson relied heavily on intuition rather than sheer mathematical prowess.

Describing Anderson’s approach to physics, Yu recalled him saying, “Theoretical physics is not just doing calculations. It's setting up the problem so that any fool could do the calculation.”

His Nobel-winning work on electron localization is a testament to that keen physical understanding. For decades, physicists had assumed that electrons flowed uniformly throughout metal. But after noticing some strange results from an experiment at Bell Labs, Anderson realized that electrons were not diffusing through the metal. Creating a simple model, he showed that impurities in the metal would lead to disorder, causing electrons to become stuck, or localized.

“He would look at experimental phenomena, and then he would reach for a very ambitious interpretation of the facts. It’s something striking,” said Shivaji Sondhi, a condensed matter physicist at Princeton.

At first, electron localization was mostly dismissed because it was so against the grain. But by 1977, when he received the prize, there could be no doubt. Since its acceptance, the phenomenon has been observed in other contexts; in some materials, even light exhibits what is now called Anderson localization.

Over the years, Anderson frequently clashed with particle physicists, who he felt were wrong in asserting that theirs was a more fundamental science. Ironically, one of his most significant contributions would be in particle physics. In 1962, Anderson applied what he’d learned from superconductivity to address a question at the heart of physics: How do particles acquire mass?

In a superconductor, a small change to the initial conditions results in a dramatically different final state where there is zero resistance. This “spontaneous symmetry breaking” is analogous to a ball balanced at the top of a hill, where a small push could send it to a valley on either side. Anderson realized this spontaneous symmetry breaking could be used to explain how gauge bosons—particles that govern forces—could have mass. Two years later, particle physicists including Peter Higgs expanded on his work. Today, the way gauge bosons get their mass is usually referred to as the Higgs mechanism, not the Anderson-Higgs mechanism. But it would not have been developed without Anderson importing the concept of broken symmetry from condensed matter research.

“This is an amazing story because it starts in magnetism and took him up to something of cosmic significance,” said Coleman.

Anderson also worked to explain the odd properties of superfluid helium: At a cold enough temperature, helium suddenly transforms into a strange, zero viscosity liquid that flows without friction. Like superconductivity, superfluidity was another phenomenon that exhibited symmetry breaking—a topic he would return to again and again.

The abrupt changes in behavior exhibited when symmetry is broken suggested to Anderson a different way of conceiving the universe. While everything might be reducible to fundamental laws, the reverse is not true—“the whole becomes not only more but very different from the sum of its parts.” Reconstructing even a single red blood cell from the level of quarks and electrons is infeasible, if not impossible.
“The more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society,” Anderson wrote in More is Different.

To Anderson, the reductionism espoused by particle physicists was wrong. There was fundamental work to be done at every level of complexity in the universe because of emergent properties. Though the paper never explicitly used the word “emergence,” it said what it needed with the title alone: Add more, and the system is different.

During the ‘80s, this focus led him to Santa Fe, where he helped found the Institute and played a role, especially in the development of complexity economics. In 1987, Anderson worked with fellow Nobel laureate, economist Kenneth Arrow, to organize a conference at the Institute. For over a week, economists and scientists joined—and butted—heads to puzzle out the next frontier in economics.

“There was a sense of excitement that these ideas were really new, and it was a big opportunity,” said External Professor Doyne Farmer, a physicist who attended the conference.

W. Brian Arthur, an economist and SFI External Professor, recalled a notable exchange in which Anderson challenged the widely relied-upon assumption that people are rational actors.

“Phil just screwed up his face,” said Arthur, who is an external faculty member at SFI. “He said ‘You guys really believe that?’”

With scientists challenging economists, and economists reworking their preconceptions, the field of complexity economics was born. Drawing from mathematical techniques used by physicists, economists developed a way of modeling a dynamic economy that is always adapting.

“Having him at meetings, stirring the pot and throwing out ideas,made a huge difference,” said Farmer.

Anderson continued to be deeply involved with SFI until 2001, when he retired from the Steering Committee. While he was involved, he used his reputation to bring experts like physicist Per Bak to SFI and helped convince Arrow and other backers of the economics program that its unconventional early work had value.

“Phil was kind of a godfather in all of this,” said Arthur.

In his later years, Anderson focused on high-temperature superconductors. He presented the first theory to explain the phenomenon, but abandoned it for nearly a decade, believing it to be wrong. Numerous questions still remain about high-temperature superconductivity, but Anderson’s early work still provides one of the best working models.

Anderson remains largely responsible for the field of condensed matter as it is today, from coining the term “condensed matter” to fighting for its fundamental nature.

“He encouraged the field to think of itself ... as the gateway to a garden of wonders,” said Sondhi.

As a senior scientist, he also opined on policy. Anderson leveraged his stature politically, joining physicists who campaigned against the Reagan-era “Star Wars” missile defense system, and later butting heads with them when he fought against particle physics projects like the planned Superconducting Super Collider.

Even among Nobel laureates, Anderson stood out. A 2006 study that purported to measure “creativity” based on citation networks placed him at the top of highly-cited physicists.

“He had a very broad-ranging intellect, and could always come at any problem and then think about it from a different point of view,” Yu said.

“And Phil was very prepared to let his colleagues know that without pluralism and empiricism science morphs into metaphysics," Krakauer added. "I remember having lunch with Phil at the Institute for Advanced Study in Princeton. He asked a group of us what we 'thought of the theologians at the institute?' We were all a little confused by his question unaware that there were any in residence until he clarified his question, 'the string theorists!'. We all looked around rather sheepishly while Phil beamed his skepticism to the room.”

In addition to his work in physics, Anderson also played Go, which he had picked up while living in Japan. He could be mischievous about it, as Arthur remembers.

“I said, 'Oh, are you any good at Go?' Phil shrugs his shoulders. 'Yes. I suppose.' I said 'How good?' Typical Phil, you have to pump all this out of him. And Phil says 'Well, there are four people in Japan who can beat me.' And there's dead silence. Half a minute later, we're all just sitting open-mouthed, staring at Phil. And then Phil says, 'But they meditate.' As if that was cheating,” Arthur said.

Anderson was, in fact, a master. In 2007, he was conferred a lifetime achievement award from the Nihon Ki-in, the Japanese professional Go association.

“That was very much Phil. Layers and layers and layers of smooth water, but down below, an incredible machine of a mind,” Arthur said.

Readers who knew Anderson are invited to share remembrances over social media. Comments can be added to SFI's announcements on Twitter and on Facebook and can also be emailed to news@santafe.edu.

[By Daniel Garisto]

Read the obituary in The New York Times (March 30, 2020)

Read the obituary in Science (March 30, 2020)

Read the obituary in Physics World (March 30, 2020)

Read the tribute in Scientific American (March 30, 2020)

Read the obituary in The Washington Post (April 1, 2020)

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