“After a certain high level of technical skill is achieved,” Albert Einstein famously remarked, “science and art tend to coalesce in aesthetics, plasticity, and form.”

I’ve long believed he was right. I can point to many moments in my career as a theoretical physicist when I’ve been guided as much by aesthetic intuition in engaging our deepest dilemmas about the behavior of subatomic particles, space, time, and the nature of reality, as I have been by mathematical logic. Aesthetics is always present in theoretical physics, in sometimes inarticulable and undepictable ways. But never have the mathematical and aesthetic aspects of my work found such striking synthesis as in the geometric objects that my colleagues and I came to call “adinkras.”

Adinkras are geometric objects whose underlying principles, and forms, have bolstered our understanding of the mathematical description of physical law. Lending visual form to some of the hardest problems in mathematical and theoretical physics, they’ve proved hugely useful in helping us understand relationships in the microscopic world according to the precepts of quantum theory and “supersymmetry,” the aspect of string theory to which I’ve devoted most of my career (and about which, more in a moment). But more than that, adinkras have shaped an understanding of subatomic physics in ways that transcend the specific questions they were created to help us see.

Human brains, as neuroscientists tell us, are often better at understanding problems we can visualize. And so it has proven to be the case with these adinkras. The laws of physics are typically represented in equations that are opaque to anyone who has not devoted their life to their interpretation. Adinkras are visualizations that represent the language of mathematics in a geometric object. The story of adinkras and of our discovery of them earlier this century, like many advances in mathematics, reaches back decades—and runs, for me, back to my first days as a student at MIT, where I arrived as an undergraduate in 1969.

As the first member of my family to attend college, I was what you could call a DEI kid from the wrong side of the tracks. As a teenager, I’d grown up in Orlando, Florida, in an area of that southern city—the so-called Parramore District—which from the 1890s was designated as the place where “colored people” were permitted to live, west of downtown and across a set of north-south railroad tracks that bisect the city. Jones High School, then the only secondary school in Orlando that Black students could attend, wasn’t a well-funded or well-supported institution. But I had some wonderfully committed and capable teachers. And at age 14, I learned from a TV program about the existence of the Massachusetts Institute of Technology. It became my dream to go there—a dream that came true when M.I.T. decided to let in 50 African American students in the fall of 1969, the first time the university admitted more than a handful of students from outside its traditional feeder schools and elite networks worldwide.

I was fortunate to be one of those students, and gratified to thrive so much as an undergrad that I earned two B.S. degrees in four years, one in mathematics and one in physics. I stayed in Cambridge for graduate school. As a PhD student, I undertook and then defended M.I.T.’s first-ever thesis on the topic of “supersymmetry.” In 1977, this wasn’t a topic that anyone else—faculty, researchers, graduate students––knew anything about. Through my sense of aesthetics, I was convinced that it represented a vital new strain of inquiry in theoretical physics. I was proven right in the decades that followed, and we’re still wrestling with the profound possible implications of supersymmetry today.

Sylvester James Gates, Jr. as a Project Interphase instructor at MIT, 1975.

Courtesy of the MIT Museum

The putative discovery of antimatter, which dates from the 1920s, revealed a world of opposites. For almost every kind of particle, there exists an antiparticle: its exact, perfect opposite. If an electron spirals to the left, in a magnetic field, a positron will spiral to the right. If an electron is repelled from a source, a positron is attracted to it. This wasn’t science fiction. Antimatter could be created, and annihilated in the laboratory, and in nature. Supersymmetry took this deeper. It posits that for every particle, there is also a supersymmetric partner that interchanges the most inviolable quantum characteristics of matter—that for every boson, as one fundamental kind of subatomic particle is called, there exists a partner particle, a fermion, with different spin properties.

Supersymmetry is also known by the sobriquet SUSY; it grew from what was, in the 1970s, the still-novel field of string theory, which suggests that the subatomic world is composed of vibrating loops. This idea was profoundly unifying. There wasn’t a zoo of disconnected particles—just different notes on the same kind of fundamental string. In the unification was a hope for a theory of everything. Supersymmetry, by positing how elementary particles correspond and relate, suggested how such theories could be shaped.

By 1995, when I began working with a graduate student named Lubna Rana, many more people in our field were thinking about supersymmetry. Lubna, with whom I went on to publish several papers in this field, also happened to be my first female grad student in physics. I began our work together, as one does with any tyro student, by giving her a sort of starter problem—a task to test a student’s preparation and will to be successful in the difficult field of mathematical and theoretical physics. And so it was in Lubna’s case that I gave her a problem relating to the history and implications of various supersymmetric field theories.

One of the most beautiful things about mathematical-enabled research is that one can arrive at conclusions without knowing others have done the same beforehand. And in looking into the origins of supersymmetric field theories, we were struck to discover precursors to these theories in the work of mathematicians working on both sides of the divide between the Soviet Union and Western Europe during the Cold War. Though separated by the Iron Curtain, we could share ideas. We built on theirs to explore the mathematical structures undergirding supersymmetry. As I guided Lubna’s thesis to its completion, we wrote a series of papers about these mathematical models. We uncovered more and more interesting properties about the subatomic realm. Without quite realizing it, I had taken a giant step to realize my unexpressed dream––to find an intricate piece of hidden mathematics that accurately described something equally hidden in nature.

Expressing the mathematical structures and making them useful, however, involved a further step—as I found at a conference in France, at Luminy outside Marseille, in 2006. At that gathering of mathematicians, the nearby Calanques National Park was magnificent, but my presentation was not. The talk was a total failure that left me with a sharp sense that I needed a better way to communicate what we already knew across the language gap separating mathematics and physics. Luckily, by then I had begun to develop a way to bridge this gap.

A couple of summers before, I was in the republic of Georgia, visiting that nation's capital of Tbilisi, when I engaged in a typical morning habit of theoretical physicists around the world: I opened my laptop and looked at the website called “arXiv,” a digital portal that chronicles evolving innovations across many scientific fields in near real-time—including physics, biology, economics, computer science, electrical engineering, quantitative finance, mathematics, and statistics. There, I happened upon an interesting paper on supersymmetry, whose authors included a researcher in New York named Michael Faux, to whom I wrote an email which commenced several weeks of intense correspondence. This correspondence quickly morphed, as I continued my travels, into elaborating diagrams for which we realized we needed a name. As we rushed to finish a research paper on these symbols, I was in the West African country of Benin. Perhaps inspired by my location at the time, Michael suggested the name “adinkra,” which he explained originated among the Akan peoples of West Africa, who have long used similarly-named symbols to convey abstract and weighty concepts with beautiful designs, like learning from the past, the omnipotence of God, and unity of life. The name “adinkras,” to me, seemed apt. Thus was born the name for our paper, "Adinkras: A Graphical Technology for Supersymmetric Representation Theory." And thus began our adventures with these symbols, which were technically graphs in the realm of mathematics that encoded data in two-dimensional systems about the behavior of equations in higher dimensions. Like the sublime insights described by the same title, and as I found when I began discussing adinkra diagrams at gatherings like that conference near Marseille, our findings proved even more useful and revelatory than I hoped.

Adinkras choreograph the relationships between particles and make it possible to bring our visual and geometric intuitions to bear on the domain of supersymmetry. But more than that, by translating the essence of our discoveries into other realms of mathematics, they widen the net of mathematicians and scientists who can readily appreciate their findings and potentially contribute to them. These diagrams are more than mere pictures: they can lead to new understandings of what is being studied.

For example, we found that some adinkras could be broken up into two smaller parts, both of which were also adinkras—and that by folding, compressing, and coalescing the dots and links of one adinkra, another adinkra could be formed. Though not all such manipulations of adinkra result in new adinkra, by assigning binary words to the dots in an adinkra and following a specific process of transformation, its SUSY properties can be reliably preserved. From this discovery, we noted that the equations which adinkras represent exhibit properties held by a specific class of error-correcting codes used in computer communications.

About the latter mind-blowing idea, I’ve been asked often to speak in public, over the past couple of decades and especially after The Matrix films came out: What if reality itself is a computer simulation? It should be noted that this question itself is not a scientific one—and it is prompted not from studying equations directly, but from exploring their representations as adinkras, visual objects that continue to yield unexpected payoffs.

Now 20 years after their discovery, I’m only more convinced that when we found these adinkras, we stepped onto a new mathematical continent. The verification of supersymmetry in nature remains on the proverbial bucket list for theoretical physicists, who were thrilled by the once-unthinkable discovery, a decade ago and at the Large Hadron Collider in Switzerland, of the Higgs boson. The discovery of supersymmetry may occur decades or centuries from now. That is how progress, and our understanding of the nature of reality, works: Mother nature doesn’t care if I’m alive or dead when supersymmetry is found. But there’s great satisfaction in being part of the process we call progress. And I take great pleasure in being tagged to find, with the help of these adinkras, truths no one else has. ♦