Revisiting the peaks of Nobel laureate Chen-ning Yang’s remarkable career

In the latest instalment of his exclusive series for the South China Morning Post, American theoretical physicist and Nobel laureate Frank Wilczek pays tribute to the mathematical beauty of Yang’s contributions. Read his previous articles here. Chen-ning (Frank) Yang, a towering figure in modern physics, died on October 18, 2025 in Beijing, shortly after his 103rd birthday. Let us celebrate his profound contributions to our understanding of the world, his remarkable life and his living legacies. The landscape of Yang’s work features many peaks, but two tower above all: the discovery in 1954, together with Robert Mills, of what became known as the Yang-Mills equations; and the Nobel Prize-winning suggestion in 1956, together with Tsung-Dao Lee, that the weak interactions violated parity (left-right) symmetry. These were historic achievements and they deserve to be seen that way. Thus inspired, let’s do some sightseeing. In 1889 Heinrich Hertz wrote that “these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them”. For Hertz, this was not a philosophical flourish but a lived truth. James Clerk Maxwell’s system of equations, first set down in 1864, brought electricity, magnetism and light within a single elegant structure. Twenty years later, Maxwell’s equations enabled Hertz – using little more than spark gaps and loops of wire as generator and receiver – to project electromagnetic waves across his laboratory. From that moment flowed the modern era of wireless communication, which makes us all neighbours today. Beyond their practical consequences, Maxwell’s equations slowly transformed how theoretical physics itself was done. It took decades to understand Maxwell’s equations properly, but the rewards were profound. For doing so revealed not only special relativity but also a new principle, now called gauge symmetry, that Yang eventually generalised. The precise mathematics of gauge symmetry is extraordinarily beautiful but it can only be fully appreciated in the framework of quantum field theory. Here, a very rough analogy will have to serve. When we measure lengths, we might express our results in centimetres, inches, light years, or according to any other scale. The “gauge symmetry” in this context is simply the statement that no physical result can depend on the choice of measurement unit. The gauge symmetry of electrodynamics is a more sweeping statement of the same kind. It allows for independent choices of electric charge units at different places and times. This is called local gauge symmetry. When local gauge symmetry is spelled out mathematically, the result is an astonishing piece of magic: electric and magnetic fields and the Maxwell equations they obey pop out automatically. They are conjured up as the mechanism that correlates electric charge units across space and time. Briefly, in the language of particles, photons are the avatars of electromagnetic gauge invariance. Yang proposed a grand generalisation of this idea that could potentially explain the existence and properties of other fundamental particles. Whereas electromagnetic gauge symmetry is concerned with one kind of charge (i.e. electric charge), so the possible unit choices correspond to points on a line, Yang imagined a world with several kinds of interchangeable charges. Then the allowed unit choices correspond to points in higher-dimensional structures, and local gauge symmetry needs several avatars. With two charges you get three photon-like particles and with three charges you get eight, for example. Just as with the original Maxwell equations, it took years for physicists to understand Yang’s generalisation properly. There were technical challenges in reconciling it with quantum theory, but also a more basic problem: the new particles were predicted to have zero mass. If such zero-mass particles existed, they would be easy to produce, like photons. So where were they? Two answers to that basic challenge emerged. One was spontaneous symmetry breaking. According to this answer, the stable solutions of the equations have less symmetry than the equations themselves. In this way, one can keep the equations that local gauge invariance suggests but avoid the implication of zero mass. This answer applies to the weak interaction (with two kinds of charge). Here the Yang-Mills avatars are heavy particles, the so-called W and Z bosons. The other was confinement. According to this answer, the massless particles attract one another so strongly that they are unstable in isolation but quickly accumulate into massive lumps. This answer applies to the strong interaction (with three kinds of charge, whimsically called “colours”). Here the Yang-Mills avatars are the eight gluons of quantum chromodynamics, seen fleetingly but unmistakably emerging from high-energy collisions of protons. Thus, Yang’s daring imaginative constructions extending the Maxwell equations came to join them as worthy partners. Together, they provide the foundation for our understanding of the fundamental electromagnetic, weak and strong forces of nature. Hertz’s quotation has come to look like prophecy. The title of Lee and Yang’s great paper was “Question of Parity Conservation in Weak Interactions”. The question they considered, in common language, was whether the fundamental laws of physics show a distinction between left and right. It is the question of whether the objects and events you see in a mirror obey the same fundamental laws as objects and events in the real – or unreflected – world. There are obvious ways in which the answer is “no”. In the real world, most people are right-handed and have their hearts on the left side, but in the reflected world it’s just the opposite, for example. More profoundly, Louis Pasteur in 1848 discovered that biology answers with an emphatic “no” at the molecular level: the mirror-reflected versions of most reasonably complex biomolecules are biologically inert or even poisonous. But the fundamental laws of physics, as they were known in 1956, when applied to fundamental particles, seemed to answer “yes”. This contrast was what made Pasteur’s discovery so shocking and profound – the mirror molecules, once taken out of their biological context, had identical physical and chemical properties. Lee and Yang were provoked by some subtle hints from new phenomena observed at particle accelerators – most notably the “theta-tau puzzle” (a hot topic at the time, now so thoroughly solved that it’s become awkward even to state in modern terms) – to make a critical, quantitative analysis of the evidence for parity symmetry in fundamental physics. They concluded that the evidence was excellent for most areas of physics but essentially non-existent for the weak interaction. They suggested how new experiments could clarify the issue. Within a few months, a team led by the gifted Chinese-American experimentalist Chien-Shiung Wu showed that parity was violated by the weak interaction. Lee and Yang received the Nobel Prize in record time, in 1957. Follow-up work showed that parity violation was no mere curiosity. Once people looked, they discovered that it was ubiquitous in the weak interaction. Indeed, left-right asymmetry was so consistently, amazingly big that people struggled to accommodate it theoretically. The story of this struggle, which played out over about 15 years, is too complicated to retell here. But its conclusion makes a fitting, poetic climax for our tour. In an imaginary world where electrons and their relatives and quarks have zero mass, maximal parity is easy to arrange. We don’t live in that world – those particles have non-zero masses. But the same spontaneous symmetry breaking that allows the W and Z bosons to have mass also allows the electrons and quarks to pick up a little mass while preserving their near-maximal parity violation. Here again, the ideal world of zero mass and perfect symmetry – which seemed too good to be true – turns out to be true after all, but hidden. As Einstein said: “Subtle is the Lord, but malicious He is not.” Much more could be said about Yang’s scientific work and legacy, but here I will only add two brief comments. First, he made brilliant contributions to our understanding of material systems in the same style: proposing beautiful conceptual and mathematical structures that were superficially “too good for this world” but turned out to anticipate hidden realities – e.g., for experts: hard-core bosons, Yang-Baxter equations. Second, the study of parity violation catalysed a parallel investigation of “time-parity”, that is, the symmetry of fundamental physical laws under reversal of the direction of time. This too, like parity, turns out to hold almost, but not quite, precisely. The quest to reach a proper understanding of time-parity has become a major frontier of contemporary physics, leading into axions and dark matter. Chen-ning Yang was born in 1922 in Hefei, Anhui province. He grew up in an academic household. His father, Yang Ko-Chuen, was a mathematician at Tsinghua University. The China of his youth, however, was a country at war. During the Sino-Japanese conflict, Yang studied in makeshift classrooms while bombs sometimes fell in the distance. After earning his master’s degree at Tsinghua (then exiled to Kunming) under the physicist Wu Ta-You, Yang won a fellowship to study in the United States. At the University of Chicago, he completed his PhD under Edward Teller in 1948. He soon joined the Institute for Advanced Study in Princeton – an environment shaped by the spirits of Einstein, Weyl and von Neumann. It was there that he met another young Chinese physicist and newly minted Chicago PhD, Tsung-Dao Lee. In 1966, Yang moved to Stony Brook, where he founded the Institute for Theoretical Physics that now bears his name. There he built a community grounded in rigorous thought and open exchange. Several of his students and associates went on to become leading physicists around the world. Beginning in the 1970s, as China reopened to the world, Yang returned to his homeland as both teacher and bridge. His lectures at Peking and Tsinghua universities drew overflowing audiences. He became an active advocate for China’s scientific renewal, emphasising the need for both material resources and the intellectual freedom that allows creativity to flourish. “China will need not only laboratories but also the spirit of open discussion that makes science grow,” he observed. Let me close with two brief Yang quotations. From his Nobel acceptance speech: “When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.” Reflecting on a century of discovery during his 2021 centenary address at Tsinghua University, Yang suggested that the ultimate destination of the scientist was a state of grace: “We set out to uncover truth, only to behold wonder.”

Revisiting the peaks of Nobel laureate Chen-ning Yang’s remarkable career

.css-1c6uqr6{color:inherit;font-weight:inherit;font-size:inherit;font-family:inherit;line-height:inherit;overflow-wrap:break-word;}The inspirational Chinese physicist, who lived to the age of 103, was renowned for two historic achievements

The inspirational Chinese physicist, who lived to the age of 103, was renowned for two historic achievements