# Mathematician Elliott Lieb wins Kyoto Prize for pioneering quantum discoveries

Princeton University’s Elliott Lieb is one of the three recipients of the 2023 Kyoto Prize. He won the mathematical sciences category, for “pioneering mathematical research in physics, chemistry and quantum information science based on many-body physics.”

The Kyoto Prize, a major international distinction, is presented by the Inamori Foundation of Japan to honor the lifetime achievements of those who have contributed significantly to the scientific, cultural and spiritual betterment of humankind. The award, which is presented annually in the categories of basic science, advanced technology, and arts and philosophy, includes a cash prize of 100 million yen, or approximately $700,000.

Lieb, Princeton’s Eugene Higgins Professor of Physics, Emeritus, and Professor of Mathematical Physics, Emeritus, held a joint appointment in the departments of math and physics until his retirement. In recent years, he has won some of the most prestigious prizes in both fields, including the Carl Friedrich Gauss Prize from the International Mathematical Union and the Medal for Exceptional Achievement in Research from the American Physical Society.

“I always felt — and not too many people felt! — that physics can use some pure mathematics, and mathematics can use some physics,” said Lieb, who celebrated his 90th birthday last July. “Pure mathematics can lead to new ideas in physics, and of course, physics can influence mathematics by bringing forth good problems that intrinsically have a mathematical solution. They’re intrinsically mathematical questions, but physicists aren’t asking it as a mathematical question. To formulate it as a mathematical question can lead to answers that are unexpected, and by means that are unexpected.”

“This is great news and a very well-deserved recognition for Elliott’s many foundational contributions to mathematics and physics,” said Herman Verlinde, chair of the Department of Physics and the Class of 1909 Professor of Physics. “Elliott’s ability to obtain rigorous answers to fundamental questions about physical systems, often long before these questions are widely recognized as important, is truly unique. The impact of his pioneering work on all parts of theoretical science is enormous and still growing: many recent developments in quantum information science, statistical mechanics and quantum chemistry build on classic results and beautiful mathematical structures that Elliott uncovered many years ago. I’m proud to have him as a colleague.”

“Elliott Lieb is a remarkably influential and prolific mathematician,” said Igor Rodnianski, chair of the Department of Mathematics, “who has made pathbreaking contributions to several branches of mathematics connected to physical phenomena: quantum many-body systems, statistical physics, condensed matter physics, analysis and functional inequalities, just to name a few. His work has had a deep and long lasting influence on both mathematics, where it introduced new tools applicable far beyond the problems they were originally intended for, and physics, where it explained and predicted new phenomena. Elliott’s impact, through his work, which for the last 50 years has been conducted as a professor at Princeton, and through his students, postdocs and followers cannot be overestimated. We admire and cherish his achievements. Congratulations, Elliott!”

The award citation noted that Lieb “established a foundation for mathematical research in fields such as physics, chemistry, and quantum information science. His contributions to the development of mathematical analysis are significant as well. He is one of intellectual giants in the field of mathematical sciences.”

Lieb’s research focused on the mathematically rigorous analysis of “quantum many-body systems,” which are systems composed of numerous elements governed by quantum mechanics.

Lieb devoted years to researching the stability of matter, yielding an analytical result known as the Lieb-Thirring inequality and numerous other achievements, including the mathematical foundation of the density functional theory, which is crucial in quantum chemical calculations; proof of various fundamental results in quantum spin systems; the proposal of the AKLT spin model that provided a template for topological phases of quantum matter; and much more.

His research results in quantum systems are closely linked to quantum information theory, which underpins next-generation technologies such as quantum computers and quantum cryptography. Among these, his proof of the strong subadditivity of quantum entropy, initially a product of pure mathematical interest, has since become the foundation of quantum information theory and is now a staple in textbooks within this field.

Lieb and the other 2023 laureates — Ryuzo Yanagimachi of the University of Hawaiʻi at Mānoa and artist Nalini Malani — will receive a diploma and a Kyoto Prize medal in addition to the prize money.

Princeton’s recent Kyoto Prize recipients include ecologist Brian Grenfell, the Kathryn Briger and Sarah Fenton Professor of Ecology and Evolutionary Biology and Public Affairs, in 2022; computer scientist Andrew Yao, the William and Edna MacAleer Professor of Engineering and Applied Science, Emeritus, in 2021; astrophysicist Jim Gunn, the Eugene Higgins Professor of Astronomy, Emeritus, in 2019; physicist Edward Witten, a 1976 Ph.D. graduate, a senior scholar in physics at Princeton and an emeritus professor of natural sciences at the Institute for Advanced Study, in 2014; ecologists Peter and Rosemary Grant, the Class of 1877 Professor of Zoology, Emeritus, and Senior Research Biologist, Emeritus, in 2009; biologist Simon Levin, the James S. McDonnell Distinguished University Professor in Ecology and Evolutionary Biology, in 2005; and LCD inventor George Heilmeier, a 1962 Ph.D. graduate in electrical engineering, in 2005.