*Emeritus Wykeham Professor David Sherrington comments on his friend and colleague Giorgio Parisi’s Nobel prize winning work.*

I am delighted that my friend and colleague Giorgio Parisi has been recognised by the award of the 2021 Nobel Prize in Physics. He is an outstandingly brilliant, innovative scientist whose work has had a transformational influence in understanding complex cooperative behaviour in many-body systems involving a combination of quenched (or slowly-changing) disorder with competitive interactions and constraints. His innovations have involved devising radically new physical concepts, radically new mathematics, special-purpose computers for simulation, machines and new algorithms, and highly innovative conceptual and practical applications. The most famous of his discoveries concerns a highly-nontrivial scheme indicating a novel complex structure of macrostates, with remarkable unanticipated consequences, implications, and applications in many scenarios.

### Important and highly cited work

Giorgio started his professional career in elementary particle physics and field theory, producing very important and highly cited work in that area, such as the Altarelli-Parisi evolution equations for parton densities, but was attracted to the topic for which he received the Nobel Prize by an intriguing mathematical and conceptual problem found in an attempt to model theoretically the behaviour of some alloys of magnetic and non-magnetic metals, known as spin glasses. These alloys have not themselves had important application, but the journey to understand them, substantially stimulated and regularly driven by his brilliant insights, discoveries and leadership, has exposed a cornucopia of new ideas and approaches, regularly identified and spearheaded by him, and produced very significant advances in many fields, including not only several material systems, but also in computational and information science, biology, and financial markets, and with great further potential.

He has also made many other major seminal contributions to many other topics in condensed matter and statistical physics, of which I might note particularly the Kardar-Parisi-Zhang equation describing dynamic scaling of growing interfaces, the theory of fragile glasses, and stochastic resonance.

### Radical resolution

His famous discovery mentioned above, known as replica symmetry breaking (RSB), refers to the solution of a major mathematical and conceptual challenge to solve a puzzle generated by earlier theoretical attempts to understand an intriguing feature observed experimentally in some metallic magnetic alloys. The concept of introducing artificial replicas of a system, studying correlations between them in an ensemble of instances, and finally taking a limit as the number of replicas goes to zero was introduced in an ingenious seminal, but approximate, study by Edwards and Anderson. I then went on to study, along with Kirkpatrick, a related but potentially exactly solvable analogue and demonstrated that a seemingly reasonable assumption of a symmetry of correlations between two different replicas was incorrect. The need for something more subtle was further demonstrated by studies of excitations in replica space, but with no successful resolution. Parisi took up the challenge and devised a mind-blowing mathematical solution, requiring the invention of hitherto unknown mathematics, which dealt with the difficulty, albeit that to mere mortals its physical meaning remained unclear. Shortly thereafter he presented a clear and enlightening physical picture of its meaning, opening up a new world of important new ‘mental images’, that have been drivers of modern complex systems conceptualisation and progress ever since, in many application scenarios. Further analysis provided many further subtilities and concepts.

His unusual and non-rigorous mathematics was initially viewed with scepticism by rigorous mathematical physicists and probabilists, but it also intrigued and excited several of them. After much work, and the development of significant further new mathematics and concepts, it has now been proven rigorously in studies which have driven major advances also in probability theory and rigorous statistical mechanics.

### Building a European community

I feel I should also mention a sequence of European networks that have involved Oxford, set up by Giorgio, Nicolas Sourlas and myself, starting in 1987 with one entitled ‘Statistical Mechanics and its Applications to Complex Problems in Physics, Engineering and Biology’; the title already indicating the expanding horizons of the field. These networks, supported by a vision in Europe’s collective strength, spearheaded the formation of a strong European community of scholars, advancing the theory and application of complexity studies while US physics was largely distracted by different fashion, and continuing successfully.

I hope that Parisi’s Nobel award will lead to a better recognition of the potential value of methodologies of theoretical condensed matter physics in devising and studying minimal models, not just to understand (and, eventually apply) real materials, but also to develop new deep concepts and methods, both mathematical and computational, leading to novel fruitful application widely to systems and problems that often seem physically far beyond those which were the initial stimulus.