Condensed matter physics is about the properties of real materials. Real stuff that you can see and touch and that you can use to make very practical things like TV screens and mobile phones. Yet, I find it fascinating and somewhat ironic that in condensed matter theory very abstract ideas and mathematical techniques keep cropping up (and being extremely useful): variable spatial dimensions, imaginary frequencies, topology, Chern numbers, conformal invariance, ...
Yet, there is a danger with abstraction. Theoretical condensed matter is not pure mathematics. Perhaps, too often fancy and beautiful mathematics is prized over physical intuition and insight. Theory may take precedence over experiment. How does one find the appropriate balance?
This is part of broader issues about the role of abstraction and formality in education.
Pierre de Gennes (1932-2007) was arguably the founder of soft matter as a research field, as recognized by the Nobel Prize in Physics in 1991. He began his career working on superconductivity and went on to develop a unified framework to understand soft matter (liquid crystals, polymers, foams, colloids...), introducing ideas such as order parameters, scaling, renormalisation, and universality.
After his Nobel, de Gennes gave many lectures in French high schools, which were then published as a book, Fragile Objects: Soft Matter, Hard Science, and the Thrill of Discovery. I highly recommend it, both as a popular introduction to soft matter, but also to hear the perspective of a great scientist on education and research.
de Gennes spent almost his whole life living and working in France. In the book he rants about the French system, particularly its obsession with entrance exams, mathematics, formality, and the abstract.
“Manual skills, visual acumen, the sense of observation, an interest for the physical world which surrounds us, are all qualities that are neglected or downgraded.”
“To work in a garage seems to me the best initiation to a professional life.”
“Ignorance of the real world causes grave distortions.”
“the positivist prejudice”
I found this fascinating because one thing de Gennes is famous for is showing how some properties of a polymer can be understood by considering a theory involving a vector of dimension n, where n was a continuous variable, in the limit where n approaches zero! That is pretty abstract! But, I guess the point is that he is not against abstraction, exams, and mathematics, per se. Rather, he is against them taking on a life of their own.
de Gennes concerns are also shared by Henri Alloul (well known for beautiful NMR experiments on strongly correlated electron materials) author of Introduction to the Physics of Electrons in Solids. In the Preface, he writes,
In many countries, teaching traditions have always given pride of place to a formal, and essentially deductive, presentation of the physics, i.e., starting from formal hypotheses and leading up to observable consequences. This deductive approach leaves a purely a posteriori verificational role to observation, and hides the thinking that has gone into building up the models in the first place. Here we shall adopt the opposite approach, which begins with the fact that in science in general, and in solid state physics in particular, the qualitative understanding of a phenomenon is an important step which precedes the formulation of any theoretical development. We thus urge the reader to carry out a careful examination of the deeper significance of experimental observations, in order to understand the need for specific models and carry out realistic approximations.
The debate about abstract mathematics is also central to contrasting views about the Institute for Advanced Study at Princeton.
de Gennes's views would have also resonated with Harry Kroto who shared The Nobel Prize in Chemistry for the discovery of buckyballs. He credited playing with Meccano as a child as very important in his scientific development.
