Andrew Zangwill contacted me because he is working on scientific biography of Phil Anderson. I think this is overdue. I would argue that Phil is the greatest theoretical physicist of the second half of the twentieth century. I would argue this on similar grounds to why I think Linus Pauling was the greatest theoretical chemist of the first half of the twentieth century. Crucially, their scientific legacies have extended far beyond condensed matter physics and chemistry, respectively.
Specifically, Pauling did not just make essential contributions to our understanding of chemical bonding, x-ray crystallography, and quantum chemistry. His impact went far beyond chemistry. Francis Crick said Pauling was the "father of molecular biology." He proposed and elucidated alpha helices and beta sheets in proteins. Furthermore, he began the whole field of molecular medicine, by showing the molecular basis of a specific disease, sickle cell anemia.
Phil Anderson has made incredibly diverse and valuable contributions to condensed matter physics (anti-ferromagnetism, localisation, weak localisation, magnetic impurities in metals, Kondo problem, poor mans scaling, superfluid 3He, spin liquids, RVB theory of superconductivity... ).
I can think of three significant and profound influences of Phil beyond condensed matter physics.
Codifying and elucidating the concept of emergence (and the limitations of reductionism) in all of science, in More is Different in 1972.
Laying ground work for the Higgs boson in 1963 by connecting spontaneous gauge symmetry breaking and mass.
Elucidating spin glasses in a way that was key to John Hopfield's development of a particular neural network and to the notion of a "rugged landscape", relevant in protein folding and evolution. Anderson described these connections nicely in two pages in Physics Today in 1990.
Are there other examples?
Who do you think is the greatest theoretical physicist of the second half of the twentieth century?
[n.b. If you are thinking Feynman, he did path integrals and QED before 1950].