"Selection rules governing the disintegration of a particle into two photons are derived from the general principle of invariance under rotation and inversion. The polarization state of the photons is completely fixed by the selection rules for initial particles with spin less than 2. These results which are independent of any specific assumption about the interactions may possibly offer a method of deciding the symmetry nature of mesons which decay into two photons."

"The spontaneous magnetization of a two-dimensional Ising model is calculated exactly. The result also gives the long-range order in the lattice."

"With the advent of special and general relativity, the symmetry laws gained new importance. Their connection with the dynamic laws of physics takes on a much more integrated and interdependent relationship than in classical mechanics, where logically the symmetry laws were only conse- quences of the dynamical laws that by chance possess the symmetries. Also in the relativity theories the realm of the symmetry laws was greatly enriched to include invariances that were by no means apparent from daily experience. Their validity rather was deduced from, or was later confirmed by complicated experimentation. Let me emphasize that the conceptual simplicity and intrinsic beauty of the symmetries that so evolve from complex experiments are for the physicists great sources of encouragement. One learns to hope that Nature possesses an order that one may aspire to comprehend. It was, however, not until the development of quantum mechanics that the use of the symmetry principles began to permeate into the very language of physics. The quantum numbers that designate the states of a system are often identical with those that represent the symmetries of the system. It in- deed is scarcely possible to overemphasize the role played by the symmetry principles in quantum mechanics."

"The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S'N. For some Rs this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-½ fermions is reduced to a generalized Fredholm equation."

"In a letter to Ampère dated 3 September 1822, Faraday lamented, "I am unfortunate in a want of mathematical knowledge and the power of entering with facility into abstract reasoning, I am obliged to feel my way by facts closely placed together." ... Faraday's "facts" were his experiments, both published and unpublished. During a period of 23 years, 1831–54, he compiled the results of those experiments into three volumes, called Experimental Researches in Electricity ... A most remarkable thing is that there was not a single formula in this monumental compilation, which showed that Faraday was feeling his way, guided only by geometric intuition without any precise algebraic formulation."

"Many physicists recall October 1957 as a time of excitement and legend. In that year, at the age of 35, Yang won the Nobel Prize in Physics. Yang and Lee thereby became the first Chinese laureates. The significance of the award lay not only in the academic achievement, but also in the boost it provided to the self-belief of a nation. Before that, the scientific talent of the Chinese had been questioned. Ching-Wu Chu, a distinguished physicist specialized in superconductivity and a member of the US National Academy of Sciences, was in high school at the time. He spent his spare time reading every news report he could find about Yang, and talked earnestly to his classmates about “parity non-conservation” – a subject on which they could understand nothing. Tsu-Teh Chou, a professor of physics at the University of Georgia, was dining at a tiny Chinese restaurant in Liverpool, England, 12 years later, and overheard both the chef and the owner talking proudly about Yang’s achievements."