Hermann Weyl, mathematician

Weyl was one of the greats among twentieth century mathematicians. I read his book, Group Theory and Quantum Mechanics, as a student. This book was written at an unlucky time (first ed. in German, 1928). Dirac had predicted the existence of positively charged particles of the same mass as the electron, in 1927. Since at that time there were no such particles, but the proton existed and lacked its own theory, Weyl tried out the idea that the proton was the predicted positively charged particle; its mass was conjectured by Weyl to have been altered from that of the electron by gravitational interactions. This was reported in the book; so an otherwise useful account of group theory suffered from the distraction of this brave attempt. The positron was discovered just after Weyl's book was published. You can also read about Weyl here, and about Weyl and the Nazi regime, look here.

Weyl had discovered a theory of two-component neutrinos in about 1931, and this was refuted by Pauli, since it violated parity conservation. In 1955-1956, Pauli famously refused to believe in the suggestion by Yang and Lee that parity was not a symmetry, but had to admit it after the experiments were reported by Wu. Perhaps Pauli was reluctant to retract his criticism of Weyl's work on the two-component neutrino, which (knowing him) was probably quite forceful. Salam told me later that Weyl had said to him that "physicists must find physics very difficult", in connection with the difficulty over parity raised by the "tau/theta" puzzle. I learnt later that this joke had been said by Hilbert who had corrected a mistake in Einstein's first proposal for the form of the equations of motion in general relativity. Hilbert showed that Einstein's proposal could not be derived from a Lagrangian, and suggested a modified version, derived from what is now called the "Einstein-Hilbert Lagrangian". Perhaps Weyl was referring to Pauli when he used the term "physicists". The title of my paper refers to a two-component massless particle.

I thank Laurens Gunnarsen for pointing out an error in an earlier version of this page.