ABSTRACT
It was 1993, and superstrings, the ‘theory of everything,’ was the rage. Arthur Jaffe, a senior member of the physics department at Harvard and for several years chair of the mathematics department, along with Frank Quinn, a mathematician at Virginia Tech, penned the following in the pages of the Bulletin of the American Mathematical Society:
Theoretical physics and mathematical physics have rather different cultures, and there is often a tension between them. Theoretical work in physics does not need to contain verification or proof, as contact with reality can be left to experiment. Thus the sociology of physics tends to denigrate proof as an unnecessary part of the theoretical process. Richard Feynman used to delight in teasing mathematicians about their reluctance to use methods that “worked” but that could not be rigorously justified. 1
Jaffe and Quinn quickly added that mathematicians, unsurprisingly, retaliated: as far as they were concerned, physicists’ proofs carried about as much weight as the person who claimed descent from William the Conqueror … with only two gaps. Nor has tension between cultures been restricted to the axis of theory/mathematics. Albert Einstein and Paul Dirac famously derided putative experimental refutations of major theories, and experimentalists have never hesitated to mock what they considered to be the aimless speculation of theorists. One cartoon, widely circulated in the physics community during the 1970s, portrayed a balance scale with thousands of offprints labeled “theory” heaped on one side, outweighed by a single paper marked “experiment” on the other. Beneath these cross-currents of jibes and jests lie substantive disagreement about what constitutes an adequate demonstration, and, ultimately, a clash over whose pilings sink sufficiently deep to stabilize further construction. What vouchsafes knowledge, and for whom?