This paper provides an account of a specific operation – the removal of the thymus gland (thymectomy) to treat the rare neurological condition myasthenia gravis – from its first performance in 1936, by the American surgeon Alfred Blalock, to the publication in 2016 of an international multicentre randomised controlled trial (RCT) of the technique. Thymectomy was the subject of a transatlantic controversy in the 1950s, in which the main players were the English surgeon Geoffrey Keynes, and American neurologists and surgeons from New York, Boston, and the Mayo Clinic. The resolution of this controversy involved the use of increasingly sophisticated statistical techniques, but also crucially other influences including the social transformation of thoracic surgery, and competition between the leading American centres. The consensus achieved after this controversy was challenged in the late 1970s, eventually prompting the implementation of a trial acceptable to twenty-first-century evidence-based medicine. This account will demonstrate that surgical innovation in the period covered required increasing attention to the statistical basis of patient selection and outcome evaluation; that the processes of technical innovation cannot be regarded as separate from developments in the professional culture of surgery, and that one of the consequences of these changes has been the gradual eclipse of the prestigious autonomous surgeon.