From Galileo to Gauss, many have extolled the special position of mathematics in the natural sciences. Gauss’s (1856) view that ‘Mathematics is the queen of science’ may afford bragging rights to scholars in fields involving extensive mathematical formalism, but the practical implications for research management and science policy are far from clear. Should university managers prioritise mathematical scholarship in order to excel in natural sciences? More generally, to what extent is success in any discipline related to success in another, and which subjects play the most central role? We tackle these questions using a new data set covering research output and labour inputs for 31 fields-of-research at 900 leading universities worldwide over a 21-year period. Results indicate that structure matters and that physics and more recently biological science occupy a central position in the landscape of science.