An interest in geometry and algebra was shown by Ross while he was a pupil at Springhill School where he won prizes for mathematics. It was while reading one these prizes in India in 1882 that he became determined to make a study of mathematics and this enthusiasm continued throughout his life resulting in many mathematical works, some of which were published.

His greatest mathematical achievements were in solid space algebra and in epidemiology. Ross regarded much of his mathematical work to be of more importance than his medical work: ‘In my own opinion my principal work has been to establish the general laws of epidemics (M 9/1/49).