David John Simms (13 January 1933 – 24 June 2018) was an Indian-born Irish mathematician who was a Fellow Emeritus and former Associate Professor of Mathematics at Trinity College, Dublin. Born in Sankeshwar, Mysore (the state now known as Karnataka), India, he specialized in differential geometry and geometric quantisation. He was a member of the Royal Irish Academy from 1978 and was a member of the Editorial Board of the journal Mathematical Proceedings of the Royal Irish Academy.