Professor Malcolm Sambridge has made lasting fundamental contributions to the understanding of the Earth and its internal processes through new mathematical approaches to analysing complex geophysical datasets. His robust approaches to modelling diverse observational data – including statistically meaningful estimates of uncertainty – has had wide-ranging impact in geoscientific research. Malcolm’s work has changed the way in which we analyse seismic waves for the structure of the Earth’s interior, model landscape evolution, understand populations of mineral ages from isotopic microanalysis, and interpret infrared absorption spectra associated with hydrous crystal defects in silicate minerals.