After undergraduate studies in mathematics and philosophy at Cambridge, Gillies became a graduate student of Karl Popper and Imre Lakatos at the London School of Economics, where he completed a PhD on the foundations of probability.
Gilles is a past President and a current Vice-President of British Society for the Philosophy of Science. From 1982 to 1985 he was an editor of the British Journal for the Philosophy of Science.
Gillies is probably best known for his work on confirmation theory, his attempt to simplify and extend Popper’s theory of corroboration. He proposes a novel "principle of explanatory surplus", likening a successful theoretician to a successful entrepreneur. The entrepreneur generates a surplus (of income) over and above his initial investment (of funds) to meet the necessary expenses of the enterprise. Similarly, the theoretician generates a surplus (of explanations) over and above his initial investment (of assumptions) to make the necessary explanations of known facts. The size of this surplus is held to be a measure of the confirmation of the theory - but only in qualitative, rather than quantitative, terms.
Gillies has researched the philosophy of science, most particularly the foundations of probability; the philosophy of logic and mathematics; and the interactions of artificial intelligence with some aspects of philosophy, including probability, logic, causality and scientific method.