To categorize the innumerable works which are published every year in mathematics is a superhuman task, on account of the close-knit network, almost impossible to unravel, of links which bind together the various theories, and which are the mainsprings of their progress. The list which follows, then, must not be seen as anything else than a very approximate indication of the various directions in which mathematical research might be taken, with respect to problems which often do not seem to point in these directions.