Mathematics is standardly seen as evolving in a way that is strikingly different from the way in which empirical sciences evolve. Since the work of Kuhn, Lakatos and others it has become widely accepted that there are episodes in which central concepts of an empirical science undergo a radical shift in meaning, that there are `revolutions' in empirical sciences, and that empirical theories can be falsified by empirical data (even though this process of falsification is more complex than was once thought). Not so for mathematics. Conventional wisdom has it that the meaning of mathematical concepts does not radically change over a short period of time, that there is a cumulative process of growth of mathematical knowledge, and that mathematical theories cannot be falsified by empirical data. The author of the present paper belongs to the ``maverick'' tradition in the philosophy of mathematics that wants to describe the evolution of mathematical knowledge in Lakatosian terms. He argues that the concept of an axiom has radically changed in the history of mathematics (through the work of Hilbert), that mathematical knowledge does not always grow in a cumulative way, and that there is a process of refutation of mathematical theories which proceeds according to the criteria of sophisticated falsifiability described by Lakatos. In this sense, mathematical theories are argued to be quasi-empirical. For more on this controversy, see for instance the reviews by \textit{J. Burgess} and \textit{P. Ernest} of ``The Mathematical Experience Study Guide'' by \textit{R. Hersh} et al. in Philos. Math., III. Ser. 5, No. 2, 175-188 (1997)] (see also Zbl 0837.00001).