The title of this paper was borrowed from the heading of a chapter in Davis and Hersh's celebrated book The mathematical experience.¹ Here, however, we have inserted a question-mark: is it really true, as some people maintain, that mathematics has lost its certainty? For the sake of simplicity, we refer to this conception as mathematical fallibilism which is a feature of the quasi-empiricism initiated by Lakatos and popularized by Davis and Hersh, Kline, Tymoczko and many others. In this paper we would like to make a critical survey of this viewpoint which constitutes an interesting trend in philosophy of mathematics today.