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This paper surveys Bolzano's Beyträge zu einer begründeteren  Darstellung der Mathematik (Contributions to a better-grounded presentation of  mathematics) on the 200th anniversary of its publication.  The first and only published  issue presents a definition of mathematics, a classification of its subdisciplines, and  an essay on mathematical method, or logic.  Though underdeveloped in some areas  (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative  work, where Bolzano presents a remarkably modern account of axiomatics and the  epistemology of the formal sciences.  We also discuss the second, unfinished and  unpublished issue, where Bolzano develops his views on universal mathematics. Here we  find the beginnings of his theory of collections, for him the most fundamental of the  mathematical disciplines.  Though not exactly the same as the later Cantorian set  theory, Bolzano's theory of collections was used in very similar ways in mathematics,  notably in analysis.  In retrospect, Bolzano's debut in philosophy was a remarkably  successful one, though its fruits would only become generally known much later

The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics