ABSTRACT
Bernard Bolzano changed with time his views on the distinctive object of mathematical science. In the prime of his life he regarded it as a formal science whose every truth is 'purely conceptual', and which is busied more with relation than with quantity. Like Augustus De Morgan, his partial counterpart in England, Bolzano insisted strongly on the need for a mathematical methodology, and for more collaboration between logic and mathematics. He complains that so few of his contemporaries are both mathematicians and philosophers, and is anxious in all his mathematical writings to be judged by these few alone. Bolzano's 'horror geometriae' was certainly no denigration of geometry as a science in its own right, but only a disinclination to let it be applied in patches to hide the weak spots in analysis. In the history of real function theory, Bolzano's counter example was a feat but not a contribution, since others had become historic when his became known.
