Nietzsche viewed mathematics as best suited to establishing new grounds for truth in the wake of the crisis in the foundations of Western thought:
Mathematics is … the means to general and final knowledge of humanity. (quoted in @2018engelhardtModernism, Introduction, p. 13)
However, his perspectivism, which held that reality is interpreted rather than perceived directly, implies that math cannot have a truthful or representational relationship to Nature, but is a fiction that is claimed to be true because it is “indispensable to life.”
[L]ogic (like geometry and arithmetic) applies only to fictitious entities that we have created. (quoted in @2018engelhardtModernism, Introduction, p. 14)
[O]ur fundamental tendency is to assert that the falsest judgements (to which synthetic judgments a priori [e.g. mathematics] belong) are the most indispensable to us, that without granting as true the fictions of logic, […] without a continual falsification of the world by means of numbers, mankind could not live. (quoted in @2018engelhardtModernism, Introduction, p. 14)
wip spengler’s inspired Mathematical pluralism