Just like René Descartes'La Géométrie from Discours de la méthode (1637) might have had a profound influence on mathematics, also Immanuel Kant's Transzendentale Ästhetik from Kritik der reinen Vernunft (1781) might have had a profound influence on mathematics.
In his Habilitationsvortrag (1854), Bernhard Riemann talked about his success in the task given by Carl Friedrich Gauß to "update" Kant's intuition in the face of new facts like non-Euclidean geometry. When this talk (and a sketch of the elaboration of the "proposal") was published in 1867 as
Ueber die Hypothesen, welche der Geometrie zu Grunde liegen
On the Hypotheses which lie at the Bases of Geometry
it lead to responses like the one from Hermann Helmholtz in 1868
Ueber die Thatsachen, die der Geometrie zum Grunde liegen
The Origin and Meaning of Geometrical Axioms
which in the end also influenced Sophus Lie's On a class of geometric transformations (1871), which in turn also had an influence of Felix Klein's Erlanger Programm (1872).
Well, maybe the influence of Kant or Riemann or Helmholtz or Lie, or even Klein wasn't such important, but still these developments were always responses to earlier published philosophical positions.