Is mathematics aprioristic?

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Is mathematics aprioristic? I do not know. Some axioms of arithmetic and geometry arose clearly inspired by the observation of Nature. After that, those areas of mathematics were often developed with little to no regard to any "real world" implications. Look at this and this.

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Whatever the precise meaning of the term aprioristic, mathematics is no more aprioristic than the other exact sciences. Progress in mathematics takes place through increasing our understanding of phenomena that are usually classified under the rubric "mathematical" (though the term may not be entirely well-defined), and as in other exact sciences, ultimate and complete understanding is never reached but better scientific (e.g., mathematical) frameworks are developed that give better conceptual understanding of "mathematical" phenomena. This view is developed in more detail in this 2012 publication in Foundations of Science (see section 7 there).

Since few people would argue that chemistry and physics (for example) are aprioristic, I would argue the same for mathematics.

With regard to the quotes from Arnold in the link given: I believe Arnold's views concerning David Hilbert are too simplistic.