Sunday Reflection

From Philip Davis and Reuben Hersh's "The Mathematical Experience":
(I don't necessarily agree with this sentiment, but do find it interesting)

" We maintain that:

1)  All the standard philosophical viewpoints rely in an essential way on some notion of intuition.
2)  None of them even attempt to explain the nature and meaning of the intuition which they postulate.
3)  A consideration of intuition as it is actually experienced leads to a notion which is difficult and complex, but it is not inexplicable or unanalyzable. A realistic analysis of mathematical intuition is a reasonable goal, and should become one of the central features of an adequate philosophy of mathematics….

"Mathematics does have a subject matter, and its statements are meaningful. The meaning, however, is to be found in the shared understanding of human beings, not in an external nonhuman reality. In this respect, mathematics is similar to an ideology, a religion, or an art form; it deals with human meanings, and is intelligible only within the context of culture. In other words, mathematics is a humanistic study. It is one of the humanities."

[…If you have a favorite math-related passage that might make a nice Sunday morning reflection here let me know (SheckyR@gmail.com). If I use one submitted by a reader, I'll cite the contributor.]