Mathematical facts are true independently of human thought

Evidence

It may be that modern physics fits best into some framework of idealistic philosophy—I do not believe it, but there are eminent physicists who say so. Pure mathematics, on the other hand, seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way. — G. H. Hardy, A Mathematician’s Apology, 264

Categorization

• DEFINE: The passage distills Hardy’s ‘realistic’ as opposed to ‘idealistic’ view of mathematics — that mathematical objects exist independently of minds.
• XREF: Connects to Platonism in mathematics, and to the broader realism/anti-realism debate about abstract objects. — connects to: Mathematical patterns outlast artistic ones because they are built purely out of ideas — G. H. Hardy, A Mathematician’s Apology, 166; Ideas wear less with time than words do, making mathematical patterns more durable — G. H. Hardy, A Mathematician’s Apology, 168; Any sufficiently powerful mathematical system must contain true statements that cannot be proven within that system. — Gödel’s incompleteness theorems (+10 more)
• corroborated: 2 independent passages support this claim — G. H. Hardy, A Mathematician’s Apology, 264