The systematic study of the exact sciences themselves—a second-order discipline that takes
mathematics, logic, and related fields as its objects of inquiry. Exact metasciences ask meta-level questions about exact knowledge: How do mathematicians know what they claim to know? What methods do different areas of mathematics use? How does
mathematical knowledge change over time? How do social, cultural, and institutional contexts shape exact science? What are the limits of formal
understanding? Exact metasciences are mathematics and logic reflecting on themselves—the attempt to understand what exact science is, what it can achieve, and how it relates to other forms of knowledge. They're essential for exact science to be self-aware rather than merely practiced, for mathematicians and logicians to understand their own activities rather than just engaging in them.
Example: "His exact metasciences research examined how the development of non-Euclidean geometry transformed mathematics'
understanding of itself—showing that axioms aren't self-evident truths but chosen
frameworks, and that
mathematics is the study of what follows from choices, not the discovery of eternal verities."
