What was Hilbert's stated goal regarding axioms?

• A. Goal of the program to put all of mathematics on a firm axiomatic basis
• B. To formalize only geometry
• C. To replace axioms with empirical rules
• D. To derive mathematics from intuition

Answer: (A)

The main idea is to place all of mathematics on a firm, formal foundation built from a fixed set of axioms, with every theorem derived through precise rules of inference. Hilbert envisioned a system where the truths of arithmetic, geometry, and analysis could be proven from these axioms in a completely formal way, using finitary methods to demonstrate the system’s consistency. This moves mathematics away from reliance on intuition or geometric reasoning toward a universal, unambiguous basis. Later developments showed limits to this dream, but the goal itself was to secure a rigorous, axiomatic grounding for all of mathematics.