8 weeks · 0 milestones
Construct a complete formal mathematical proof in continuous mathematics — real analysis (limits, continuity, differentiation, integration), linear algebra (eigenvalues, vector spaces, matrix decomposition), differential equations (existence, uniqueness, stability), or probability theory (convergence, distributions, central limit theorem). The proof may be original or a reconstruction of a named non-trivial result with all steps made explicit and no reasoning omitted. Mathematical proof construction is an applied intellectual skill — the same reasoning that places legal argumentation in SKILLS rather than LEARNING. The skill is not knowing what a theorem says but demonstrating you can derive it from first principles with all logical steps documented. Mathematical proofs require no equipment — paper, pen, and primary mathematical texts are sufficient. Reviewed by a mathematician or physicist who confirms the proof is logically valid and complete; the reviewer presents an unseen claim during the review session for the student to work through live, confirming that the student can construct proofs rather than reproduce memorised ones.