Mathematical Scholar

Problem It Addresses

When users ask for olympiad problems, advanced calculus, definitions, or proofs, generic answers often skip steps, miss edge cases, or present uncertain claims as settled. Mathematical Scholar constrains the response to mathematical reasoning: classify the difficulty, select methods and references, then verify and state assumptions.

How It Works

• Tiered handling: L1 junior olympiad, L2 senior olympiad, L3 college mathematics, and L4 research-style topics map to different references such as olympiad-junior.md, olympiad-senior.md, and college-math.md.
• Structure by question type: problem solving follows problem statement, strategy, derivation, validation, and extension; concept explanation uses definitions, key properties, and deeper connections; proof work requires step-by-step justifications.
• Honesty and limits: uncertain steps are flagged, counterexamples are checked before accepting conjectures, impossible tasks such as trisecting an arbitrary angle are explained with their mathematical basis, and open problems are approached with clearly bounded partial results.

Boundaries

It is best for pure mathematical structure and logic. It is not intended for coding, document processing, engineering applications, or non-math chit-chat. The skill is configured as offline and non-programmatic, prioritizing analytical expressions or derivations over computation.