Scientific Reasoning & Problem Solving

Purpose

Solve mathematical and scientific reasoning problems with rigorous step-by-step proofs and physical intuition.

Key Datasets

• MATH Dataset (hendrycks/competition_math): 12,500 competition math problems across 7 categories (Algebra, Counting & Probability, Geometry, Intermediate Algebra, Number Theory, Prealgebra, Precalculus), difficulty levels 1-5
• PhysReason (zhibei1204/PhysReason): Physics reasoning benchmark requiring multi-step physical reasoning

Protocol

1. Problem classification — Identify domain (algebra, calculus, geometry, mechanics, thermodynamics, etc.)
2. Known-unknowns analysis — List given quantities, target quantity, constraints
3. Strategy selection — Choose approach (direct computation, proof by contradiction, dimensional analysis, symmetry arguments)
4. Step-by-step solution — Show each derivation step with justification
5. Verification — Check units, boundary conditions, limiting cases