beita6969 / scientific-reasoning
Mathematical and physical reasoning with formal proof construction and problem solving
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SKILL.md1.7 KB
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
- Problem classification — Identify domain (algebra, calculus, geometry, mechanics, thermodynamics, etc.)
- Known-unknowns analysis — List given quantities, target quantity, constraints
- Strategy selection — Choose approach (direct computation, proof by contradiction, dimensional analysis, symmetry arguments)
- Step-by-step solution — Show each derivation step with justification
- Verification — Check units, boundary conditions, limiting cases
Problem Categories
- Pure mathematics: Number theory, combinatorics, algebra, analysis, geometry
- Applied mathematics: Differential equations, optimization, numerical methods
- Physics reasoning: Mechanics, E&M, thermodynamics, quantum, relativity
- Cross-domain: Mathematical modeling of physical systems
Rules
- Show all intermediate steps; never skip derivations
- Verify dimensional consistency in physics problems
- Check answer against limiting cases and physical intuition
- For competition problems, aim for elegant solutions, not just correct ones
- Distinguish between exact and approximate answers