## TL;DR
Neuro-symbolic AI integrates neural learning with symbolic reasoning — combining the pattern recognition power of deep learning with the systematic generalization of logic. AlphaGeometry proved the paradigm by solving Olympiad-level geometry.

## Core Explanation
Neural strengths: pattern recognition from raw data (images, text, speech), robustness to noise, and scalability. Symbolic strengths: explicit knowledge representation, compositional reasoning, interpretable inference chains, and systematic generalization to unseen combinations. Integration strategies: (1) Neuro → Symbolic: neural network extracts structured representations from raw input; (2) Symbolic → Neuro: symbolic knowledge guides neural learning; (3) Neuro ⇔ Symbolic: tight coupling in reasoning loops.

## Detailed Analysis
Key applications: scientific discovery (AI Feynman deduces physical laws from data), theorem proving (AlphaGeometry, Lean Copilot), visual question answering (neuro-symbolic concept learner), and robotics (task and motion planning with learned affordances). Differentiable programming allows embedding symbolic operations (satisfiability, logic inference) as differentiable layers.

## Further Reading
- "The Third Wave of AI" (DARPA)
- IBM Neuro-Symbolic AI Lab
- PyReason: Neuro-Symbolic Framework