While LLMs can mimic human-like language, mathematical reasoning poses unique challenges:
Fundamentally, maths does not require statistical consensus to be right.
1. **Symbolic Manipulation:** Mathematics relies heavily on symbols and notation. Manipulating equations requires understanding algebraic principles, not just pattern completion.
2. **Logical Progression:** Solving problems often involves a series of logical steps that must be followed precisely. LLMs may generate steps that seem plausible but not always logically valid.
3. **Conceptual Understanding:** Higher-level mathematics involves abstract concepts such as limits, imaginary numbers, and multi-dimensional spaces, which require innate and deep comprehension.
4. **Error Handling:** In mathematics, an error in one step invalidates the entire solution. LLMs may not recognize or correct these errors autonomously.
https://arxiv.org/pdf/2410.05229