“It’s a tempting story. After all, LLMs can write code, generate documentation, and even produce what looks like a mathematical model. But LLMs are pattern generators. They predict the next word, token, or code snippet based on what they’ve seen in their training. This makes them extraordinary for drafting, summarizing, or translating ideas into a different form. But they don’t prove anything. They don’t guarantee feasibility, optimality, or even correctness.

Optimization solvers live in a very different universe. A solver takes a clearly defined objective and constraints, then searches (often through billions of possibilities) using decades of algorithmic advances. When a solver returns an answer, you can test it, verify feasibility, and often prove that it is optimal. That rigor is the very reason we trust solvers to make billion-dollar decisions in supply chains, energy systems, finance, and beyond.

Rather than thinking of LLMs as replacements, the real power comes when we combine the two. An LLM can help a planner articulate a problem in natural language, suggest new constraints, or explain why a model is infeasible. The solver then does what it does best: provide mathematically rigorous solutions.” Link