Why do people who are good at math come up with solutions? The truth about the 'trial and error' not written in model answers

When solving math problem sets, have you ever had questions like these?"Why did they decide to factorize here?""Why did they ...
The Verge

All the drama around AI’s takeover of mathematics

OpenAI is giving $5 million to help mathematicians make sense of AI-generated research. “Staggering.” “Overwhelming.” “Unprecedented.” “Surreal.” “Pure insanity.” Those were among the descriptions ...