What is the origin of the idiom "thinking cap" and when to use it?

The idiom "thinking cap" likely originated from the idea of wearing a special cap or hat that symbolizes one's readiness to engage in deep thinking or problem-solving. The term "cap" here is metaphorical and signifies a mental state of concentration and intellectual effort. This figurative expression has been in use since at least the early 20th century and is related to the notion of putting on a cap as a symbolic act of focusing one's mental faculties. It is used to encourage someone to engage their intellectual abilities, concentrate, and come up with creative solutions or ideas. It is often employed in a lighthearted or playful context to suggest that someone should put on their metaphorical "thinking cap" to address a challenge or task requiring mental effort.