Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.
About this quote
- What does it mean?
- Math relies on intuition for spontaneous judgments and ingenuity to structure those judgments.
- In plain terms
- Math uses gut feelings and smart ways to organize them.
- What can you take from it?
- Trust intuition but organize it carefully.
Where it applies
Putting it to work
Questions to consider
- Do you rely more on feeling or logic?
- How do you structure your thoughts?
Another view
Intuition can sometimes mislead without structure.
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