How to FULLY understand a definition?

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Understanding mathematical definitions, such as tensors or the fundamental theorem of calculus (FTC), often eludes even experienced mathematicians, as memorization and problem-solving do not equate to true comprehension. Many participants in the discussion express that they can repeat definitions and proofs but struggle to grasp the underlying concepts fully. The challenge lies in the abstract nature of mathematics, where intuitive understanding often remains out of reach despite familiarity with the rules and properties. The conversation highlights that true understanding may come from the ability to explain concepts simply, yet this remains a difficult benchmark to achieve. Ultimately, the quest for deeper insight into mathematical ideas continues to be a complex and evolving journey.
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complexPHILOSOPHY said:
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