I consider that a man's brain originally is like a little empty attic, and you have to stock it with such furniture as you choose.
Arthur Conan DoyleRead
As one reads mathematics, one needs to have an active mind, asking questions, forming mental connections between the current topic and other ideas from other contexts, so as to develop a sense of the structure, not just familiarity with a particular tour through the structure.
Interpretation
What this quote means
Mathematics requires active engagement and connections to understand its deeper structure.
William Thurston's quote emphasizes the importance of an active and inquisitive mindset when studying mathematics. Rather than merely memorizing procedures, one should strive to create links between different mathematical concepts and broader ideas, fostering a comprehensive understanding of mathematical structures.
Themes
MathematicsActive MindUnderstandingConnectionsStructure
In practice
Example use cases
In a lecture about advanced mathematics, a professor could quote this to inspire students to engage more deeply with the material.
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