“Experience has shown repeatedly that a mathematical theory with a rich internal structure generally turns out to have significant implications for the understanding of the real world, often in ways no one could have envisioned before the theory was developed.” WorldWayRealTurnsUnderstandingRichTheoryStructureSignificantMathematicalInternalsReal WorldImplications Author:William Thurston
“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.” NeedsMindIdeasTeachingParticularConnectionsAskingMathematicsStructureCurrentsActiveMathTopicsFamiliarityAsking QuestionsActive Minds Book:Three-Dimensional Geometry and Topology, Volume 1 Source: Three-Dimensional Geometry and Topology, Volume 1
