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See: Math, Good math

Distinguish and investigate the many dimensions of math, such as beauty, insight, learning, humanity.

Questions about the big picture in mathematics

• Discovery: What are the ways of figuring things out in mathematics? We can study mathematics as an activity by which we create and solve mathematical problems. These techniques are much more limited than the mathematical output which they generate.
• Organization: How can mathematics be organized so as to survey the most basic concepts from which it arises and understand it in terms of its most fundamental divisions and how they relate to each other?
• Beauty Mathematicians are guided by a sense of beauty. What is meant by beauty? What principles determine it? How does beauty lead to mathematical insight?
• Education What resources are available to mathematicians that would help them most effectively learn mathematics so as to try to understand it as a whole? How might mathematicians collaborate effectively in trying to understand the big picture?
• Insight? What are the most fruitful insights in trying to understand mathematics? How can such insights best be stated?
• Implicit math What concepts express intuitions that are prior to explicit mathematics and make it possible?
• History How can the history of mathematical discovery inform frameworks for the future development of mathematics?
• Humanity? What parts or aspects of mathematics are specific to the human mind, body, culture, society, and what might be more broadly meaningful to other species in the universe?

Understanding math requires approaching it from several directions

• Understanding it combinatorially
• Doing calculations, gaining familiarity, instincts, intuition
• Understanding it structurally, algebraically
• Understanding the purpose
• Understanding examples, counterexamples
• Understanding problems