What is the relation between geometry and arithmetic? How can we model the motion of the heavenly bodies? What roles do diagrams and imagination play in a demonstrative proof? What is the structure of good reasoning? Can there be mathematics of the infinite and the infinitesimal? Are there multiple geometries? Students study original and influential works of mathematics, demonstrating hundreds of theorems to one another in class, and inquiring into the foundations of geometry, mathematical physics, logic, number theory, set theory, algebra, analysis, multi-variable calculus, differential equations, and astronomy.
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