The Structure of Mathematics
A structural path from arithmetic to category theory
- Counting without things
- Undoing a step
- Reasoning without plugging in
- Change that preserves structure
- Agreement between two operations
- Expressions before interpretation
- Polynomials as universal objects
- Forbidding interaction
- Objects in a linear world
- Transformations preserving linearity
- Independent directions and dimension
- Making dimension visible
- Coordinates and matrices
- From linear structure to geometric space
- Rigid transformations