I am currently working through the mathematics required to understand the PoincarĂ© Conjecture and the possible solution recently proposed. I want to blog my journey and I started out summarising the basic foundations of pure mathematics necessary to get to the conjecture-specific parts. Now that I've got to explaining the conjecture, posts are about the background in differential geometry to understand the proofs.

#### Pages in this category

Journey to the Poincare Conjecture
Posted Sept. 17, 2004; Updated Aug. 10, 2007
Poincare Project: Thinking Like a Pure Mathematician
Posted Sept. 19, 2004; Updated Aug. 10, 2007
Poincare Project: Adding Structure to Sets
Posted Sept. 21, 2004; Updated Aug. 10, 2007
Poincare Project: Metric Spaces
Posted Oct. 14, 2004; Updated Aug. 10, 2007
Poincare Project: Open Balls and Continuity
Posted Oct. 28, 2004; Updated Aug. 10, 2007
Poincare Project: Open Sets
Posted Nov. 1, 2004; Updated Aug. 10, 2007
Poincare Project: Topologies and Topological Spaces
Posted Nov. 11, 2004; Updated Aug. 10, 2007
Poincare Project: Injections, Surjections and Bijections
Posted Nov. 17, 2004; Updated Feb. 8, 2005
Poincare Project: Further Thoughts on Topologies and Open Sets
Posted Nov. 20, 2004; Updated Feb. 8, 2005
Poincare Project: Homeomorphisms
Posted Nov. 29, 2004; Updated July 1, 2005
Poincare Project: Connectedness, Closed Sets and Topological Properties
Posted Dec. 7, 2004; Updated Feb. 8, 2005
Poincare Project: A Basis for a Topology
Posted Dec. 10, 2004; Updated Feb. 8, 2005
Poincare Project: The Standard Topology for Ordered Sets
Posted Dec. 23, 2004; Updated Feb. 8, 2005
Poincare Project: Open Coverings and Compactness
Posted Dec. 30, 2004; Updated Aug. 20, 2005
Poincare Project: More on Compactness
Posted Jan. 22, 2005; Updated Aug. 9, 2007
Poincare Project: Separation Axioms
Posted Jan. 27, 2005; Updated Aug. 10, 2007
Poincare Project: More on Separation Axioms
Posted Jan. 29, 2005; Updated Feb. 8, 2005
Poincare Project: Manifolds
Posted Feb. 11, 2005
Poincare Project: Switching from Analysis to Algebra
Posted March 6, 2005
Poincare Project: Binary Operations
Posted March 14, 2005
Poincare Project: Associativity
Posted March 14, 2005
Poincare Project: Identities and Monoids
Posted March 16, 2005; Updated Aug. 9, 2007
Poincare Project: Inverses
Posted March 19, 2005
Poincare Project: Groups
Posted March 26, 2005
Poincare Project: Paths
Posted April 21, 2005
Poincare Project: Topological Properties Revisited
Posted April 27, 2005
Paths as homeomorphisms of the closed interval from 0 to 1
Posted May 28, 2005; Updated June 1, 2005
Homotopy
Posted June 3, 2005
Continuous Functions are between Topological Spaces not Sets
Posted June 8, 2005; Updated Aug. 9, 2007
Path Homotopy
Posted July 1, 2005
Homotopy as a Way of Distinguishing Topological Spaces
Posted July 9, 2005; Updated July 10, 2005
Equivalence Relations
Posted July 16, 2005; Updated Sept. 28, 2005
Equivalence Classes
Posted Aug. 3, 2005
Homotopy Classes and Simple Connectedness
Posted Aug. 6, 2005
Closed Manifolds
Posted Aug. 20, 2005; Updated Aug. 9, 2007
The Poincare Conjecture
Posted Aug. 31, 2005
Number of Connected One-Dimensional Manifolds
Posted Sept. 22, 2005; Updated Oct. 2, 2005
The Circle is Not Simply Connected
Posted Oct. 2, 2005; Updated Aug. 9, 2007
Poincare Update
Posted Sept. 5, 2006
Coordinate Systems
Posted Oct. 22, 2006; Updated Aug. 9, 2007
Coordinate Systems and Metrics
Posted Nov. 19, 2006
Metrics in Two or More Dimensions
Posted Jan. 15, 2007
Linear Spaces
Posted Feb. 28, 2007
Arrow-type Vectors
Posted March 21, 2007; Updated Aug. 9, 2007
Linear Spaces: Duck Typing and Tuples
Posted Aug. 9, 2007
Stack-Type Vectors, Part I
Posted Aug. 14, 2007
Stack-Type Vectors, Part II
Posted Aug. 23, 2007
Stack-Type Vectors, Part III
Posted Dec. 15, 2007
Arrows and Stacks as Duals
Posted March 22, 2008
One-Forms Form Linear Spaces
Posted March 23, 2008
Coordinate Systems and Stack-Type Vectors
Posted March 28, 2008
Metrics As Mappings Between Arrows and Stacks
Posted May 4, 2008
Metrics Provide An Inner Product
Posted May 11, 2008

The original post was in the category: mathematics but I'm still in the process of migrating categories over.