Eigentlich ist die Luft aus dem Thema ja langsam raus, aber das finde ich wirklich eine gute Idee: James Tauber arbeitet nach und nach in seinem Poincaré Project die Poincare Vermutung und den Beweis auf verständlichem Niveau auf.

I am currently working through the mathematics required to understand the Poincaré Conjecture and the possible solution recently proposed. I want to blog my journey and I'm starting out summarising the basic foundations of pure mathematics necessary to get to the conjecture-specific parts.
So weit ist er schon gekommen:

* Journey to the Poincare Conjecture
* Poincare Project: Thinking Like a Pure Mathematician
* Poincare Project: Adding Structure to Sets
* Poincare Project: Metric Spaces
* Poincare Project: Open Balls and Continuity
* Poincare Project: Open Sets
* Poincare Project: Topologies and Topological Spaces
* Poincare Project: Injections, Surjections and Bijections
* Poincare Project: Further Thoughts on Topologies and Open Sets
* Poincare Project: Homeomorphisms
* Poincare Project: Connectedness, Closed Sets and Topological Properties
* Poincare Project: A Basis for a Topology
* Poincare Project: The Standard Topology for Ordered Sets
* Poincare Project: Open Coverings and Compactness
* Poincare Project: More on Compactness
* Poincare Project: Separation Axioms
* Poincare Project: More on Separation Axioms
* Poincare Project: Manifolds
* Poincare Project: Switching from Analysis to Algebra
* Poincare Project: Associativity
* Poincare Project: Binary Operations
* Poincare Project: Identities and Monoids
* Poincare Project: Inverses
* Poincare Project: Groups
* Poincare Project: Paths
* Poincare Project: Topological Properties Revisited
* Paths as homeomorphisms of the closed interval from 0 to 1
* Homotopy
* Continuous Functions are between Topological Spaces not Sets
* Path Homotopy
* Homotopy as a Way of Distinguishing Topological Spaces
* Equivalence Relations
* Equivalence Classes
* Homotopy Classes and Simple Connectedness
* Closed Manifolds
* The Poincare Conjecture
* Number of Connected One-Dimensional Manifolds
* The Circle is Not Simply Connected
* Poincare Update