Topology
Branch · 1890s-1930s · Mathematics, stage 2: Map the branches
Topology studies what survives when a shape is stretched or bent but not cut or glued, which means it drops distance and keeps only which points are near which. Poincaré gave the subject its first systematic treatment in 1895 and introduced algebraic invariants that tell shapes apart by attaching groups to them. The algebraic side was sharpened in the 1920s and 1930s, in part through Noether's insistence that homology be treated in terms of groups, and topology then spread into analysis, geometry, and physics.
What it claims
- Nearness, not distance, is the basic geometric idea.
- The properties worth studying are those preserved by continuous deformation.
- Shapes that cannot be told apart by inspection can be told apart by algebraic quantities attached to them.
Key ideas
People
Sources
- Topology Wikipedia
- Topology history MacTutor History of Mathematics
