Contrasting Terrains on Comet Churyumov-Gerasimenko
Image Credit: ESA / Rosetta / MPS for OSIRIS Team; MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA
Pretty good history of the Poincare conjecture. How the conjecture led to all kinds of other problems and concepts. As Josh Morgan and mathematicians well known, Henri Poincare is considered the first to make topology a field of mathematics like algebra, geometry, and analyses(calculus). The history of topology goes back to Leondard Euler and the famous Konigsberg bridge problem. Frederick Gauss had some vague notions about it - specifically about genus of a curve. His student Bernard Riemann derived much topology from complex analyses. He mapped a sphere onto a plane and showed that the two valued complex numbers leads to a two sheeted surface. Or, a sphere is topologically a two sheeted surface. Riemann surfaces classify complex analyses functions. The Mobius strip was also invented back in the 1800s before Henri Poincare's work.