In the mid nineteenth century, the Gauss–Bonnet theorem linked the Euler characteristic to the Gaussian curvature.
•
In 1857, Riemann introduced the concept of Riemann surfaces as part of a study of the process of analytic continuation; Riemann surfaces are now recognized as one-dimensional complex manifolds.
•
Henri Poincaré's 1895 paper Analysis Situs studied three-and-higher-dimensional manifolds(which he called "varieties"), giving rigorous definitions of homology, homotopy (which had originally been defined in the context of late nineteenth-century knot theory, developed by Maxwell and others), and Betti numbers and raised a question, today known as the Poincaré conjecture, based his new concept of the fundamental group.
•
In 2003, Grigori Perelman proved the conjecture using Richard Hamilton's Ricci flow, this is after nearly a century of effort by many mathematicians.
history | American Museum of Natural History | Natural History Museum | History | History (U.S. TV channel) | natural history | Field Museum of Natural History | History of China | National Museum of Natural History | The History Channel | Natural history | Jewish history | Swedish Museum of Natural History | Natural History | National Museum of American History | Carnegie Museum of Natural History | art history | AP United States History | History of Texas Tech University | The History of the Decline and Fall of the Roman Empire | oral history | History of the Jews in Germany | History Detectives | Black History Month | A History of the World in 100 Objects | History of India | History of the Jews in Poland | History of Bavaria | Washington County History & Landmarks Foundation | History (TV channel) |