ManifoldIn mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an -dimensional manifold, or -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane.
Hyperkähler manifoldIn differential geometry, a hyperkähler manifold is a Riemannian manifold endowed with three integrable almost complex structures that are Kähler with respect to the Riemannian metric and satisfy the quaternionic relations . In particular, it is a hypercomplex manifold. All hyperkähler manifolds are Ricci-flat and are thus Calabi–Yau manifolds. Hyperkähler manifolds were defined by Eugenio Calabi in 1979. Equivalently, a hyperkähler manifold is a Riemannian manifold of dimension whose holonomy group is contained in the compact symplectic group Sp(n).
Evolution of human intelligenceThe evolution of human intelligence is closely tied to the evolution of the human brain and to the origin of language. The timeline of human evolution spans approximately seven million years, from the separation of the genus Pan until the emergence of behavioral modernity by 50,000 years ago. The first three million years of this timeline concern Sahelanthropus, the following two million concern Australopithecus and the final two million span the history of the genus Homo in the Paleolithic era.
Human intelligenceHuman intelligence is the intellectual capability of humans, which is marked by complex cognitive feats and high levels of motivation and self-awareness. With intelligence, humans can learn, form concepts, understand, apply logic and reason, including the capacities to recognize patterns, plan, innovate, solve problems, make decisions, retain information, and use language to communicate. There are conflicting ideas about how intelligence is measured, ranging from the idea that intelligence is fixed at birth to the idea that it is malleable and can change depending on a person's mindset and efforts.
History of geometryGeometry (from the γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today.
Eugenio BeltramiEugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times.
