Science and myths's video: Einstein Million dollar question Poincare Conjecture

Poincare conjecture, million dollar question in topology, conjecture—now proven to be a true theorem—that every simply connected, closed, three-dimensional manifold is topologically equivalent to S3, which is a generalization of the ordinary sphere to a higher dimension (in particular, the set of points in four-dimensional space that are equidistant from the origin). The conjecture was made in 1904 by the French mathematician Henri Poincare, who was working on classifying manifolds when he noted that three-dimensional manifolds posed some special problems. This problem became one of the most important unsolved problems in algebraic topology. “Simply connected” means that a figure, or topological space, contains no holes. “Closed” is a precise term meaning that it contains all its limit points, or accumulation points (the points such that no matter how close one comes to any of them, other points in the figure, or set, will be within that distance). A three-dimensional manifold is a generalization and abstraction of the notion of a curved surface to three dimensions. “Topologically equivalent,” or homeomorphic, means that there exists a continuous one-to-one mapping, which is a generalization of the concept of a function, between two sets. The 3-sphere, or S3, is the set of points in four-dimensional space at some fixed distance to a given point. Poincare later extended his conjecture to any dimension, or, more specifically, to the assertion that every compact n-dimensional manifold is homotopy-equivalent to the n-sphere (each can be continuously deformed into the other) if and only if it is homeomorphic to the n-sphere. In other words, the n-sphere is the only bounded n-dimensional space that contains no holes. For n = 3, this reduces to his original conjecture. Now to know more watch this video till the end. Thanks for watching.. Social accounts link Instagram- https://www.instagram.com/scienceandmyths/ Facebook Page- https://www.facebook.com/ScienceAndMyths/ Einstein भी नहीं दे पाए इस सवाल का जबाब | Million dollar question Poincare Conjecture FAIR-USE COPYRIGHT DISCLAIMER This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.