Sir Michael Francis Atiyah was a British-Lebanese mathematician specialising in geometry.
In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space.
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject.
In vector calculus and differential geometry the generalized Stokes theorem, also called the Stokes–Cartan theorem, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. It is a generalization of Isaac Newton's fundamental theorem of calculus that relates two-dimensional line integrals to three-dimensional surface integrals.
Mornington Crescent is a game featured in the BBC Radio 4 comedy panel show I'm Sorry I Haven't a Clue (ISIHAC), a series that satirises panel games.
In mathematics, an embedding is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.
In mathematics, a Haken manifold is a compact, P²-irreducible 3-manifold that is sufficiently large, meaning that it contains a properly embedded two-sided incompressible surface. Sometimes one considers only orientable Haken manifolds, in which case a Haken manifold is a compact, orientable, irreducible 3-manifold that contains an orientable, incompressible surface.
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index is equal to the topological index. It includes many other theorems, such as the Chern–Gauss–Bonnet theorem and Riemann–Roch theorem, as special cases, and has applications to theoretical physics.
Ian Nicholas Stewart is a British mathematician and a popular-science and science-fiction writer. He is Emeritus Professor of Mathematics at the University of Warwick, England.
In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S → M satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors often have different definitions.
Sir Simon Kirwan Donaldson is an English mathematician known for his work on the topology of smooth (differentiable) four-dimensional manifolds, Donaldson–Thomas theory, and his contributions to Kähler geometry. He is currently a permanent member of the Simons Center for Geometry and Physics at Stony Brook University in New York, and a Professor in Pure Mathematics at Imperial College London.
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or n-manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space.
Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates.
In mathematics, a differentiable manifold of dimension n is called parallelizable if there exist smooth vector fields
In mathematics, the Weeks manifold, sometimes called the Fomenko–Matveev–Weeks manifold, is a closed hyperbolic 3-manifold obtained by (5, 2) and (5, 1) Dehn surgeries on the Whitehead link. It has volume approximately equal to 0.942707… and David Gabai, Robert Meyerhoff, and Peter Milley (2009) showed that it has the smallest volume of any closed orientable hyperbolic 3-manifold. The manifold was independently discovered by Jeffrey Weeks (1985) as well as Sergei V. Matveev and Anatoly T. Fomenko (1988).
In topology, an area of mathematics, the virtually Haken conjecture states that every compact, orientable, irreducible three-dimensional manifold with infinite fundamental group is virtually Haken. That is, it has a finite cover that is a Haken manifold.
In mathematics, an immersion is a differentiable function between differentiable manifolds whose derivative is everywhere injective. Explicitly, f : M → N is an immersion if
Alan David Weinstein is a professor of mathematics at the University of California, Berkeley, working in the field of differential geometry, and especially in Poisson geometry.
Ian Agol is an American mathematician who deals primarily with the topology of three-dimensional manifolds.
Finchley Central is a mind game in which two players take turns naming stations in the London Underground. The first person to name Finchley Central is the winner. Of course, the first player could say "Finchley Central" straight away, but as maths professor Jonathan Partington notes,
An opening move of "Finchley Central" is too much of a cheat, and you might wish to start with, say, Liverpool Street, when, assuming that your opponent isn't rude enough to reply with Finchley Central, leaves you with a mate on your second move.
