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The strictest version of the problem was solved in 2023, after an initial discovery in 2022. The einstein problem can be seen as a natural extension of the second part of Hilbert's eighteenth problem, which asks for a single polyhedron that tiles Euclidean 3-space, but such that no tessellation by this polyhedron is isohedral. [3]
Einstein himself considered the introduction of the cosmological constant in his 1917 paper founding cosmology as a "blunder". [3] The theory of general relativity predicted an expanding or contracting universe, but Einstein wanted a static universe which is an unchanging three-dimensional sphere, like the surface of a three-dimensional ball in four dimensions.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
As was shown by Einstein, the only form of accelerated motion that cannot be non-locally described is the one due to gravitation. Einstein was also unsatisfied with the fact that inertial frames are preferred over accelerated frames. Thus over the course of several years (1908–1915), Einstein developed general relativity.
Einstein also recognized another element of the definition of an exact solution: it should be a Lorentzian manifold (meeting additional criteria), i.e. a smooth manifold. But in working with general relativity, it turns out to be very useful to admit solutions which are not everywhere smooth; examples include many solutions created by matching ...
Here’s another problem that’s very easy to write, but hard to solve. All you need to recall is the definition of rational numbers. Rational numbers can be written in the form p/q, where p and ...
The solutions of the Einstein field equations are metrics of spacetime. These metrics describe the structure of the spacetime including the inertial motion of objects in the spacetime. As the field equations are non-linear, they cannot always be completely solved (i.e. without making approximations).
A college student just solved a seemingly paradoxical math problem—and the answer came from an incredibly unlikely place. Skip to main content. 24/7 Help. For premium support please call: 800 ...