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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]
In 2023, Kaplan was part of the team that solved the einstein problem, a major open problem in tiling theory and Euclidean geometry. The problem is to find an "aperiodic monotile", a single geometric shape which can tesselate the plane aperiodically (without translational symmetry) but which cannot do so periodically. The discovery is under ...
David Smith is an amateur mathematician and retired print technician from Bridlington, England, [1] who is best known for his discoveries related to aperiodic monotiles that helped to solve the einstein problem. [2] [3]
In March 2023, four researchers, David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, announced the proof that the tile discovered by David Smith is an aperiodic monotile, i.e., a solution to the einstein problem, a problem that seeks the existence of any single shape aperiodic tile. [3]
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.
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Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame. Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.
Edward Witten (born August 26, 1951) is an American theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics.