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He argued that the toolbox of physics enables a practitioner like Edward Witten to go beyond standard mathematics, in particular the geometry of 4-manifolds. The tools of a physicist are cited as quantum field theory , special relativity , non-abelian gauge theory , spin , chirality , supersymmetry , and the electromagnetic duality .
Certain paper-folding problems do not have efficient algorithms. Computational intractability results show that there are no such polynomial-time algorithms that currently exist to solve certain folding problems. For example, it is NP-hard to evaluate whether a given crease pattern folds into any flat origami. [47]
No matter how many problems we solve, there will always be other problems that cannot be solved within the existing rules. […] Because of Gödel's theorem, physics is inexhaustible too. The laws of physics are a finite set of rules, and include the rules for doing mathematics, so that Gödel's theorem applies to them." [48]
The following is a list of notable unsolved problems grouped into broad areas of physics. [1]Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result.
During this period there was little distinction between physics and mathematics; [18] as an example, Newton regarded geometry as a branch of mechanics. [19] Non-Euclidean geometry, as formulated by Carl Friedrich Gauss, János Bolyai, Nikolai Lobachevsky, and Bernhard Riemann, freed physics from the limitation of a single Euclidean geometry. [20]
Origami, the art of paper folding, has aesthetic qualities and many mathematical connections. One can study the mathematics of paper folding by observing the crease pattern on unfolded origami pieces. [16] Combinatorics, the study of counting, has artistic representations which some [who?] find mathematically beautiful. There are many visual ...
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Physics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. [1] Physics is one of the most fundamental scientific disciplines. [2] [3] [4] A scientist who specializes in the field of physics is called a physicist.