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...p and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of ...and firmly established around 1870. Modern [[group theory]]—a very active mathematical discipline—studies groups in their own right.{{cref|a}} To explore groups, ...

...the "Quine-Putnam indispensability thesis," an argument for the reality of mathematical entities,<ref>Colyvan, Mark, [http://plato.stanford.edu/archives/fall2004/e ...The following year, he was selected as Walter Beverly Pearson Professor of Mathematical Logic, in recognition of his contributions to [[philosophy of logic]] and m ...

...The Euclidean algorithm has been generalized further to other mathematical structures, such as [[knot (mathematics)|knots]] and [[multivariate polynomial]]s. ...ef>Stark, p. 16.</ref> although the latter notation is also used for other mathematical concepts, such as two-dimensional [[coordinate vector|vectors]]. ...

...mathematical proof|Proofs]] have been formulated with varying degrees of [[mathematical rigour]], taking into account preferred development of the real numbers, ba ...generally unrelated to 0.999…, but they are of considerable interest in [[mathematical analysis]]. ...

...will limit the overall speed-up available from parallelization. Any large mathematical or engineering problem will typically consist of several parallelizable par ...h is generally difficult to implement and requires correctly designed data structures. ...

...lgorithm was, to the best of their knowledge, free from any statistical or mathematical weakness."<ref>{{cite book|first=D.W.|last=Davies|coauthors=W.L. Price|titl | Second workshop, discussing mathematical foundation of DES ...

In this context, "[[almost surely]]" is a mathematical term with a precise meaning, and the "monkey" is not an actual monkey; rath ...azoa]]n genome in this other sense: both have "combinatorial, hierarchical structures" that greatly constrain the immense number of combinations at the alphabet ...

...w class of preferred motions, too, defines a geometry of space and time—in mathematical terms, it is the [[geodesic]] motion associated with a specific [[connectio ...time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a [[conformal structure]].<ref>E.g. {{Harvnb|Ehlers|197 ...

...ef> To transfer ions into and out of the neuron, the membrane provides two structures. Ion pumps use the cell's energy to continuously move ions in and out. They ...0978}}</ref> through the atomic-resolution [[X-ray crystallography|crystal structures]],<ref name="doyle_1998">{{cite journal | author = Doyle DA, Morais Cabral ...

...the synthesis of huge amounts of kinetic and [[gene expression]] data into mathematical models of entire organisms. Although this goal is far in the future for any ...ef>{{cite journal |author=Dirr H, Reinemer P, Huber R |title=X-ray crystal structures of cytosolic glutathione S-transferases. Implications for protein architect ...

...ber 23, 1846,<ref name="Hamilton" /> Neptune was the first planet found by mathematical prediction rather than by [[empirical observation]]. Unexpected changes in ...res that can persist for several months, they are thought to be [[vortex]] structures.<ref name=apj125/> Often associated with dark spots are brighter, persisten ...

...ion of water molecules, and in 1905 [[Albert Einstein]] produced the first mathematical analysis of the motion.<ref> ...s 1924 proposal that particles behave to an extent like waves, developed a mathematical model of the atom that described the electrons as three-dimensional [[wavef ...