main webpage W Topic Geometry arXiv (Cornell University) On the Solvability Complexity Index Hierarchy and Towers of Algorithms 2015 This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{sp}(A)$ of classes o… Article Open Geometry Open Article Page

Geometry

Branch of mathematics Geometry (from Ancient Greek __ γεωμετρία (_geōmetría ) 'land measurement'; from __ γῆ ( gê ) 'earth, land' and __ μέτρον ( métron ) 'a measure') is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a _geometer . Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Critical Symbolic Virtual Narrative Open Geometry Open Article Page

Exploring foci of: arXiv (Cornell University) On the Solvability Complexity Index Hierarchy and Towers of Algorithms 2015 This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{sp}(A)$ of classes of bounded operators $A = \{a_{ij}\}_{i,j \in \mathbb{N}} \in \mathcal{B}(l^2(\mathbb{N}))$, given the matrix elements $\{a_{ij}\}_{i,j \in \mathbb{N}}$, that are sharp in the sense that they achieve the boundary of what a digital computer can achieve. Similarl… Open Article Page

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Explore Geometry W Topic Geometry arXiv (Cornell University) On the Solvability Complexity Index Hierarchy and Towers of Algorithms 2015 This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{sp}(A)$ of classes o… Article Critical Symbolic Virtual Narrative Open Geometry Open Article Page