Results 21 to 30 of about 436,373 (139)
Hilbert's Program Then and Now [PDF]
, 2005 Hilbert's program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to "dispose of the foundational questions in mathematics once and for all, "Hilbert proposed a two-pronged approach in 1921: first ...
Zach, Richard
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Mathematical foundation of quantum annealing [PDF]
Journal of Mathematical Physics, 2008 Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundations of quantum annealing.
Satoshi Morita, Hidetoshi Nishimori
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Embracing the Crisis in the Foundations of Mathematics [PDF]
, 2013 The crisis in the foundations of mathematics is a conceptual crisis. I suggest that we embrace the crisis and adopt a pluralist position towards foundations. There are many foundations in mathematics.
Friend, Michèle
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, 1969 This article discusses what can be proved about the foundations of mathematics using the notions of algorithm and information. The first part is retrospective, and presents a beautiful antique, Godel's proof, the first modern incompleteness theorem, Turing's halting problem, and a piece of postmodern metamathematics, the halting probability Omega.
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“In Mathematical Language”: On Mathematical Foundations of Quantum Foundations
EntropyThe argument of this article is threefold. First, the article argues that from its rise in the sixteenth century to our own time, the advancement of modern physics as mathematical-experimental science has been defined by the invention of new mathematical structures. Second, the article argues that quantum theory, especially following quantum mechanics,
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Computational reverse mathematics and foundational analysis [PDF]
, 2018 Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which
Eastaugh, Benedict
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String and M-theory: answering the critics
, 2011 Using as a springboard a three-way debate between theoretical physicist Lee Smolin, philosopher of science Nancy Cartwright and myself, I address in layman's terms the issues of why we need a unified theory of the fundamental interactions and why, in my ...
A. Garrett Lisi +11 more
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Mathematical Foundations of Computational Electromagnetism [PDF]
, 2018 This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief
Assous, Franck +2 more
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Mathematical foundations of the GraphBLAS [PDF]
2016 IEEE High Performance Extreme Computing Conference (HPEC), 2016 The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments.
Kepner, Jeremy +15 more
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Perspectives for proof unwinding by programming languages techniques [PDF]
, 2016 In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory.
Ilik, Danko
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