metamathematical notion

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• mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …   Universalium

• History of logic — Philosophy ( …   Wikipedia

• Algorithm characterizations — The word algorithm does not have a generally accepted definition. Researchers are actively working in formalizing this term. This article will present some of the characterizations of the notion of algorithm in more detail. This article is a… …   Wikipedia

• History of the Church-Turing thesis — This article is an extension of the history of the Church Turing thesis.The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

• History of the Church–Turing thesis — This article is an extension of the history of the Church–Turing thesis. The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

• Church–Turing thesis — Church s thesis redirects here. For the constructive mathematics assertion, see Church s thesis (constructive mathematics). In computability theory, the Church–Turing thesis (also known as the Church–Turing conjecture, Church s thesis, Church s… …   Wikipedia

• Brouwer-Hilbert controversy — A foundational controversy in twentieth century history of mathematics opposed L. E. J. Brouwer, a supporter of intuitionism, and David Hilbert, the founder of formalism.BackgroundThe background for the controversy was set with David Hilbert s… …   Wikipedia

• logic, philosophy of — Philosophical study of the nature and scope of logic. Examples of questions raised in the philosophy of logic are: In virtue of what features of reality are the laws of logic true? ; How do we know the truths of logic? ; and Could the laws of… …   Universalium

• Philosophy of mathematics — The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of …   Wikipedia

• Proof theory — is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively defined data structures such as plain lists, boxed… …   Wikipedia

• List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… …   Wikipedia