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The year's finest mathematical writing from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2018 makes available to a wide audience many pieces not easily found anywhere else-and you don't need to be a mathematician to enjoy them. These essays delve into the history, philosophy, teaching, and everyday aspects of math, offering surprising insights into its nature, meaning, and practice-and taking readers behind the scenes of today's hottest mathematical debates.James Grime shows how to build subtly mischievous dice for playing slightly unfair games, David Rowe investigates the many different meanings and pedigrees of mathematical models, and Michael Barany traces how our appreciation of the societal importance of mathematics has developed since World War II. In other essays, Francis Su extolls the inherent values of learning, doing, and sharing mathematics, and Margaret Wertheim takes us on a mathematical exploration of the mind and the world-with glimpses at science, philosophy, music, art, and even crocheting. And there's much, much more.In addition to presenting the year's most memorable math writing, this must-have anthology includes an introduction by the editor and a bibliography of other notable pieces on mathematics.This is a must-read for anyone interested in where math has taken us-and where it is headed.

Mathematics --- Accuracy and precision. --- Alan Turing. --- Algebra I. --- Algebra II. --- Algebra. --- American Mathematical Society. --- Applied mathematics. --- Approximation algorithm. --- Arithmetic. --- Big Science. --- Boolean satisfiability problem. --- Calculation. --- Candidate solution. --- Combinatorial proof. --- Computational geometry. --- Computational mathematics. --- Computational science. --- Computer Science Teachers Association. --- Computer scientist. --- David Hilbert. --- Discrete mathematics. --- Dynamic programming. --- Education. --- Educational Studies in Mathematics. --- Experimental mathematics. --- Foundations of mathematics. --- Fundamental theorem of algebra. --- Geometry. --- Gödel's incompleteness theorems. --- Hardness of approximation. --- Heuristic. --- Hilbert space. --- Homological mirror symmetry. --- Interdisciplinary Contest in Modeling. --- International Mathematical Union. --- Joint Policy Board for Mathematics. --- Language of mathematics. --- Learning sciences. --- Liberal arts education. --- Linear algebra. --- Logic. --- London Mathematical Society. --- MIT Mathematics Department. --- Mathematica. --- Mathematical Association of America. --- Mathematical Reviews. --- Mathematical analysis. --- Mathematical and theoretical biology. --- Mathematical beauty. --- Mathematical logic. --- Mathematical physics. --- Mathematical practice. --- Mathematical problem. --- Mathematical proof. --- Mathematical sciences. --- Mathematical software. --- Mathematician. --- Mathematics education. --- Mathematics. --- Meaningful learning. --- New Math. --- Nobel Prize in Physics. --- Number theory. --- Numerical analysis. --- Open problem. --- Optimization problem. --- Philosophy of mathematics. --- Prime number. --- Proof by exhaustion. --- Proof complexity. --- Propositional calculus. --- Pure mathematics. --- Pythagorean theorem. --- Quadratic formula. --- Quantum geometry. --- Ramsey theory. --- Rational trigonometry. --- Recreational mathematics. --- Reverse mathematics. --- Riemann hypothesis. --- Riemannian geometry. --- Robustness (computer science). --- Satisfiability modulo theories. --- Schur's theorem. --- Science education. --- Sign (mathematics). --- Society for Industrial and Applied Mathematics. --- Solver. --- The College Mathematics Journal. --- The Mathematical Experience. --- The Mathematical Intelligencer. --- The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --- The Value of Science. --- Theoretical computer science. --- Topological combinatorics. --- Traditional mathematics. --- Trigonometric tables. --- Turing machine. --- Variable (mathematics). --- Writing.

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A facsimile edition of Alan Turing's influential Princeton thesisBetween inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton.A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine.Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Logic, Symbolic and mathematical. --- Turing, Alan, --- Alan Perlis. --- Alan Turing. --- Algorithm. --- Alonzo Church. --- Applicable mathematics. --- Automated theorem proving. --- Axiomatic system. --- Boolean algebra. --- Boolean satisfiability problem. --- C++. --- Calculus of constructions. --- Cantor's diagonal argument. --- Central limit theorem. --- Church–Turing thesis. --- Computability theory. --- Computability. --- Computable function. --- Computable number. --- Computation. --- Computer architecture. --- Computer program. --- Computer science. --- Computer scientist. --- Computer. --- Computing Machinery and Intelligence. --- Computing. --- Coq. --- Cryptography. --- Decision problem. --- Donald Gillies. --- EDVAC. --- ENIAC. --- Enigma machine. --- Entscheidungsproblem. --- Formal system. --- Foundations of mathematics. --- Georges Gonthier. --- Gödel's incompleteness theorems. --- Haskell Curry. --- Howard Aiken. --- Instance (computer science). --- Iteration. --- J. Barkley Rosser. --- John Tukey. --- John von Neumann. --- Kenneth Appel. --- Kepler conjecture. --- Konrad Zuse. --- Lecture. --- Lisp (programming language). --- Logic for Computable Functions. --- Logic in computer science. --- Logic. --- Logical framework. --- Marvin Minsky. --- Mathematica. --- Mathematical analysis. --- Mathematical logic. --- Mathematical proof. --- Mathematician. --- Mathematics. --- Model of computation. --- Monotonic function. --- Natural number. --- Notation. --- Number theory. --- Numerical analysis. --- Oswald Veblen. --- Parameter (computer programming). --- Peano axioms. --- Peter Landin. --- Presburger arithmetic. --- Probability theory. --- Processing (programming language). --- Programming language. --- Proof assistant. --- Quantifier (logic). --- Recursion (computer science). --- Recursion. --- Result. --- Rice's theorem. --- Riemann zeta function. --- Satisfiability modulo theories. --- Scientific notation. --- Simultaneous equations. --- Skewes' number. --- Solomon Feferman. --- Solomon Lefschetz. --- Systems of Logic Based on Ordinals. --- The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --- Theorem. --- Theory of computation. --- Theory. --- Topology. --- Traditional mathematics. --- Turing Award. --- Turing machine. --- Turing's proof. --- Variable (computer science). --- Variable (mathematics).