Philip J. Davis | Academic Influence

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According to Wikipedia, Philip J. Davis was an American academic applied mathematician. Davis was born in Lawrence, Massachusetts. He was known for his work in numerical analysis and approximation theory, as well as his investigations in the history and philosophy of mathematics. He earned his degrees in mathematics from Harvard University , and his final position was Professor Emeritus at the Division of Applied Mathematics at Brown University.

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Philip J. Davis's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Papers

Methods of Numerical Integration (1985) (2924)
Introduction to functional analysis (1959) (1486)
Interpolation and approximation (1965) (1314)
The Mathematical Experience (1982) (1245)
The Schwarz function and its applications (1974) (375)
Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz (1959) (213)
Descartes' Dream: The World According to Mathematics (1986) (187)
A generalization of the Bernstein polynomials (1999) (148)
Chapter 6 – Automatic Integration (1984) (103)
The convexity of Bernstein polynomials over triangles (1984) (101)
Fidelity in mathematical discourse: is one and one really two? (1972) (94)
Philosophy of Science: The Link Between Science and Philosophy (1957) (87)
Errors of Numerical Approximation for Analytic Functions (1953) (80)
Abscissas and Weights for Gaussian Quadratures of High Order (1956) (79)
Elements of the theory of functions (1967) (68)
A Construction of Nonnegative Approximate Quadratures (1967) (59)
What Is Mathematical Intuition (2006) (58)
Applied Mathematics as Social Contract (1987) (55)
Triangle formulas in the complex plane (1964) (48)
Spirals: From Theodorus to Chaos (1993) (47)
On the estimation of quadrature errors for analytic functions (1954) (43)
Visual theorems (1993) (40)
Advances in Orthonormalizing Computation (1961) (38)
Additional abscissas and weights for Gaussian quadratures of high order: Values for n=64, 80, and 96 (1958) (30)
Plane regions determined by complex moments (1977) (30)
IGNORING THE SINGULARITY IN APPROXIMATE INTEGRATION (1965) (29)
Are There Coincidences in Mathematics (1981) (26)
Some Monte Carlo experiments in computing multiple integrals (1956) (25)
Cyclic Transformations of Polygons and the Generalized Inverse (1977) (24)
THE RISE, FALL, AND POSSIBLE TRANSFIGURATION OF TRIANGLE GEOMETRY: A MINI-HISTORY (1995) (22)
Entropy and Society: Can the Physical/ Mathematical Notions of Entropy Be Usefully Imported into the Social Sphere? (2011) (21)
The Lore of Large Numbers (1961) (20)
The Mathematical Experience, Study Edition (2011) (20)
Formac Meets Pappus Some Observations on Elementary Analytic Geometry by Computer (1969) (20)
A Multiple Purpose Orthonormalizing Code and its Uses (1954) (19)
Some geometrical theorems for abscissas and weights of Gauss type (1961) (19)
Iterative Processes in Elementary Geometry (1983) (18)
An application of doubly orthogonal functions to a problem of approximation in two regions (1952) (17)
On the analytic continuation of mapping functions (1958) (16)
Proof, Completeness, Transcendentals, and Sampling (1977) (15)
The Mathematics of Matrices (1966) (15)
On the Use of Transcendentals for Program Testing (1981) (15)
On a problem in the theory of mechanical quadratures (1955) (14)
Complete sequences and approximations in normed linear spaces (1957) (14)
On the deterministic and stochastic approximation of regions (1977) (14)
Simple quadratures in the complex plane. (1965) (13)
What Do I Know? A Study of Mathematical Self-Awareness (1985) (13)
The Fourfold Classification in Plato's Philebus (1979) (12)
UNSPLIT K*'S. (1969) (12)
Mathematics & Common Sense: A Case of Creative Tension (2006) (12)
Mathematical encounters of the second kind (1996) (11)
Interpolation and orthonormal systems (1952) (11)
Cyclic transformations of n-gons and related quadratic forms (1979) (11)
Minkowski iteration of sets (1980) (10)
Approximate Integration over Infinite Intervals (1984) (10)
The Thread: A Mathematical Yarn (1983) (9)
A circulant formulation of the Napoleon-Douglas-Neumann theorem (1983) (9)
The Nature of Proof (1986) (9)
The Geometry of An Art: The History of the Mathematical Theory of Perspective from Alberti to Monge ‐ by Kirsti Andersen (2008) (9)
In Mind of Johnson: A Study of Johnson the Rambler (1989) (9)
Double integrals expressed as single integrals or interpolatory functionals (1972) (8)
A Brief Look at Mathematics and Theology (2002) (8)
Bound for the P-Condition Number of Matrices With Positive Roots (1961) (8)
Otto Neugebauer: Reminiscences and Appreciation (1994) (8)
The Companion Guide to the Mathematical Experience (1995) (7)
Nonnegative interpolation formulas for uniformly elliptic equations (1968) (7)
Why Victorian Literature Still Matters (2008) (7)
The Tree of Mathematics (1958) (6)
3.1416 And All That (1969) (6)
Additional simple quadratures in the complex plane (1968) (6)
Welcome to the World-Wide Web (1995) (5)
ON REPRESENTATIONS AND EXTENSIONS OF BOUNDED LINEAR FUNCTIONALS DEFINED ON CLASSES OF ANALYTIC FUNCTIONS (1954) (5)
What is an Abstraction (1985) (5)
Napoleon’s Theorem (1997) (5)
ON SIMPLE QUADRATURES (1953) (5)
Infinity and the Mind. The Science and Philosophy of the Infinite. By Rudy Rucker (1984) (5)
On the Applicability of Linear Differential Operators of Infinite Order to Functions of Class L 2 (B) (1952) (4)
The Schwarz Function and Its Applications: Properties in the Large of the Schwarz Function (1974) (4)
A theorem for kernel functions (1951) (4)
Thomas Campion: lyrick-doctor in physicke. (1969) (4)
On an equivalent definition of the transfinite diameter (1952) (4)
Fascinating Mathematical People: Interviews and Memoirs (2011) (4)
Unity and Disunity and Other Mathematical Essays (2015) (4)
On the Selection of Test Data for Recursive Mathematical Subroutines (1981) (4)
ON THE ZEROS OF TOTAL SETS OF POLYNOMIALS (1952) (4)
Packing inequalities for circles. (1963) (3)
The Companion Guide to the Mathematical Experience, Study Edition (2003) (3)
Chapter 4 – Error Analysis (1984) (3)
The Decline and Resurgence of the Visual in Mathematics (2006) (3)
Linear functionals and analytic continuation problems. (1953) (3)
Numerical computation of the transfinite diameter of two collinear line segments (1957) (3)
The Education of a Mathematician (2000) (3)
Remembering Philip Rabinowitz (2009) (2)
Accuracy of Monte Carlo methods in computing finite Markov chains (1960) (2)
Completeness theorems for sets of differential operators (1953) (2)
What should the public know about mathematics (1993) (2)
Abu Rayhan al-Biruni (2011) (2)
The Humanistic Aspects of Mathematics and Their Importance (1990) (2)
Immigration and Americanization: Selected Readings (2017) (2)
Equisum matrices and their permanence (2000) (2)
The Field of Social Service (2010) (2)
The Schwarz Function and Its Applications: What Figure is the Power of a Circle? (1974) (2)
Extraordinarily ordinary: the life of Samuel Johnson (1997) (2)
New winds blowing in applied mathematics (2015) (2)
The Prospects for Mathematics in a Multi-Media Civilization (1999) (2)
Group matrices for the quaternion and generalized dihedral groups (1986) (2)
Complex biorthogonality for certain sets of polynomials (1954) (2)
Some SEAC Computations of Subsonic Fluid Flows by Bergman’s Method of Integral Operators (1960) (2)
The mathematics of matrices : a first book of matrix theory and linear algebra (1965) (1)
Tea at Amalienborg (1995) (1)
The Man on the Moon (1983) (1)
Mathematics, substance and surmise: Views on the meaning and ontology of mathematics (2015) (1)
Thomas Gray, Philosopher Cat (1988) (1)
When Mathematics Says No (1986) (1)
Varieties of Mathematical Experience (2012) (1)
Mathematics by Fiat (1980) (1)
Fascinating Mathematical People (2011) (1)
Naïve Thoughts on the Paradox of Gödel (2001) (1)
On Ambiguity in Mathematics (2006) (1)
What Is Meant by the Word ""Random""? (2006) (1)
New Mathematical Library.@@@Numbers: Rational and Irrational.@@@What is Calculus About?@@@An Introduction to Inequalities.@@@Geometric Inequalities.@@@The Contest Problems Book.@@@The Lore of Large Numbers. (1962) (1)
Chapter 1: Definitions. (2018) (1)
Semi-dense closure of systems of functions (1968) (1)
On the nonexistence of simplex integration rules for infinite integrals (1972) (1)
A complex Pompeiu problem (1966) (1)
Unity and Disunity in Mathematics (2013) (1)
The Search Begins (1995) (1)
Mickey Flies the Stealth (2003) (1)
Mathematical Evidence: Why Do I Believe a Theorem? (2006) (0)
Mathematics at the Razor's Edge (2006) (0)
Lessons in the Danish Language and Literature (1995) (0)
The Plain Brown Envelope (1995) (0)
The Art of Squeezing (1985) (0)
Of Maps and Mathematics (1985) (0)
The Problem That Saved a Man’s Life (1985) (0)
The media and mathematics look at each other (2006) (0)
The House That Geometry Built (1985) (0)
“Mr. Milton, Mr. Bradley—Meet Andrey Andreyevich Markov” (1985) (0)
The Glory of the Realm (1995) (0)
More Pressure Is Applied (1995) (0)
When Should One Add Two Numbers (2006) (0)
Bridging the Two Cultures: Paul Valéry (2011) (0)
Bridging the Two Cultures: (2021) (0)
Thomas Gray in Copenhagen (1995) (0)
Mickey Flies the Stealth: Mathematics, War and Entertainment (2006) (0)
Unity in Major Themes: Convergence vs. Arbitrariness in the Development of Mathematics (2012) (0)
Quantification in Today's World (2006) (0)
The Next Step in Maintaining Peacetime Readiness. (2021) (0)
The two culture controversy: A mathematician’s view a half century later (2015) (0)
The Robust Way: ‘The Man Said, No’ (2016) (0)
The Logic of Mathematics Can Spawn Monsters (2006) (0)
How Common Sense Impacts Mathematical Reasoning: Some Very Simple Problems (2006) (0)
Conjugate Coordinates in the Plane (2014) (0)
Johnson: Sanity and Syntax (2011) (0)
An Application of the Theory of Basic Series to Theorems of Bernstein-Widder Type (1950) (0)
BOUNDEDNESS AND ASYMPTOTICS OF A MATRIX ITERATION (2005) (0)
The Magic Mirror (1995) (0)
Application to Elementary Fluid Mechanics (2014) (0)
In Which I Meet Lord Dacre (2011) (0)
The Schwarz Function and the Dirichlet Problem (2014) (0)
The Lore of Large Numbers: Bibliography (1961) (0)
The Soul of a Canary (1995) (0)
Elementary Geometrical Facts (2014) (0)
The Fabricated Letters of Antony and Cleopatra (2011) (0)
Selected Topics in Mathematics (2012) (0)
Mathematical Communication, Conceptual Understanding & Students' Attitudes Toward Mathematics (2009) (0)
Proof and other Dilemmas: When Is a Problem Solved? (2008) (0)
The Lore of Large Numbers: Preface (1961) (0)
Approximate Integration in Two or More Dimensions (1984) (0)
Victorian Hard Wiring (2009) (0)
The Lore of Large Numbers: Dedication (1961) (0)
Ancient loons : stories David Pingree told me (2012) (0)
The Lore of Large Numbers: Answers to Selected Problems (1961) (0)
Conversation with a Bouillabaisse (1995) (0)
The Lore of Large Numbers: LARGE NUMBERS AT WORK (1961) (0)
Bona Fides Established (1995) (0)
Mathematics Is Not Required. (2003) (0)
Overcoming employee campaign obstacles. (1991) (0)
Part I In the Beginning (2000) (0)
Pompeiu’s Magic Seven (1985) (0)
Thomas Gray in Copenhagen: In Which The Philosopher Cat Meets The Ghost Of Hans Christian Andersen (2013) (0)
In Principle We Can…: Mathematical Existentialism (2006) (0)
Lecture : Supplies, Demands, and Pseudoflows [sp'''] .. Reduction to Maximum Flow (2016) (0)
The Lore of Large Numbers: LARGE NUMBERS AND THEIR ARITHMETIC (1961) (0)
Biographical Memoirs: Gerard Piel (2007) (0)
Knowledge in Numbers (1984) (0)
The decline, fall, and current resurgence of visual geometry: Mathematics as a multisemiotic enterprise (2015) (0)
Abu Ma'ashar and the Hurrians (2011) (0)
Welcome to the White House: An Interactive Citizen's Handbook (1995) (0)
Schwarz Functions and Iterations (2014) (0)
Index to the Mathematical Gazette (1975) (0)
Additional simple quadratures in the complex plane (1968) (0)
Diamonds Around Her Neck (1995) (0)
The Collaboration Renewed (1995) (0)
The Schwarz Function and Differential Geometry (1974) (0)
Thomas Gray Arrives on the Scene (1995) (0)
REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS (2010) (0)
Geometrical Interpretation of the Schwarz Function; Schwarzian Reflection (2014) (0)
Schwarz Functions of Specified Type (2014) (0)
From Certainty to Fallibility (2012) (0)
The Relevance of the Irrelevant Beginning (2014) (0)
list of Chauvenet Prize winners (2013) (0)
Perturbation Bounds for Matrix Eigenvalues (Rajendra Bhatia) (1989) (0)
Mathematical Products (2018) (0)
Explorers of the Nth Dimension (1985) (0)
Division in the Cellar (1985) (0)
The Mathematical Landscape (2012) (0)
Mathematical Proof and Its Discontents (2006) (0)
Why Counting Is Impossible (2006) (0)
Immigration from the Immigrant's Point of View (1915) (0)
A Good Bit More Is Revealed (1995) (0)
Mathematics and Common Sense: Relations and Contrasts (2006) (0)
A Few Thoughts on Mathematics and Theology (2011) (0)
Are People Hard Wired to Do Mathematics (2006) (0)
The stage set the record straight, kindly but firmly (2007) (0)
The Logical Lie Detector (1985) (0)
The Business of Inequalities (1985) (0)
The Code of the Primes (1985) (0)
Ringing Down the Curtain (2011) (0)
Simplicity, Complexity, Beauty (2006) (0)
Inconsistencies and Their Virtues (2006) (0)
The Schwarz Function and Its Applications: Dictionary of Functional Relationships (1974) (0)
Perhaps YOU Have (1995) (0)
Platonism vs. Social Constructivism (2006) (0)
The Schwarz Function for an Analytic Arc (2014) (0)
The Lore of Large Numbers: Weights, Measures, and Equivalents (1961) (0)
The Kongekat’s Story (1995) (0)
My early experiences with scientific computation (2009) (0)
Computational Experiences in the Pre-Electronic Days (2015) (0)
Ancient Loons: Stories Pingree Told Me (2011) (0)
The Lore of Large Numbers: Formulas for Measurement (1961) (0)
Evidence in mathematics (2015) (0)
Mathematics, politics, and law (2015) (0)
Math Mixes It Up with Baseball (2006) (0)
Where Is Mathematical Knowledge Lodged and Where Does It Come From (2006) (0)
Spengler’s mathematics considered and a Phoenix reborn? (2015) (0)
Henri ’ s Crystal Ball (2008) (0)
The Xerox PARC map server: an interactive hypermedia map viewer (1995) (0)
Linear functional equations and interpolation series (1954) (0)
Astrology as Early Applied Mathematics (2006) (0)
Bibliographical and Supplementary Notes (2014) (0)
Sample Group Activities (1995) (0)
Siva and Parvati (2011) (0)
The Victorian Bump and Where to Find It (2009) (0)
The Abacus and the Slipstick (1985) (0)
Chapter 3 – Approximate Integration over Infinite Intervals (1984) (0)
Numbers, Point and Counterpoint (1985) (0)
The mathematical experience / Philip J. Davis, Reuben Hersh (1981) (0)
Found on Stroeget (1995) (0)
Mathematics Brings Forth Entities Whose Existence Is Counterintuitive (2006) (0)
The Band-Aid Principle (1985) (0)
Lucas Fysst’s Dream: The Wienerbroed and the Cat (1995) (0)
Conformal Maps, Reflections, and their Algebra (2014) (0)
South Africa: the real problem. (1985) (0)
St. Christopher the Dog-Faced (2011) (0)
Derivatives and integrals (2020) (0)
Out of what stuff do we make mathematics (2015) (0)
Charles-Benôit Hase (2016) (0)
A Note to Instructors (1995) (0)
Postulates—The Bylaws of Mathematics (1985) (0)
On Multivariate Bernstein Polynomials (2020) (0)
If Mathematics Says ""No"" Does It Really Mean It? (2006) (0)
Abraham J. Sachs (2011) (0)
What Is Mathematics (2006) (0)
Gerald J. Toomer (2011) (0)
Probability and Common Sense: A Second Look (2006) (0)
Nineteenth-Century Juliet (1996) (0)
The unicorn or mathematical ontology (2015) (0)
What the Victorians Can Still Do For Us (2007) (0)
The Loons and How I Got to Know Them (2011) (0)
Rules and Their Exceptions (2006) (0)
Carpenter and the Napoleon Ascription (1997) (0)
Chaos Off Camera (1995) (0)
The Rothschild I Knew (1997) (0)
Enter David Pingree, My Protagonist (2011) (0)
Instructions Are Received (1995) (0)
The Spider and the Fly (1985) (0)
The Mathematical Beauty Contest (1985) (0)
Can the mathematical/physical notions of entropy be usefully imported into the social sphere? (2015) (0)
Topics for Expository Research Papers (1995) (0)
Chaos and Polygons (1985) (0)
Spectral Dialogue in Nyhavn (1995) (0)
Civics for New Americans (2007) (0)
Opinion: Paraconsistent thoughts about consistency (2002) (0)
A Walk in the Neighborhood (1985) (0)
The World According to Network Theory (0)
Land Grant Application- Davis, Philip (Fayette) (2017) (0)
The Lore of Large Numbers: Some Selected Magnitudes in Science (1961) (0)
Lecture Series in Differential Equations. Session 8. Numerical Solutions. (1969) (0)
Paper Product Loading Aid for a Goodwill Employee (1993) (0)
Additional Simple Quadratures in the Complex Plane. (Short Communication). (1968) (0)
The Paradox of ""Hitting It Big"" (2006) (0)
Poinsot’s Points and Lines (1985) (0)
Lunch at Villa Fredenskjold (1995) (0)
How Amazing! What a Surprise! (2005) (0)
The Man Who Began His Lectures with “Namely” (1997) (0)
You can't be a mensch and not do it... Ein Kommentar (2001) (0)

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What Are Philip J. Davis's Academic Contributions?

Philip J. Davis is most known for their academic work in the field of mathematics. They are also known for their academic work in the fields of

Philip J. Davis has made the following academic contributions:

The Mathematical Experience

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