# Philip J. Davis

American mathematician

## Philip J. Davis's AcademicInfluence.com Rankings

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Mathematics

## Philip J. Davis's Degrees

- Bachelors Mathematics University of Maryland, College Park

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## Why Is Philip J. Davis Influential?

(Suggest an Edit or Addition)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.

## Philip J. Davis's Published Works

### Published Works

- Methods of Numerical Integration (1985) (2913)
- Introduction to functional analysis (1959) (1482)
- Interpolation and approximation (1965) (1347)
- The Mathematical Experience (1982) (1273)
- The Schwarz function and its applications (1974) (391)
- Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz (1959) (221)
- Descartes' Dream: The World According to Mathematics (1986) (187)
- A generalization of the Bernstein polynomials (1999) (150)
- Chapter 6 – Automatic Integration (1984) (103)
- The convexity of Bernstein polynomials over triangles (1984) (103)
- Fidelity in mathematical discourse: is one and one really two? (1972) (95)
- Philosophy of Science: The Link Between Science and Philosophy (1957) (89)
- 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)
- What Is Mathematical Intuition (2006) (62)
- A Construction of Nonnegative Approximate Quadratures (1967) (62)
- Applied Mathematics as Social Contract (1987) (55)
- Triangle formulas in the complex plane (1964) (51)
- Spirals: From Theodorus to Chaos (1993) (47)
- On the estimation of quadrature errors for analytic functions (1954) (43)
- Visual theorems (1993) (41)
- Advances in Orthonormalizing Computation (1961) (38)
- IGNORING THE SINGULARITY IN APPROXIMATE INTEGRATION (1965) (30)
- Plane regions determined by complex moments (1977) (30)
- Additional abscissas and weights for Gaussian quadratures of high order: Values for n=64, 80, and 96 (1958) (30)
- Are There Coincidences in Mathematics (1981) (26)
- Cyclic Transformations of Polygons and the Generalized Inverse (1977) (26)
- Some Monte Carlo experiments in computing multiple integrals (1956) (25)
- THE RISE, FALL, AND POSSIBLE TRANSFIGURATION OF TRIANGLE GEOMETRY: A MINI-HISTORY (1995) (24)
- Entropy and Society: Can the Physical/ Mathematical Notions of Entropy Be Usefully Imported into the Social Sphere? (2011) (21)
- Iterative Processes in Elementary Geometry (1983) (20)
- 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)
- Some geometrical theorems for abscissas and weights of Gauss type (1961) (19)
- A Multiple Purpose Orthonormalizing Code and its Uses (1954) (19)
- On the analytic continuation of mapping functions (1958) (17)
- An application of doubly orthogonal functions to a problem of approximation in two regions (1952) (17)
- On the deterministic and stochastic approximation of regions (1977) (15)
- On the Use of Transcendentals for Program Testing (1981) (15)
- Proof, Completeness, Transcendentals, and Sampling (1977) (15)
- The Mathematics of Matrices (1966) (15)
- On a problem in the theory of mechanical quadratures (1955) (14)
- Complete sequences and approximations in normed linear spaces (1957) (14)
- What Do I Know? A Study of Mathematical Self-Awareness (1985) (13)
- Simple quadratures in the complex plane. (1965) (13)
- Cyclic transformations of n-gons and related quadratic forms (1979) (13)
- Mathematics & Common Sense: A Case of Creative Tension (2006) (12)
- UNSPLIT K*'S. (1969) (12)
- The Fourfold Classification in Plato's Philebus (1979) (12)
- A circulant formulation of the Napoleon-Douglas-Neumann theorem (1983) (11)
- Interpolation and orthonormal systems (1952) (11)
- Approximate Integration over Infinite Intervals (1984) (11)
- Mathematical encounters of the second kind (1996) (11)
- Minkowski iteration of sets (1980) (10)
- The Thread: A Mathematical Yarn (1983) (9)
- In Mind of Johnson: A Study of Johnson the Rambler (1989) (9)
- The Geometry of An Art: The History of the Mathematical Theory of Perspective from Alberti to Monge ‐ by Kirsti Andersen (2008) (9)
- The Nature of Proof (1986) (9)
- Double integrals expressed as single integrals or interpolatory functionals (1972) (8)
- Otto Neugebauer: Reminiscences and Appreciation (1994) (8)
- A Brief Look at Mathematics and Theology (2002) (8)
- Bound for the P-Condition Number of Matrices With Positive Roots (1961) (8)
- Nonnegative interpolation formulas for uniformly elliptic equations (1968) (7)
- The Companion Guide to the Mathematical Experience (1995) (7)
- Why Victorian Literature Still Matters (2008) (7)
- Additional simple quadratures in the complex plane (1968) (7)
- The Tree of Mathematics (1958) (6)
- 3.1416 And All That (1969) (6)
- Welcome to the World-Wide Web (1995) (5)
- What is an Abstraction (1985) (5)
- ON SIMPLE QUADRATURES (1953) (5)
- Infinity and the Mind. The Science and Philosophy of the Infinite. By Rudy Rucker (1984) (5)
- Napoleon’s Theorem (1997) (5)
- ON REPRESENTATIONS AND EXTENSIONS OF BOUNDED LINEAR FUNCTIONALS DEFINED ON CLASSES OF ANALYTIC FUNCTIONS (1954) (5)
- ON THE ZEROS OF TOTAL SETS OF POLYNOMIALS (1952) (4)
- Numerical computation of the transfinite diameter of two collinear line segments (1957) (4)
- Chapter 4 – Error Analysis (1984) (4)
- The Schwarz Function and Its Applications: Properties in the Large of the Schwarz Function (1974) (4)
- On the Applicability of Linear Differential Operators of Infinite Order to Functions of Class L 2 (B) (1952) (4)
- On the Selection of Test Data for Recursive Mathematical Subroutines (1981) (4)
- Unity and Disunity and Other Mathematical Essays (2015) (4)
- On an equivalent definition of the transfinite diameter (1952) (4)
- A theorem for kernel functions (1951) (4)
- Thomas Campion: lyrick-doctor in physicke. (1969) (4)
- Fascinating Mathematical People: Interviews and Memoirs (2011) (4)
- Packing inequalities for circles. (1963) (3)
- Linear functionals and analytic continuation problems. (1953) (3)
- The Education of a Mathematician (2000) (3)
- The Companion Guide to the Mathematical Experience, Study Edition (2003) (3)
- The Decline and Resurgence of the Visual in Mathematics (2006) (3)
- The Field of Social Service (2010) (2)
- Abu Rayhan al-Biruni (2011) (2)
- Extraordinarily ordinary: the life of Samuel Johnson (1997) (2)
- The Humanistic Aspects of Mathematics and Their Importance (1990) (2)
- Some SEAC Computations of Subsonic Fluid Flows by Bergman’s Method of Integral Operators (1960) (2)
- Completeness theorems for sets of differential operators (1953) (2)
- Group matrices for the quaternion and generalized dihedral groups (1986) (2)
- Immigration and Americanization: Selected Readings (2017) (2)
- The Prospects for Mathematics in a Multi-Media Civilization (1999) (2)
- What should the public know about mathematics (1993) (2)
- Remembering Philip Rabinowitz (2009) (2)
- Equisum matrices and their permanence (2000) (2)
- Accuracy of Monte Carlo methods in computing finite Markov chains (1960) (2)
- New winds blowing in applied mathematics (2015) (2)
- Complex biorthogonality for certain sets of polynomials (1954) (2)
- Chapter 1: Definitions. (2018) (2)
- The Schwarz Function and Its Applications: What Figure is the Power of a Circle? (1974) (2)
- Naïve Thoughts on the Paradox of Gödel (2001) (1)
- When Mathematics Says No (1986) (1)
- Unity and Disunity in Mathematics (2013) (1)
- On Multivariate Bernstein Polynomials (2020) (1)
- Mathematics, substance and surmise: Views on the meaning and ontology of mathematics (2015) (1)
- A complex Pompeiu problem (1966) (1)
- The mathematics of matrices : a first book of matrix theory and linear algebra (1965) (1)
- Thomas Gray, Philosopher Cat (1988) (1)
- On Ambiguity in Mathematics (2006) (1)
- Mathematics by Fiat (1980) (1)
- Tea at Amalienborg (1995) (1)
- The Search Begins (1995) (1)
- Semi-dense closure of systems of functions (1968) (1)
- The Man on the Moon (1983) (1)
- Fascinating Mathematical People (2011) (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)
- Mickey Flies the Stealth (2003) (1)
- On the nonexistence of simplex integration rules for infinite integrals (1972) (1)
- Varieties of Mathematical Experience (2012) (1)
- What Is Meant by the Word ""Random""? (2006) (1)
- Can the mathematical/physical notions of entropy be usefully imported into the social sphere? (2015) (0)
- BOUNDEDNESS AND ASYMPTOTICS OF A MATRIX ITERATION (2005) (0)
- The Lore of Large Numbers: Formulas for Measurement (1961) (0)
- Mathematics Brings Forth Entities Whose Existence Is Counterintuitive (2006) (0)
- The Schwarz Function and Its Applications: Dictionary of Functional Relationships (1974) (0)
- list of Chauvenet Prize winners (2013) (0)
- Mathematics, politics, and law (2015) (0)
- Derivatives and integrals (2020) (0)
- The Man Who Began His Lectures with “Namely” (1997) (0)
- In Which I Meet Lord Dacre (2011) (0)
- Topics for Expository Research Papers (1995) (0)
- Lecture : Supplies, Demands, and Pseudoflows [sp'''] .. Reduction to Maximum Flow (2016) (0)
- The Paradox of ""Hitting It Big"" (2006) (0)
- Conversation with a Bouillabaisse (1995) (0)
- The Kongekat’s Story (1995) (0)
- The Schwarz Function and the Dirichlet Problem (2014) (0)
- The Xerox PARC map server: an interactive hypermedia map viewer (1995) (0)
- The World According to Network Theory (0)
- Schwarz Functions and Iterations (2014) (0)
- The Logic of Mathematics Can Spawn Monsters (2006) (0)
- When Should One Add Two Numbers (2006) (0)
- Mathematical Products (2018) (0)
- The Robust Way: ‘The Man Said, No’ (2016) (0)
- Instructions Are Received (1995) (0)
- Biographical Memoirs: Gerard Piel (2007) (0)
- How Common Sense Impacts Mathematical Reasoning: Some Very Simple Problems (2006) (0)
- Bridging the Two Cultures: (2021) (0)
- Of Maps and Mathematics (1985) (0)
- Mathematics at the Razor's Edge (2006) (0)
- The Plain Brown Envelope (1995) (0)
- Math Mixes It Up with Baseball (2006) (0)
- The Victorian Bump and Where to Find It (2009) (0)
- What Is Mathematics (2006) (0)
- Charles-Benôit Hase (2016) (0)
- Are People Hard Wired to Do Mathematics (2006) (0)
- Schwarz Functions of Specified Type (2014) (0)
- The Art of Squeezing (1985) (0)
- Mathematics and Common Sense: Relations and Contrasts (2006) (0)
- The Relevance of the Irrelevant Beginning (2014) (0)
- Simplicity, Complexity, Beauty (2006) (0)
- An Application of the Theory of Basic Series to Theorems of Bernstein-Widder Type (1950) (0)
- The Lore of Large Numbers: Preface (1961) (0)
- A Few Thoughts on Mathematics and Theology (2011) (0)
- The mathematical experience / Philip J. Davis, Reuben Hersh (1981) (0)
- Computational Experiences in the Pre-Electronic Days (2015) (0)
- Astrology as Early Applied Mathematics (2006) (0)
- South Africa: the real problem. (1985) (0)
- The Next Step in Maintaining Peacetime Readiness. (2021) (0)
- Poinsot’s Points and Lines (1985) (0)
- More Pressure Is Applied (1995) (0)
- “Mr. Milton, Mr. Bradley—Meet Andrey Andreyevich Markov” (1985) (0)
- Sample Group Activities (1995) (0)
- The Band-Aid Principle (1985) (0)
- Selected Topics in Mathematics (2012) (0)
- Enter David Pingree, My Protagonist (2011) (0)
- The Problem That Saved a Man’s Life (1985) (0)
- Chapter 3 – Approximate Integration over Infinite Intervals (1984) (0)
- Paper Product Loading Aid for a Goodwill Employee (1993) (0)
- The Mathematical Landscape (2012) (0)
- Mathematics Is Not Required. (2003) (0)
- The Collaboration Renewed (1995) (0)
- Lucas Fysst’s Dream: The Wienerbroed and the Cat (1995) (0)
- Thomas Gray in Copenhagen (1995) (0)
- The Fabricated Letters of Antony and Cleopatra (2011) (0)
- Victorian Hard Wiring (2009) (0)
- Chaos Off Camera (1995) (0)
- St. Christopher the Dog-Faced (2011) (0)
- In Principle We Can…: Mathematical Existentialism (2006) (0)
- A Good Bit More Is Revealed (1995) (0)
- Spengler’s mathematics considered and a Phoenix reborn? (2015) (0)
- Thomas Gray Arrives on the Scene (1995) (0)
- The Business of Inequalities (1985) (0)
- Probability and Common Sense: A Second Look (2006) (0)
- What the Victorians Can Still Do For Us (2007) (0)
- The Lore of Large Numbers: Answers to Selected Problems (1961) (0)
- Rules and Their Exceptions (2006) (0)
- Numbers, Point and Counterpoint (1985) (0)
- The two culture controversy: A mathematician’s view a half century later (2015) (0)
- Civics for New Americans (2007) (0)
- You can't be a mensch and not do it... Ein Kommentar (2001) (0)
- Unity in Major Themes: Convergence vs. Arbitrariness in the Development of Mathematics (2012) (0)
- Johnson: Sanity and Syntax (2011) (0)
- Lessons in the Danish Language and Literature (1995) (0)
- The stage set the record straight, kindly but firmly (2007) (0)
- Perhaps YOU Have (1995) (0)
- Diamonds Around Her Neck (1995) (0)
- The Rothschild I Knew (1997) (0)
- Ringing Down the Curtain (2011) (0)
- Additional simple quadratures in the complex plane (1968) (0)
- Approximate Integration in Two or More Dimensions (1984) (0)
- Land Grant Application- Davis, Philip (Fayette) (2017) (0)
- Bona Fides Established (1995) (0)
- The decline, fall, and current resurgence of visual geometry: Mathematics as a multisemiotic enterprise (2015) (0)
- The Lore of Large Numbers: LARGE NUMBERS AT WORK (1961) (0)
- The Mathematical Beauty Contest (1985) (0)
- How Amazing! What a Surprise! (2005) (0)
- Out of what stuff do we make mathematics (2015) (0)
- Inconsistencies and Their Virtues (2006) (0)
- The Abacus and the Slipstick (1985) (0)
- Mickey Flies the Stealth: Mathematics, War and Entertainment (2006) (0)
- Mathematical Evidence: Why Do I Believe a Theorem? (2006) (0)
- The House That Geometry Built (1985) (0)
- From Certainty to Fallibility (2012) (0)
- Siva and Parvati (2011) (0)
- The media and mathematics look at each other (2006) (0)
- Spectral Dialogue in Nyhavn (1995) (0)
- Application to Elementary Fluid Mechanics (2014) (0)
- The Soul of a Canary (1995) (0)
- The Schwarz Function and Differential Geometry (1974) (0)
- Thomas Gray in Copenhagen: In Which The Philosopher Cat Meets The Ghost Of Hans Christian Andersen (2013) (0)
- Welcome to the White House: An Interactive Citizen's Handbook (1995) (0)
- Found on Stroeget (1995) (0)
- Abraham J. Sachs (2011) (0)
- Elementary Geometrical Facts (2014) (0)
- Mathematical Communication, Conceptual Understanding & Students' Attitudes Toward Mathematics (2009) (0)
- REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS (2010) (0)
- The unicorn or mathematical ontology (2015) (0)
- Evidence in mathematics (2015) (0)
- Nineteenth-Century Juliet (1996) (0)
- The Spider and the Fly (1985) (0)
- Perturbation Bounds for Matrix Eigenvalues (Rajendra Bhatia) (1989) (0)
- Opinion: Paraconsistent thoughts about consistency (2002) (0)
- The Lore of Large Numbers: Weights, Measures, and Equivalents (1961) (0)
- The Logical Lie Detector (1985) (0)
- Lecture Series in Differential Equations. Session 8. Numerical Solutions. (1969) (0)
- The Lore of Large Numbers: Some Selected Magnitudes in Science (1961) (0)
- The Lore of Large Numbers: Dedication (1961) (0)
- The Glory of the Realm (1995) (0)
- Additional Simple Quadratures in the Complex Plane. (Short Communication). (1968) (0)
- Ancient Loons: Stories Pingree Told Me (2011) (0)
- The Loons and How I Got to Know Them (2011) (0)
- Part I In the Beginning (2000) (0)
- Bibliographical and Supplementary Notes (2014) (0)
- Linear functional equations and interpolation series (1954) (0)
- Platonism vs. Social Constructivism (2006) (0)
- Chaos and Polygons (1985) (0)
- Knowledge in Numbers (1984) (0)
- Gerald J. Toomer (2011) (0)
- Conjugate Coordinates in the Plane (2014) (0)
- The Lore of Large Numbers: Bibliography (1961) (0)
- The Code of the Primes (1985) (0)
- Why Counting Is Impossible (2006) (0)
- Where Is Mathematical Knowledge Lodged and Where Does It Come From (2006) (0)
- Division in the Cellar (1985) (0)
- Pompeiu’s Magic Seven (1985) (0)
- The Lore of Large Numbers: LARGE NUMBERS AND THEIR ARITHMETIC (1961) (0)
- Quantification in Today's World (2006) (0)
- Postulates—The Bylaws of Mathematics (1985) (0)
- Proof and other Dilemmas: When Is a Problem Solved? (2008) (0)
- A Note to Instructors (1995) (0)
- Explorers of the Nth Dimension (1985) (0)
- Bridging the Two Cultures: Paul Valéry (2011) (0)
- If Mathematics Says ""No"" Does It Really Mean It? (2006) (0)
- Index to the Mathematical Gazette (1975) (0)
- Geometrical Interpretation of the Schwarz Function; Schwarzian Reflection (2014) (0)
- Mathematical Proof and Its Discontents (2006) (0)
- Lunch at Villa Fredenskjold (1995) (0)
- A Walk in the Neighborhood (1985) (0)
- My early experiences with scientific computation (2009) (0)
- Ancient loons : stories David Pingree told me (2012) (0)
- The Magic Mirror (1995) (0)
- Carpenter and the Napoleon Ascription (1997) (0)
- Abu Ma'ashar and the Hurrians (2011) (0)
- The Schwarz Function for an Analytic Arc (2014) (0)
- Henri ’ s Crystal Ball (2008) (0)
- Conformal Maps, Reflections, and their Algebra (2014) (0)
- Overcoming employee campaign obstacles. (1991) (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: