Bibliography of Philip J. Davis

Philip J. Davis is the sole author, except where otherwise indicated.

Posthumous publications are listed separately.


ACM --- Association for Computing Machinery
AMS --- American Mathematical Society
MAA --- Mathematical Association of America.
SIAM --- Society for Industrial and Applied Mathematics


  1. Uniqueness Classes for Sets of Linear Functionals, Ph.D. thesis, Harvard University, 1950.
  2. The Lore of Large Numbers, New York: Random House, 1961. 165 pps.
  3. Interpolation and Approximation, New York: Blaisdell Pub. 1963. xiv+393 pps.
    Reprinted, Dover Publications, 1975.
  4. The Mathematics of Matrices: A First Book of Matrix Theory and Linear Algebra, New York, Blaisdell, 1965, xiii+348 pps.
    Reprinted Malabar, Fla.: R.E. Krieger, 1984.
  5. Numerical Integration, by Philip Davis and Philip Rabinowitz Waltham Mass.: Blaisdell Pub., 1967. ix+230 pps.
  6. 3.1416 and all that by Philip Davis and William G. Chinn. New York: Simon and Schuster, 1969.
    Reprinted Boston: Birkhäuser, 1985.
  7. The Schwarz Function and its Applications, MAA, 1974. xi+228 pps.
  8. Methods of Numerical Integration, by Philip Davis and Philip Rabinowitz. New York: Academic Press, 1975. xii+459 pps.
    Reprinted, Orlando: Academic Press, 1984.
    Reprinted, Mineola, NY: Dover Publications, 2007.
  9. Circulant Matrices, New York: Wiley, 1979. xv+250 pps.
  10. The Thread: A Mathematical Yarn, Boston: Birkhäuser, 1983. 126 pps.
    Second edition: Orlando: Harcourt Brace Jovanovich, 1989. xv+124 pps.
    An excerpt was published in The Two-Year College Mathematics Journal Vol. 14, No. 2 (Mar., 1983), pp. 98-104
  11. The Mathematical Experience,, by Philip Davis and Reuben Hersh. Boston: Birkhäuser, 1981. xix+440 pps.
    Reprinted Boston: Houghton Mifflin, 1998.
    Study edition, updated with epilogues, by Philip Davis, Reuben Hersh and Elena Anne Marchisotto, Birkhäuser 2012.
    American Book Award, 1983.
    (This award is now, retroactively, considered a National Book Award -- the relation between the two awards in the early 1980's was extremely complicated.)

    An excerpt (p. 34-43) was published under the title ``The ideal mathematician'' in New directions in the philosophy of mathematics: An anthology ed. Thomas Tymoczko, Boston: Birkhäuser, 1986 pp. 177-184.
    A Russian translation of this excerpt published in Priroda No. 3, (1997), 126-128.

  12. Descartes' Dream: The World according to Mathematics, by Philip Davis and Reuben Hersh. San Diego: Harcourt Brace Jovanovich: 1986. xvi+321 pps.
    Reprinted Penguin, 1988.
    Reprinted Mineola, NY: Dover Publications, 2006.
  13. No Way: The Nature of the Impossible, edited by David A. Park and Philip J. Davis. New York: W.H. Freeman, 1987. xvi+325 pps.
  14. Thomas Gray: Philosopher Cat, San Diego: Harcourt Brace Jovanovich: 1988.
  15. Thomas Gray in Copenhagen: in which the Philosopher Cat meets the Ghost of Hans Christian Andersen, New York: Copernicus, 1995.
  16. Spirals: From Theodorus to Chaos, Wellesley, Mass.: A.K. Peters, 1993. vii+237 pps.
  17. Mathematical Encounters of the Second Kind, Boston: Birkhäuser, 1997. viii+304 pps.
  18. The Education of a Mathematician, Natick, Mass.: A.K. Peters, 2000. x+353 pps. Full Table of Contents
    An excerpt under the title Top o' the Morning to You, Prof. Synge was published in SIAM News, September 17, 2000.
  19. Mathematics and Common Sense: A Case of Creative Tension, Wellesley, Mass.: A.K. Peters, 2006. xlvi+242 pps.
  20. Ancient Loons: Tales David Pingree Told Me, CRC Press: An AK Peters Title, 2011.
  21. Unity and Disunity and Other Mathematical Essays, AMS: 2015
  22. Mathematics, Substance and Surmise: Views on the Meaning and Ontology of Mathematics edited by Ernest Davis and Philip Davis, Springer, 2015.


Educational supplements

  1. Teacher's manual for Philip J. Davis, The Mathematics of Matrices by Philip Davis and Persis Redgrave. New York: Blaisdell, 1965.
  2. The Companion Guide to The Mathematical Experience, study edition by Philip Davis, Reuben Hersh and Elena Marchisotto. Boston: Birkhäuser, 1995.

Mathematical papers

  1. Consideration of Dynamic Loads on the VerticaI Tail by the Theory of Flat Yawing Maneuvers. John Boshar and Philip Davis, NACA Report 838, 1946.
  2. Upper bound for an integral, (Solution to problem 4198, proposed by C.D. Olds), Philip Davis and A.M. Peiser, The American Mathematical Monthly, Vol. 54, No. 6 (Jun. - Jul., 1947), pp. 351-352
  3. Some theorems for infinite systems of linear equations. J. Indian Math. Soc. (N.S.) Vol. 14, 1950, 139-155.
  4. An Application of the Theory of Basic Series to Theorems of Bernstein-Widder Type. American Journal of Mathematics, Vol. 72, No. 4 (Oct., 1950), pp. 787-791
  5. A Theorem for Kernel Functions. Philip Davis and Henry Pollak Proc. AMS, Vol. 2, No. 5 (Oct., 1951), pp. 686-690
  6. On the Zeros of Total Sets of Polynomials. Philip Davis and Henry Pollak Trans. AMS, Vol. 72, No. 1 (Jan., 1952), pp. 82-103
  7. On an Equivalent Definition of the Transfinite Diameter. Philip Davis and Henry Pollak Proc. AMS, Vol. 3, No. 1 (Feb., 1952), pp. 152-155
  8. An Application of Doubly Orthogonal Functions to a Problem of Approximation in Two Regions. Trans. AMS Vol. 72, No. 1 (Jan., 1952), pp. 104-137
  9. On the Applicability of Linear Differential Operators of Infinite Order to Functions of Class L2(B). American Journal of Mathematics, Vol. 74, No. 2 (Apr., 1952), pp. 475-491
  10. Interpolation and orthonormal systems. J. Walsh and Philip Davis. Journal d'Analyse Mathématique,, Vol. 2, 1952, 1-28.
  11. On Simple Quadratures. Proc. AMS, Vol. 4, No. 1 (Feb., 1953), pp. 127-136
  12. Linear functionals and analytic continuation problems. Philip Davis and Henry Pollak, Pacific J. Math. Volume 3, Number 1 (1953), 47-72.
  13. Completeness theorems for sets of differential operators. Duke Math. J. Volume 20, Number 3 (1953), 345-357.
  14. Errors of numerical approximation for analytic functions. J. Rational Mechanics and Analysis, Vol. 2 (1953) 303-313.
  15. On Representations and Extensions of Bounded Linear Functionals Defined on Classes of Analytic Functions. Philip Davis and J. L. Walsh. Trans. AMS, Vol. 76, No. 2 (Mar., 1954), pp. 190-206
  16. Complex biorthogonality for certain sets of polynomials. Philip Davis and Henry Pollak Duke Math. J. Volume 21, Number 4 (1954), 653-667.
  17. Linear functional equations and interpolation series. Pacific J. Math. Volume 4, Number 4 (1954), 503-532.
  18. A Multiple Purpose Orthonormalizing Code and its Uses. Philip Davis and Philip Rabinowitz. 1954. J. ACM Vol. 1, No. 4 (October 1954),
  19. On a problem in the theory of mechanical quadratures, Pacific J. Math., Vol. 1, Suppl. 1 (1955) 669-674. 
  20. Complete sequences and approximations in normed linear spaces. Philip Davis and Ky Fan, Duke Mathematical Journal, Vol. 24, No. 2 (1957) 183-192.
  21. Numerical computation of the transfinite diameter of two collinear line segments. J. Research National Bureau of Standards, Vol. 58 (1957), 155-156.
  22. On the Analytic Continuation of Mapping Functions. Philip Davis and Henry Pollak. Trans. AMS, Vol. 87, No. 1 (Jan., 1958), pp. 198-225
  23. On the numerical integration of periodic analytic functions. In On numerical approximation: Proceedings of a Symposium, Madison, April 21-23, 1958. ed. R.E. Langer. U. Wisconsin Press, 1959, 45-59.
  24. Some SEAC Computations of Subsonic Fluid Flows by Bergman's Method of Integral Operators, by Philip Davis and Philip Rabinowitz, in: Bergman's Linear Integral Operator Method in theTheory of Compressible Fluid Flow. by M.Z. v. Krzywoblocki, Springer-Verlag, Wien, 1960, Appendix.
  25. Advances in orthonormalizing computation, by Philip Rabinowitz and Philip J. Davis, Advances in Computers, Vol. 2 New York:Academic Press (1961) 55-133
  26. Bound for the P-condition number of matrices with positive roots, by Philip J. Davis, Emilie Haynsworth, and Marvin Marcus. J. Research National Bureau of Standards Sect. B, Vol. 65B (1961) 13-14.
  27. Orthonormalizing codes in numerical analysis. In Survey of numerical analysis, ed. John Todd, New York: McGraw-Hill 1962, 347-379.
  28. Errors of numerical approximation for analytic functions. Survey of numerical analysis, ed. John Todd, New York: McGraw-Hill 1962, 468-484.
  29. Packing inequalities for circles. Michigan Math. J., Vol. 19, Iss. 1 (1963), 25-31.
  30. The Gamma Function and Related Functions. In The Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, ed. Milton Abramowitz and Irene A. Stegun (the big red book), NBS Applied Mathematics Series 55, National Bureau of Standards, Washington DC, 1964.
  31. Numerical Interpolation, Differentiation, and Integration, Philip J. Davis and Ivan Polonsky, The Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, ed. Milton Abramowitz and Irene A. Stegun, 1964.
  32. Triangle Formulas in the Complex Plane. Mathematics of Computation, Vol. 18, No. 88 (Oct., 1964), pp. 569-577
  33. Ignoring the Singularity in Approximate Integration. Philip J. Davis and Philip Rabinowitz J. SIAM, Series B, Numerical Analysis Vol. 2, No. 3 (1965), pp. 367-383
  34. Simple Quadratures in the Complex Plane, Pacific J. Math., Vol. 15, No. 3 (1965) 813-824.
  35. A Complex Pompeiu Problem Richard DeMar and Philip Davis Duke Mathematical Journal, Vol. 33, No. 1, (1966) 91-101.
  36. A Construction of Nonnegative Approximate Quadratures. Mathematics of Computation, Vol. 21, No. 100 (Oct., 1967), pp. 578-582
  37. Semi-dense closure of systems of functions. Duke Mathematical J., Vol. 35, (1968) 91-101.
  38. Additional simple quadratures in the complex plane. Aequationes Math. Vol. 3, 1969, 149-155.
    Abstract in Aequationes Math. Vol. 1, No. 3, 1968, 312.
  39. Double integrals expressed as single integrals or interpolatory functionals. J. Approximation Theory, Vol. 5 (1972), 276-307.
  40. Cyclic transformations of polygons and the generalized inverse. Canadian Journal of Math., Vol. 29 (1977), 756-770.
  41. Proof, completeness, transcendentals, and sampling. J. ACM, Vol. 24, no. 2, (1977) 298-310.
  42. Plane regions determined by complex moments. J. Approximation Theory, Vol. 19, no. 2 (1977), 148-153.
  43. Centralizers and circulants. Division of Applied Mathematics, Providence, RI 1978.
  44. Cyclic transformations of n-gons and related quadratic forms, Linear Algebra Appl., Vol. 25 (1979) 57-75.
  45. Minkowski iteration of sets, by Igor Najfeld, Richard Vitale, and Philip Davis, Linear Algebra Appl., Vol. 29 (1980) 259-291.
  46. On the selection of test data for recursive mathematical subroutines, by John H. Rowland and Philip J. Davis, SIAM J. Computing, Vol. 10 no. 1, 1981, 59-72.
  47. On the use of transcendentals for program testing, by John H. Rowland and Philip J. Davis, J. ACM Vol. 28, No. 1 (1981) 181-190.
  48. Iterative Processes in Elementary Geometry, Geng-Zhe Chang and Philip J. Davis, The American Mathematical Monthly, Vol. 90, No. 7 (Aug. - Sep., 1983), pp. 421
  49. A circulant formulation of the Napoleon-Douglas-Neumann theorem, by Gang-Zhe Chang and Philip J. Davis, Linear Algebra Appl. Vol. 54, (1983) 87-95.
  50. The convexity of Bernstein polynomials over triangles. by Gang-Zhe Chang and Philip J. Davis, J. Approximation Theory, Vol. 40 No. 1 (1984) 11-28.
  51. Group matrices for the quaternion and generalized dihedral groups, by K. Wang and Philip J. Davis. Computers and Mathematics with Applications. Part B Vol. 12, No. 5-6, (1986) pp. 1297-1301.
  52. Equisum matrices and their permanence, by Philip J. Davis and Igor Najfeld, Quart. Appl. Math. Vol. 58, no. 1 (2000) 151-69.


  1. Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz. The American Mathematical Monthly, Vol. 66, No. 10 (Dec., 1959), pp. 849-869.
    Reprinted in The Genius of Euler: Reflection on his life and work, ed. William Dunham, 2007.
    MAA Chauvenet Prize, 1963.
  2. The Criterion Makers: Mathematics and Social Policy. American Scientist 50:254A, 1962.
  3. The Lonesome Pine Foundation. Harper's Magazine. August 1964.
  4. Number. Scientific American Vol. 211 (September 1964), 50-59.
  5. Approximation theory in the first two decades of electronic computers. Approximation of Functions (Proc. Sympos. General Motors Research Lab. 1964) Amsterdam: Elsevier, 1965, 152-163.
  6. Numerical analysis. In The Mathematical Sciences: A Collection of Essays, ed. George A.W. Boehm, 1969.
  7. The Makefile 7 Pensees: Religious Thoughts Aroused by an Encounter with an Automatic Typist., Brown Alumni Monthly, October, 1972.
  8. Left Lib, Right Lib. The National Review. January 5, 1973. Vol. 25 No. 1, pp 32,45.
  9. Fidelity in mathematical discourse: Is one and one really two? American Mathematical Monthly, Vol. 79 (1972) 252-263. Reprinted in New directions in the philosophy of mathematics: An anthology ed. Thomas Tymoczko, Boston:Birkhäuser, 1986 pp. 163-175.
  10. Visual geometry, computer graphics, and theorems of perceived type, Proceedings of Symposia in Applied Mathematics, 20, 1974, 113-127,
  11. Nonanalytic Aspects of Mathematics and Their Implication for Research and Education, Philip J. Davis and James A. Anderson, SIAM Review, Vol. 21, No. 1 (Jan., 1979), pp. 112-127
  12. Mathematics by Fiat? The Two-Year College Mathematics Journal, Vol. 11, No. 4 (Sep., 1980), pp. 255-263
  13. Are There Coincidences in Mathematics? The American Mathematical Monthly, Vol. 88, No. 5 (May, 1981), pp. 311-320
    AMS Lester Ford Prize, 1983
  14. Toward a Philosophy of Computation, For the Learning of Mathematics Vol. 3, No. 1 (Jul., 1982), pp. 2-5
  15. Of Time and Mathematics, Franklin Lecture, Auburn University, Southern Humanities Review, vol. 18, (1983) 193-202.
  16. Metrics:Kilometers To Go Before It Sleeps, Mechanical Engineering vol. 105, August 1983, p. 27.
  17. What Do I Know? A Study of Mathematical Self-Awareness. The College Mathematics Journal, Vol. 16, No. 1 (Jan., 1985), pp. 22-41
  18. Reflections on Writing the History of Mathematics. Introduction to Mathematical People, ed. D.J. Albers and G.L. Alexanderson, Birkhäuser, 1985.
  19. When Mathematics Says No. Mathematics Magazine, Vol. 59, No. 2 (Apr., 1986), pp. 67-76. Reprinted in No Way.
  20. Rhetoric and Mathematics, by Philip Davis and Reuben Hersh, in The Rhetoric of the Human Sciences ed. Nelson, Megill, and McCloskey, U. Wisconsin Press, 1987, pp. 53-68
  21. Commentary: The Tower of Mathematical Babel, SIAM News, November 1987 (20:6)
  22. Commentary: The State and Dreams of Numerical Analysis (With Some Recollections of Rods and Bones), SIAM News, May 1988 (21:3)
  23. Article: Birthday Thoughts: AMS's One Hundredth, SIAM News, (21:5)
  24. Commentary: Shall We Raise Native Mathematicians in a Fish Pond? SIAM News, November 1988 (21:6)
  25. Applied Mathematics as Social Contract Mathematics Magazine, Vol. 61, No. 3 (Jun., 1988), pp. 139-147.
    Bulgarian translation published in Fiz.-Mat. Spis. Bulgar. Akad. Nauk. Vol. 32(65) No. 4 (1990), 297-306.
  26. Commentary: CAGD Is This Stuff Really Geometry? SIAM News, January 1990 (23:1)
  27. Commentary: What Are Mathematical Colloquia For? SIAM News, March 1990 (23/2)
  28. Article: Kikiri ki! Let's hear it for Dagstuhl! SIAM News, May 1992 (25:3)
  29. Article: Confessions of a Calculus Cop out, SIAM News, September 1992 (25:5)
  30. Commentary: American Colleges: Basket Cases or Examples of National Style? SIAM News, March 1993 (26:2)
  31. Commentary: Mathematics and the Media, with Bernhelm Booss Bavnbek, SIAM News, May 1993 (26:3)
  32. What Should the Public Know about Mathematics? Daedalus, Vol. 121, No. 1, A New Era in Computation ed. N. Metropolis and Gian-Carlo Rota, (Winter, 1992), pp. 131-138.
    Published MIT Press, 1993.
  33. Visual Theorems. Educational Studies in Mathematics, Vol. 24, No. 4, Aspects of Proof (1993), pp. 333-344
  34. Humanistic Aspects of Mathematics and their Importance. In Essays in Humanistic Mathematics, ed. Alvin M. White, 1993, 9-10.
  35. Thirty Years after the Two Culture Controversy: A Mathematician's View. In Essays in Humanistic Mathematics, ed. Alvin M. White, 1993, 79-90.
  36. Commentary: Variety in a Mathematical Career: From Manifolds to Management, SIAM News, November 1993 (26:7)
  37. Mathematics and Art: Cold Calipers against Warm Flesh? In Mathematics, Education, and Philosophy, ed. Paul Ernest, 1994, pp. 165-183.
  38. Otto Neugebauer: Reminiscences and Appreciation. The American Mathematical Monthly, Vol. 101, No. 2 (Feb., 1994), pp. 129-131
  39. Article: The Courts Count: Mathematics and the Law, SIAM News, April 1994 (27:4)
  40. The Prenatal Days of SIAM: Reminiscence and Tribute to I.E. Block, SIAM NEWS Aug/Sept 1994, Vol 27 No 7
  41. The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-History. The American Mathematical Monthly, Vol. 102, No. 3 (Mar., 1995), pp. 204-214
  42. Commentary: Entertainment: New Engine of Technological Progress? SIAM News, October 1995 (28:8)
  43. Mathematics and common sense: What is their relationship? SIAM News Letters, Vol. 28, No. 9, (1995) p. 7
    Translation in Czech published in Pokroky Mat. Fyz. Astronom. Vol. 41, No. 5, (1996) 253-256.
  44. Article: Numerical Life at the Dawn of the Digital Computer Era, SIAM News, April 1996 (29:3)
  45. Big Questions---Big Principles---Big Fiction? A discussion of the type of books that focused on BIG topics, SIAM News, December 1996 (29:10)
  46. Commentary: Voices from Vienna, SIAM News, May 1997 (30:4)
  47. Commentary: Reviewing the Review Situation: There Ought To Be a Better Way, SIAM News, June 1997 (30:5)
  48. The Prospects for Mathematics in a Multi-Media Civilization, Urania Thater, Berlin, August 21, 1998.
    Humanistic Mathematics Network Journal Vol. 19. 1999, 20-28.
    Reprinted in The Best Writings on Mathematics, 2013 ed. Mercea Pitici, Roger Penrose, pp. 1-22.
    German translation: Ein Blick in die Zukunft: Mathematik in einer Multimedia-Zivilisation. Alles Mathematik, 285-293, Vieweg, Braunschweig, 2000.
  49. The Paradox of "Hitting It Big" SIAM News, January 8, 1998
  50. Snapshots of a Lively Character: Mary Lucy Cartwright, 1900-1998 SIAM News, July 15, 1998
  51. Richard Hamming: An Outspoken Techno-Realist SIAM News, November 16, 1998
  52. Impressions of the International Congress of Mathematicians SIAM News, October 15, 1998
  53. What's in It for Women? What's in Them for Math? SIAM News, November 1, 1999
  54. Connections, Connections, Connections SIAM News, December 7, 1999
  55. Etz Hayyim, Chania, Crete, Greece. Jewish Spectator, Winter, 2000 21-22.
  56. Numerical Life at the Dawn of the Digital Computer Era SIAM News, April 1996. Reprinted SIAM News, March 16, 2000
  57. One Million Bucks for a 100% Solution SIAM News, October 21, 2000
  58. Count, Recount, and Fuzzy Math , SIAM News, January 9, 2001.
  59. Naive Thoughts on the Paradox of Gödel. Humanistic Mathematics Network Journal, May 2001, 11-20. Österreichisches Symposion zur Geschichte der Mathematik, 2004, 94-103.
  60. Congrats, Jack! Reminiscences and Appreciation [On John Todd's 80th birthday] SIAM News, July 10, 2001.
  61. Paraconsistent thoughts about consistency The Mathematical Intelligencer, Vol. 24, No. 4, (2002) 3-5.
  62. Mathematics Is Not Required. For the Learning of Mathematics, Vol. 23, No. 1 (Mar., 2003), pp. 41-42
  63. Mathematics and Hocus Pocus. SIAM News, January 30, 2003
  64. SIAM Conference on CS&E: John von Neumann at 100: SIAM Celebrates a Rich Legacy. May 30, 2003.
  65. A Letter to Christina of Denmark, Newsletter of the European Mathematical Society, March 2004, 21-24.
  66. Mathematics is a multisemiotic enterprise. Österreichisches Symposion zur Geschichte der Mathematik, 2004, 88-103.
  67. A Brief Look at Mathematics and Theology, The Humanistic Mathematics Network Journal Online, vol. 27, 2004.
  68. Happy 80th, Ulf! SIAM News, September 26, 2004
  69. Mathematical Exhibitions: Reactions and Concerns. SIAM News, December 1, 2005
  70. How I Established the Museum of Philosophy. In Educational Transformations: Changing our Lives through Mathematics. A Tribute to Stephen Ira Brown, ed. Frances Rosamond and Larry Copes, 2006, 524-528.
  71. Representing George W. Mackey (1916-2006). SIAM News, September 24, 2006
  72. The Media and Mathematics Look at Each Other. Notices of the AMS, March 2006.
    Reprinted in Mathematisation and Demathematisation: Social, Philosophical, and Educational Ramifications. ed. Uwe Gellert and Eva Jablonka. 2007. pp 187-196.
    Österreichisches Symposion zur Geschichte der Mathematik, 2006, 122-128.
  73. Crossword Puzzles Under Evolutionary Stress. SIAM News, August 7, 2007
  74. Otto Neugebauer raps my knuckles, The Mathematical Intelligencer, Vol. 29 No. 2 (2007) 16-17.
  75. Remembering Philip Rabinowitz. Philip J. Davis and Aviezri Fraenkel, Notices of the AMS, Vol. 54 No. 11 (2007) 1502-1506.
    Reprinted in The Birth of Numerical Analysis, ed. Adhemar Bultheel and Ronald Cools, Hackensack, NJ: World Scientific, 2010, 179-186.
  76. Remembering John Todd, SIAM News, December 17, 2007.
  77. Oswald Spengler's Mathematics Considered and a Phoenix Reborn. Newsletter of the European Mathematical Society, March 2008, 19-27.
  78. Will a Kiss Remain a Kiss? SIAM News, April 12, 2008
  79. Jurimath: The Flowering of an Ancient Field. SIAM News, May 18, 2008.
  80. Updating "Abramowitz and Stegun". SIAM News, September 24, 2008
  81. Why I am a (Moderate) Social Constructivist. (Part of the article ``On Platonism'' by David Mumford and Philip Davis.) Newsletter of the European Mathematical Society, Vol. 70, December 2008.
  82. When is a problem solved? In Proof and other dilemmas: Mathematics and Philosophy ed. Bonnie Gold and Roger Simons, Washington D.C.: MAA 2008.
  83. Henri's crystal ball. Philip J. Davis and David Mumford. Notices AMS, Vol. 55, No. 4, (2008) 458-466.
    Translated into Chinese in Collection of Mathematical Translations, vol. 1, 2009, 84-94.
  84. My early experiences with scientific computation. In The Birth of Numerical Analysis, ed. Adhemar Bultheel and Ronald Cools, Hackensack, NJ: World Scientific, 2010, 187-192.
  85. Bridging the Two Cultures: Paul Valéry and His Mathematics, Svenska Matematikersamfundet Medlemsutskicket, 15 May, 2009.
    Reprinted in: The Best Writing on Mathematics 2010, ed. Mircea Pitici, 2010.
  86. Mathematical rejections. European Mathematical Society Newsletter, No. 75, March, 2010. 27-29.
  87. Entropy and Society: Can the Physical/Mathematical Notions of Entropy be Usefully Imported into the Social Sphere? Journal of Humanistic Mathematics, Vol. 1 No. 1, 2011.
  88. Foreword to Fascinating Mathematical People ed. Donald Albers and Gerald Alexanderson, 2011.
  89. Unity and Disunity in Mathematics, by Bernhelm Booss-Bavnbek and Philip J. Davis, Newsletter of the European Mathematical Sociey No. 87, March 2013.
  90. Unity in Major Themes-- Convergence vs. Arbitrariness in the Development of Mathematics, by Bernhelm Booss-Bavnbek and Philip J. Davis, XI Osterreichisches Symposion zur Geschichte der Mathematik, April 2012
  91. The relevance of the irrelevant beginning, ScienceOpen Research, 2014.
  92. Mathematical Products. In Mathematics, Substance and Surmise. 2015. Reprinted in The Best Writing on Mathematics, 2017, ed. Mircea Pitici, Princeton University Press, 2018,

Book reviews

  1. Review of Differential operators and differential equations of infinite order with constant coefficients. Researches in connection with integral functions of finite order, by P. C. Sikkema, Bull. AMS Volume 60, Number 6 (1954), 586.
  2. Review of Numerical Analysis by K.S. Kunz, Bull. AMS Vol. 64 No. 3, Part I (1958) 112-113.
  3. Review of Numerical Analysis by D. R. Hartree, The American Mathematical Monthly, Vol. 66, No. 7 (Aug. - Sep., 1959), pp. 600-601
  4. Review of Numerical Methods for Scientists and Engineers, by R. W. Hamming, The American Mathematical Monthly, Vol. 70, No. 2 (Feb., 1963), p. 229
  5. Recent Publications: Numerical Methods for Scientists and Engineers American Mathematical Monthly, Vol. 70 No. 2 (1963) 229.
  6. Review of Elements of the Theory of Functions, by R. S. Guter et al., Mathematics of Computation, Vol. 22, No. 101 (Jan., 1968), pp. 212-213
  7. Review of Infinity and the Mind. The Science and Philosophy of the Infinite, by Rudy Rucker, The American Mathematical Monthly Vol. 91, No. 2 (Feb., 1984), p. 152
  8. Review of The Paradoxicon, by Nicholas Falletta, American Scientist, Vol. 72, No. 5 (September-October 1984), p. 524
  9. Handling the Information Onslaught, Review of Science, Computers, and the Information Onslaught---A Collection of Essays edited by Donald M. Derr, et al., SIAM News, November 1985 (18:6)
  10. Review of Mathematics: People, Problems, Results, by Douglas M. Campbell and John C. Higgins. The College Mathematics Journal, Vol. 17, No. 1 (Jan., 1986), pp. 108-109
  11. Review of Black Mischief: The Mechanics of Modern Science, by David Berlinski, SIAM News, November 1986 (19:6)
  12. Giving Sophie a Grade, Review of A Convergence of Lives, by Anne Hibner Koblitz, SIAM News, January 1987 (20:1)
  13. Review of An Atlas of Function, by Jerome Spanier and Keith B. Oldham, SIAM News, May 1987 (20:3)
  14. The Imagination That Burned, Review of Science, Computers and People from the Tree of Mathematics, by Stanislaw Ulam, edited by Mark Reynolds and Gian-Carlo Rota, SIAM News, September 1987 (20:5)
  15. What Is a Successful Predictor? Review of Datawars: The Politics of Modeling in Federal Policymaking by K.L. Kraemer et al., SIAM News, January 1988 (21:1)
  16. Is the Road to Geometry Paved with Polyhedra? Review of Shaping Space: A Polyhedral Approach, edited by Marjorie Senechal and George Fleck, SIAM News, July 1988 (21:4)
  17. Review of Perturbation Bounds for Matrix Eigenvalues, by Rajendra Bhatia, SIAM Review, Vol. 31, No. 1 (Mar., 1989), p. 133
  18. Math and Society: From Tare and Tret to Plastic Money. Review of Capitalism and Arithmetic: The new Math of the Fifteenth Century, by Frank J. Swetz, SIAM News, January 1989 (22:1)
  19. Profscam: The Golden Fleece, Recombed. Review of Profscam: Professors and the Demise of Higher Education by Charles J. Sykes, SIAM News, May 1989 (22:3)
  20. Has NCTM Set the Cart Before the Horse? Standards. Review of Curriculum and Evaluation Standards for School Mathematics, by the National Council of Teachers of Mathematics, SIAM News, September 1989 (22:5)
  21. I've Got a Shoe --- Who's Got a Foot? Applied Mathematics Off the Rack. Review of Symmetries of Culture. Practice of Plane Pattern Analysis by Dorothy K. Washburn and Donald W. Crow, SIAM News, November 1989 (22:6)
  22. Perfect Health for All, Review of What Kind of Life: The Limits of Medical Progressi by Daniel Callahan, SIAM News, May 1990 (23:3)
  23. Inside Roger Penrose, Review of The Emperor's New Mind by Roger Penrose, SIAM News, July 1990 (23/4)
  24. The Mathematization of Reason, review of Classical Probability in the Enlightenment by Lorraine Daston, SIAM News, November 1990 (23:6)
  25. The Crisis in Mathematical Education --- Salvation from Within? Review of On the Shoulders of Giants: New Approaches to Numeracy edited by Lynn Arthur Steen, SIAM News, January 1991 (24:1)
  26. Adjective Into Man: The Case of Joseph Liouville, Review of Joseph Liouville 1809-1882: Master of Pure and Applied Mathematics, by Jesper Lützen, SIAM News, March 1991 (24:2)
  27. Between Hope and Accomplishment, Review of Searching for Certainty: What Scientists Can Know About the Future by John L. Casti, SIAM News, May 1991 (24:3)
  28. Mathematics and Economic Competitiveness, Review of Mathematical Sciences, Technology, and Economic Competitiveness edited by James G. Glimm, SIAM News, July 1991 (24:4)
  29. The Inside and the Outside, Review of The Philosophy of Mathematics Education by Paul Ernest, SIAM News, September 1991 (24:5)
  30. Mathematics as Grand Opera, Video review of Not Kind edited by Charlie Gunn and Delle Maxwell, SIAM News, November 1991 (24:6)
  31. Ramanujan: Magician or Transcendental Professional? Review of The Man Who Knew Infinity by Robert Kanigel, SIAM News, January 1992 (25:1)
  32. Pushing Toward Multicentrism, review of Ethnomathematics: A Multicultural View of Mathematical Ideas by Marsha Ascher and The Crest of the Peacock: Non-European Roots of Mathematics by George G. Joseph, SIAM News, March 1992 (25:2)
  33. Toward a Softer, Much Less Invasive Technology, Review of Computing: A Human Activity by Peter Naur, SIAM News, July 1992 (25:4)
  34. Compare and Contrast: Sir John Herschel and Freeman Dyson, Review of Infinite in All Directions by Freeman Dyson, SIAM News, January 1993 (26:1)
  35. Passion and Structure, Review of Politics, Logic, and Love: The Life of Jean van Heijenoort by Anita Burdman Feferman, SIAM News, May 1993 (26:3)
  36. Applied Mathematician in the White House? Review of Thomas Jefferson: Statesman of Science by Silvio A. Bedini, SIAM News, August 1993 (26:5)
  37. The Sinister Genius of Charles Sanders Peirce, Review of Charles Sanders Peirce: A Life by Joseph Brent, SIAM News, October 1993 (26:6)
  38. Chaos and the New Understanding, Review of In the Wake of Chaos by Stephen H. Kellert, SIAM News, February 1994 (27:2)
  39. Mathematics and Art: The Work of Helaman Ferguson, Review of Helaman Ferguson: Mathematics in Stone and Bronze, photographs of sculpture by Helaman Ferguson and text by Claire Ferguson, SIAM News, May/June 1994 (27:5)
  40. Russell's Real Paradox: The Wise Man Is a Fool, Review of Bertrand Russell: A Life by Caroline Moorhead, SIAM News, July 1994 (27:6)
  41. Mathematics and Gambling, Review of Legalized Gambling as a Strategy for Economic Development by Robert Goodman, SIAM News, October 1994 (27:8)
  42. The Economist as Bankrupt, Review of Irving Fisher: A Biography by Robert Loring Allen, SIAM News, November 1994 (27:9)
  43. What Is the Law and Who Profits? Review of Who Owns Information? From Privacy to Public Access by Anne Wells Branscomb, SIAM News, December 1994 (27:10)
  44. Modesty Is Not a Virtue: Norbert Wiener, Review of Norbert Wiener: 1894-1964 by Pesi R. Masani and Invention: The Care and Feeding of Ideas by Norbert Wiener (foreword by Steve J. Heims), SIAM News, February 1995 (28:2)
  45. Visual Verses Linguistic/Symbolic Understanding, Review of Invention and Evolution: Design in Nature and Engineering, 2nd edition, by Michael French, SIAM News, March 1995 (28:3)
  46. Crossword Puzzles in an Information Saturated Age, review of The Standard American Heritage Dictionary, 3rd edition, SIAM News, April 1995 (28:4)
  47. What is Rational? What is Human? review of Being Digital by Nicholas Negroponte and Powers of the Rational: Science, Technology and the Future of Thought by Dominique Janicaud, SIAM News, August/September 1995 (28:7)
  48. Paul Feyerabend: Philosopher or Crank? Review of Killing Time: The Autobiography of Paul Feyerabend, SIAM News, December 1995 (28:10)
  49. Newton and the Science of Government, Review of Science and the Founding Fathers: Science in the Political Thought of Jefferson, Franklin, Adams, and Madison by I. Bernard Cohen, SIAM News, January/February 1996 (29:1)
  50. "I'm not a Luddite, but . . ." Review of The Gutenberg Elegies: The Fate of Reading in an Electronic Age by Sven Birkerts, SIAM News, March 1996 (29:2)
  51. Infoglut and Its Discontents, Review of Technopoly: The Surrender of Culture to Technology by Neil Postman, SIAM News, May 1996 (29:4)
  52. The Reluctant Miller's Tale: A Major Mathematical Mystery, Review of George Green: Mathematician and Physicist, 1793-1841: The Background to his Life and Work by D.M. Cannell, SIAM News, July/August 1996 (29:6)
  53. The Little Math That Wouldn't, Review of Math Curse by Jon Scieszka and Lane Smith, SIAM News, September 1996 (29:7)
  54. Weather, War and Mathematics, Review of The Forgiving Air: Understanding Environmental Change by Richard C.J. Somerville, The Collected Papers of Lewis Fry Richardson edited by Oliver M. Ashford et al., and Prophet or Professor? The Life and Work of Lewis Fry Richardson by Oliver M. Ashford, SIAM News, November 1996 (29:9)
  55. Rota's Mathematical World, Review of Indiscrete Thoughts by Gian-Carlo Rota, SIAM News, April 1997 (30:3)
  56. They're Voting with Their Feet, review of Talking About Leaving: Why Undergraduates Leave the Sciences by Elaine Seymour and Nancy M. Hewitt, SIAM News, July/August 1997 (30:6)
  57. The "Here" and the "There" of Mathematics: Kurt Gödel, Review of Logical Dilemmas: The Life and Work of Kurt Gödel by John W. Dawson, Jr., SIAM News, October 1997 (30:8)
  58. Mathematics in an Age of Illiteracy, Review of The Civilization of Illiteracy, Mihai Nadin, SIAM NEWS Vol. 30, No.9, November, 1997.
  59. What's Modern About Mathematics? Review of The First Moderns: Profiles in the Origins of Twentieth-Century Thought by William R. Everdell, SIAM News, December 1997 (30:10)
  60. Deus Ex Hominibus:Science, Theology, and Masculinity. Review of Pythagoras' Trousers: God, Physics, and the Gender Wars by Margaret Wertheim, SIAM News, March 8, 1998
  61. Mickey Flies the Stealth. Review of Modeling and Simulation: Linking Entertainment and Defense. A Report of the National Research Council. SIAM News, April 14, 1998.
    Reprinted in Mathematics and War, ed. Bernhelm Booss-Bavnbek and Jen Hoyrup. Birkhäuser, 2003.
  62. Art Meets Market Research: What's Rembrandt's Rating? Review of Painting By Numbers: Komar and Melamid's Scientific Guide to Art by JoAnn Wypijewski. SIAM News, May 14, 1998
  63. Education for What? A Very Good Question. Review of Education for What? The New Office Economy. By Anthony P. Carnavale and Stephen J. Rose. SIAM News, June 15, 1998
  64. Beyond the Pillars of Hercules: Soft Mathematics. Review of Goodbye Descartes: The End of Logic and the Search for a New Cosmology of the Mind by Keith Devlin. SIAM News, December 16, 1998
  65. Why Does a Public that Hates Numbers Put Up with So Many Numbers? Review of The Measure of Reality: Quantification and Western Society, by Alfred W. Crosby and Trust in Numbers: The Pursuit of Objectivity in Science and Public Life, by Theodore M. Porter. SIAM News, January 22, 1999.
  66. Testing: One, Two, Three; Testing: One, . . . Can You Hear Me Back There? Review of Executive Summary, Third International Mathematics and Science Study (TIMSS). By William Schmidt; A TIMSS Primer: Lessons and Implications for U.S. Education. By Harold W. Stevenson; The Rationality and Irrationality of International Comparative Studies. By Christine Keitel and Jeremy Kilpatrick; and Tinkering with TIMSS. By Gerald W. Bracey, SIAM News, March 22, 1999
  67. Mathematics for Poets: A Poet's Version. Review of Drawbridge Up: Mathematics --- A Cultural Anathema, and The Number Devil: A Mathematical Adventure "Zugbruecke Ausser Betrieb." By Hans Magnus Enzensberger SIAM News, April 22, 1999
  68. The One State and Its Discontents. Review of We by Yevgeny Zamyatin. SIAM News, May 22, 1999
  69. The Unbearable Objectivity of the Positive Integers. Review of 1,000 Years, 1,000 People: Ranking the Men and Women Who Shaped the Millenium, by Agnes Hooper Gottlieb et al. SIAM News, June 23, 1999
  70. From Computer Graphics Toward Computer Art. Review of The Computer in the Visual Arts. by Anne Morgan Spalter; Graphica 1: The Imaginary Made Real: The Art of Michael Trott. The World of Mathematica Graphics. and Graphica 2: The Pattern of Beauty: The Art of Igor Bakshee, The World of Mathematica Graphics. SIAM News, July 23, 1999
  71. The Aesthetic Impulse in Science and Mathematics---Merely a Matter of Words? Review of Beauty and Revolution in Science. By James W. McAllister; and "The Phenomenology of Mathematical Beauty." By Gian-Carlo Rota. SIAM News, October 1, 1999
  72. Is Pi in the Sky? Where Do You Stand on the Question? Review of The Social Construction of What? By Ian Hacking SIAM News, January 14, 2000
  73. Of Making Compilations There Is No End. Review of CRC Concise Encyclopedia of Mathematics. By Eric W. Weisstein SIAM News, March 15, 2000
  74. All---Or Nothing at All. Review of Uncle Petros and Goldbach's Conjecture. By Apostolos Doxiadis. SIAM News, April 16, 2000
  75. Is It Boole that Makes The World Go Round? Review of The Advent of the Algorithm: The Idea that Rules the World by David Berlinski. SIAM News, May 16, 2000
  76. Astrology: Early Applied Mathematics? Review of Cardano's Cosmos: The Worlds and Works of a Renaissance Astrologer... by Anthony Grafton. SIAM News, June 17, 2000
  77. The Sayings of the Fathers---And Several Mothers. Review of Mathematics: Frontiers and Perspectives, ed. V. Arnold et al., SIAM News, July 17, 2000
  78. Embedding Zero in Exposition. Review of The Nothing That Is: A Natural History of Zero. By Robert Kaplan, SIAM News, September 17, 2000
  79. Four Thousand---Or Possibly Thirty-seven Thousand---Years of Mathematics. Review of The Norton History of the Mathematical Sciences: The Rainbow of Mathematics, by Ivor Grattan-Guinness. SIAM News, November 21, 2000
  80. Slash and Dash in Cyberland. Review of Cyberselfish: A Critical Romp Through the Terribly Libertarian Culture of High Tech, by Paulina Borsook, SIAM News, December 21, 2000
  81. Extended Boundaries for Mathematical Language. Review of Language Death, by David Crystal. SIAM News March 9, 2001.
  82. Educational Enthusiasms and Their Critics. Review of Left Back: A Century of Failed School Reforms, by Diane Ravitch. SIAM News, April 9, 2001
  83. Wisdom from Xerox PARC. Review of The Social Life of Information. By John Seely Brown and Paul Duguid. SIAM News, May 9, 2001
  84. While Surfing a Handbook. Handbook of Discrete and Combinatorial Mathematics ed. Kenneth H. Rosen, SIAM News, June 10, 2001
  85. The Power of Numerics , Review of Mathematics Unlimited --- 2001 and Beyond. ed. Bjorn Engquist and Wilfried Schmid. SIAM News, September 10, 2001.
  86. From Spots and Dots to Deep Stuff. Review of The Geometry of Numbers. By C.D. Olds, Anneli Lax, and Giuliana Davidoff. SIAM News, October 13, 2001
  87. The Joy and Suffering of Research. Review of Laurent Schwartz: A Mathematician Grappling with his Century. by Larurent Schwartz, SIAM News, November 13, 2001
  88. Stringing Onward and Upward. Review of The Next 1,000 Years. Communications of the` ACM, March 2001, Vol. 44, No. 1 SIAM News, December 13, 2001
  89. Mathematics and the Modern Mind. Review of The Modern Mind: An Intellectual History of the 20th Century. By Peter Watson. SIAM News, January 2, 2002
  90. Wars Change Lives. Review of Improbable Warriors: Women Scientists and the U.S. Navy in World War II, by Kathleen Broome Williams. SIAM News, March 2, 2002
  91. Playing Ball Probabilistically. Review of Curve Ball: Baseball, Statistics and the Role of Chance in the Game. By Jim Albert and Jay Bennett. SIAM News, April 3, 2002
  92. What Does It Mean to See? Review of Visualizations: The Nature Book of Art and Science, by Martin Kemp. SIAM News, May 3, 2002
  93. Twenty-three Hard Ones. Review of The Honors Class: Hilbert's Problems and their Solvers, by Benjamin H. Yandell, SIAM News, June 3, 2002
  94. What Gerard Piel Knows. Review of The Age of Science: What Scientists Learned in the 20th Century, by Gerard Piel. SIAM News, July 3, 2002
  95. Iteration and its Consequences. Review of Indra's Pearls: The Vision of Felix Klein. By David Mumford, Caroline Series, and David Wright. SIAM News, September 6, 2002
  96. The Philosophical Poker. Review of Wittgenstein's Poker, by David Edmonds and John Eidenow, SIAM News, October 7, 2002
  97. Language, Mathematics, and Ideology. Review of From Newspeak to Cyberspeak: A History of Soviet Cybernetics, by Slava Gerovitch, SIAM News, November 7, 2002
  98. Anecdotes about Anecdotes. Review of Mathematical Apocrypha, by Steven G. Krantz. SIAM News, December 8, 2002.
  99. Is Mathematics a Unified Whole? Review of Mathematics Elsewhere: An Exploration of Ideas Across Cultures. By Marcia Ascher SIAM News, March 30, 2003
  100. Art Out of Bottles? Exploring the Invisible: Art, Science, and the Spiritual. By Lynn Gamwell SIAM News, April 30, 2003
  101. Laugh and Learn with John. Review of 777 Mathematical Conversation Starters. By John dePillis SIAM News, June 30, 2003
  102. A New Look for Historiography. Review of Computers, Visualization, and History: How New Technology Will Transform our Understanding of the Past. By David J. Staley SIAM News, July 31, 2003
  103. Debunking or Telling It as It Was? Review of Einstein's Luck: The Truth Behind Some of the Greatest Scientific Discoveries. By John Waller SIAM News, September 29, 2003
  104. The World According to Network Theory. Review of Linked: The New Science of Networks. By Albert-Laszlo Barabasi. SIAM News, October 31, 2003
  105. The PP Paradigm. The Cognitive Style of PowerPoint. by Edward Tufte. SIAM News, November 1, 2003
  106. Briefly Noted. Reviews of Origami Design Secrets: Mathematical Methods for an Ancient Art, by Robert J. Lang; and Four Colors Suffice: How the Map Problem Was Solved, by Robin Wilson. SIAM News, November 1, 2003
  107. Revealing All? Review of Science, not Art: Ten Scientists' Diaries, ed. Jon Turney. SIAM News, December 1, 2003
  108. History Squared. Review of Writing the History of Mathematics: Its Historical Development, ed. Joseph W. Dauben and Christoph J. Scriba. SIAM News, January 13, 2004.
  109. Bringing the Riemann Zeta Function to the World's Attention. Review of The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics, by Marcus de Sautoy. SIAM News, Volume 37, Number 1, January/February 2004
  110. Biting the Bullet. Mathematics and War, ed. Bernhelm Booss-Bavnbek and Jen Hoyrup. SIAM News, March 24, 2004
  111. Constants in the Universe: Their Validation, Their Compilation, and Their Mystique. Review of The Constants of Nature by John D. Barrow and Mathematical Constants, by Steven R. Finch. SIAM News, April 24, 2004
  112. Knowing vs. Knowing About. Review of Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability, by Peter Pesic. SIAM News, May 25, 2004
  113. Mathematics and Multi-Media Review of porridge, pulleys, and PiDA, Video by G.P. Csicsery; and Fermat's Last Tango, Video of a musical by Joann Sydney Lessner et al. SIAM News, June 25, 2004
  114. The Residue of Failure. Review of The Secrets of the Vaulted Sky: Astrology and the Art of Prediction. By David Berlinski. SIAM News, May 25, 2004
  115. The Language Police Knock on Math's Door. Review of The Language Police: How Pressure Groups Restrict What Students Learn, by Diane Ravitch. SIAM News, July 25, 2004
  116. The Innocent Pleasures of Simple Models. Review of From Mathematics in Nature: Modeling Patterns in the Natural World, by John A. Adam. SIAM News, October 26, 2004
  117. Mumbo Math. How Mumbo-Jumbo Conquered the World: A Short History of Modern Delusions. By Francis Wheen SIAM News, November 26, 2004
  118. Running Counter to Inert Crystallized Opinion. Review of Janos Bolyai, Non-Euclidean Geometry, and the Nature of Space, by Jeremy J. Gray, SIAM News, December 26, 2004.
  119. How Amazing! What A Surprise! Review of Beyond Coincidence. By Martin Plimmer and Brian King. SIAM News, January 28, 2005
  120. A Life of Logic and the Illogic of Life, Review of Alfred Tarski: Life and Logic, by Anita Burdman Fefeman and Solomon Feferman. SIAM News, March 1, 2005.
  121. The Legacy of Social Numbers. Review of Extreme Measures: The Dark Visions and Bright Ideas of Francis Galton, by Martin Brookes. SIAM News, April 1, 2005
  122. The Author and Her Subject: Kathleen Broome Williams on Grace Murray Hopper. Review of Grace Hopper: Admiral of the Cyber Sea, by Kathleen Broome Williams. SIAM News, May 1, 2005
  123. The Inner Turbulence of Genius: Norbert Wiener. Review of Dark Hero of the Information Age: In Search of Norbert Wiener, by Flo Conway and Jim Siegelman. SIAM News, Volume 38, Number 5, June 2005
  124. Dear Matrix Maven. Review of Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory by Dennis S. Bernstein. SIAM News, July 6, 2005
  125. Magisterial Voices of the Past. Review of Musings of the Masters: An Anthology of Mathematical Reflections,, ed. Raymond G. Ayoub. SIAM News, September 26, 2005
  126. Carissimo Papà: A Great Fish Story. Review of The Biology of Numbers: The Correspondence of Vito Volterra on Mathematical Biology ed. Giorgio Israel and Ana Millán Gasca. SIAM News, October 21, 2005
  127. Mister Mathematics: Saunders Mac Lane. Review of Saunders MacLane: A Mathematical Autobiography by Saunders MacLane. SIAM News, November 20, 2005
  128. Omega: Chaitin's Demon. Meta Math!: The Quest for Omega. By Gregory Chaitin. SIAM News, January 14, 2006
  129. To Those Who Have, Shall Be Given. Review of The Economy of Prestige: Prizes, Awards, and the Circulation of Cultural Value, by James F. English. SIAM News, April 12, 2006
  130. The Infrastructure of Mathematics: The Case of William Playfair. Review of The Commercial and Political Atlas and Statistical Breviary: A Facsimile of the Third Edition (1801) by William Playfair, ed. Howard Wainer and Ian Spence. SIAM News, May 15, 2006
  131. A.A. Albert: Chicago Mathematician. Review of A3 & His Algebra: How a Boy from Chicago's West Side Became a Force in American Mathematics. By Nancy E. Albert. SIAM News, Volume 39, Number 5, June 2006
  132. Arithmetic as It Was Taught 175 Years Ago in Providence. Review of Practical and Mental Arithmetic, on a New Plan, in which Mental Arithmetic is Combined with the Use of the Slate, by Roswell C. Smith. SIAM News, July 6, 2006
  133. A Brain on Fire: James Joseph Sylvester. Review of James Joseph Sylvester: Jewish Mathematician in a Victorian... by Karen Hunger Parshall, SIAM News, September 24, 2006
  134. Why Zeus Smoked a Pipe, or The Legitimization of Mathematics. Review of Widmung, Welterkläng und Wissenschaftslegitimisierung: Titelbilder und ihre Funktionen in der Wissenschaftlichen Revolution. [Dedications, Explanations of the World, and the Legitimization of Science: The Function of Title-Page Frontispieces During the Scientific Revolution.] By Volker Remmert, SIAM News, October 21, 2006
  135. Cleaning Up One's Prose. Review of Nonsense: A Handbook of Logical Fallacies, Revised Edition, by Robert J. Gula. SIAM News November 19, 2006.
  136. What Went On in Austria That Week: Gödel, Mozart, Bachmann. Review of Kurt Gödel: The Album by Karl Sigmund, John Dawson, and Kurt Mühlberger. SIAM News, December 22, 2006
  137. Departed Glories: Bourbaki. Review of The Artist and the Mathematician: The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Existed. By Amir D. Aczel, SIAM News, January 12, 2007
  138. The Triumphal March of the FFT (And the Ambiguities of Comprehension). Review of The Evolution of Applied Harmonic Analysis: Models of the Real World, by Elena Prestini. SIAM News, March 13, 2007
  139. A Tale of Three Cities, Two Academies, and an Opera Omnia in 76 Volumes (and Counting). Leonhard Euler. by Emil A. Fellmann. SIAM News, May 1, 2007
  140. From Fermat to Lenny Bernstein and Beyond. Review of The Best of All Possible Worlds: Mathematics and Destiny, by Ivar Ekeland. SIAM News, June 12, 2007
  141. The Rehabilitation of Olinde Rodrigues. Review of Mathematics and Social Utopias in France: Olinde Rodrigues and His Times, ed. Simon Altmann and Eduardo L. Ortiz. SIAM News, September 24, 2007.
  142. Codes of Ethics and Their Limitations. Review of Computer Ethics: A Global Perspective, by Giannis Stamatellos. SIAM News, November 19, 2007
  143. Charles Richter, His Scales, and More Scales. Review of Richter's Scale: Measure of an Earthquake, Measure of a Man, by Susan Hough. SIAM News, December 17, 2007
  144. The Z of ZF and ZFC and ZF---C. Review of Ernst Zermelo: An Approach to His Life and Work. By Heinz-Dieter Ebbinghaus. SIAM News, January 6, 2008
  145. The Ubiquitous and Seductive J Curve, Review of The J Curve: A New Way to Understand Why Nations Rise and Fall, by Ian Bremmer. SIAM News, March 14, 2008.
  146. Things Are Changing in the World of Mathematics. Review of Traumjob Mathematik! Berufswege von Frauen und Männern in der Mathematik (Dream Jobs in Mathematics! Employment Possibilities for Women and Men). By Andrea E. Abele, Helmut Neunzert, and Renata Tobies. SIAM News, June 11, 2008
  147. The Early Background of Genius. Review of Wer Ist Alexander Grothendieck? Anarchie, Mathematik, Spiritualität Teil I: Anarchie. By Winfried Scharlau. SIAM News, July 10, 2008
  148. Selecting Our Leaders. Review of Mathematics and Democracy: Designing Better Voting and Fair-Division Procedure by Steven J. Brams. SIAM News, October 21, 2008
  149. Salvation through Genomics. Review of A Life Decoded: My Life by J. Craig Ventner SIAM News, November 16, 2008.
  150. Spanning Multiple Worlds. Review of Mathematics as Metaphor: Selected Essays. By Yuri I. Manin. SIAM News, December 21, 2008
  151. Why Didn't They . . . ? Review of The Man who Loved China, by Simon Winchester. SIAM News, January 10, 2009
  152. New Winds in Applied Mathematics: The Road to Numerocracy, Review of The Numerati, by Stephen Baker, SIAM News, March 21, 2009.
  153. Plagued by Plagiarism. Review of Combating Student Plagiarism: An Academic Librarian's Guide. By Lynn D. Lampert. SIAM News, April 13, 2009
  154. Surfing Ancient Mathematics, Review of The Mathematics of Egypt, Mesopotamia, China, India, and Islam, ed. Victor Katz. SIAM News, May 18, 2009
  155. The Consummate Gamesman: John von Neumann, Review of The World as a Mathematical Game: John von Neumann and Twentieth Century Science, by Giorgio Israel and Ana Millan Gasca, SIAM News, June 15, 2009.
  156. Mathematical Cultures and Their Adherents. Review of ``The Two Cultures of Mathematics in Ancient Greece,'' by Markus Asper, in The Oxford Handbook of the History of Mathematics,, ed. Eleanor Robson and Jacqueline Stedall. SIAM News, August 1, 2009
  157. The Beauties of Mathematics Explained. Review of The Housekeeper and the Professor, by Yoko Ogawa, SIAM News, September 21, 2009.
  158. Statistics: Love 'em or Leave 'em. Review of Picturing the Uncertain World: How to Understand, Communicate, and Control Uncertainty through Graphical Display by Howard Wainer. SIAM News, September 21, 2009
  159. Expositions: Their Contents and Discontents. Review of Who Gave you the Epsilon? & Other Tales of Mathematical History. ed. Marlow Anderson, Victor Katz and Robin Wilson. SIAM News, October 18, 2009.
  160. The Limits of Analysis: Ornamentation. Review of Sipatsi: Basketry and Geometry in the Tonga Culture of Inhambane and Sipatsi Images in Colour, by Paulus Gerdes SIAM News, November 14, 2009
  161. Confronting Mathematicians. Review of Mathematicians: An Outer View of an Inner World by Mariana Cook SIAM News, December 4, 2009
  162. Who Gets the Goodies (And How the Pie is Divided), Review of How Professors Think: Inside the Curious World of Academic Judgment, by Michele Lamont. SIAM News, January 9, 2010.
  163. Our Mathematical Debt to Europe. Review of Mathematicians Fleeing from Nazi Germany: Individual Fates and Global Impact, by Reinhard Siegmund-Schultze, SIAM News, March 1, 2010.
  164. Paul Dirac: The Laconic Genius of Quantum Theory. Review of The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom, by Graham Farmelo. SIAM News, April 1, 2010
  165. The Sources of Confidence. Review of Imperfect Oracle: The Epistemic and Moral Authority of Science. By Theodore L. Brown. SIAM News, May 17, 2010
  166. Numbers: Their Genealogies, Personalities, and Functions. Numerical Notation. By Stephen Chrisomalis. SIAM News, June 22, 2010
  167. History of Science --- Lite. Review of Science: A Four Thousand Year History by Patricia Fara. SIAM News, July 23, 2010.
  168. Formulas Galore. Review of NIST Handbook of Mathematical Functions. Edited by Frank W.J. Olver. SIAM News, Volume 43, Number 7, September 2010
  169. The New Academy of Laputa. Review of Natural Computing: DNA, Quantum Bits, and the Future of Smart Machines, by Dennis Shasha and Cathy Lazere. SIAM News, October 19, 2010
  170. Communication and its Possibilities. Review of Communicating Science: Professional, Popular, Literary. By Nicholas Russell SIAM News, Volume 43, Number 9, November 2010
  171. Yau's Voice, Popularized. Review of The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions, by Shing-Tung Yau and Steve Nadis. SIAM News, December 14, 2010.
  172. The Popular and the Phony. Review of Proofiness: The Dark Arts of Mathematical Deception. by Charles Seife. SIAM News, January 24, 2011
  173. The Complexity of Complexity. Review of Compexity: A Guided Tour, by Melanie Mitchell SIAM News, March 15, 2011.
  174. A Scientific Patina for Everything Under the Sun, Review of Quantify! A Crash Course in Smart Thinking, by Göran Grimvall. SIAM News, April 6, 2011.
  175. Much Ado about Information. Review of The Information: A History, A Theory, A Flood, by James Gleick. SIAM News, June 21, 2011.
  176. Magnificent Obsessions. Review of Higher Speculations: Grand Theories and Failed Revolutions in Physics and Cosmology by Helge Kragh. SIAM News,, November 15, 2011.
  177. Tricky Mathematics. Review of Magical Mathematics: The Mathematical Ideas that Animate Great Magic Tricks by Persi Diaconis and Ron Graham. SIAM News, March 2012.
  178. Mathematics as Narrative. Review of Circles Disturbed: The Interplay of Mathematics and Narrative, ed. Apostolis Doxiadis and Barry Mazur, SIAM News, June 2012.
  179. My Poincaré, Recollected. Review of Henri Poincaré: A Scientific Biography, by Jeremy Gray, SIAM News, October 2012.
  180. Mathematics: Handmaiden to Architecture. Review of Mathematical Excusions to the World's Great Buildings, by Alexander Hahn. SIAM News, November 2012.
  181. Geometry Meets Art in an Arcimboldesque Assemblage. Review of Manifold Mirrors: The Crossing Paths of the Arts and Mathematics by Felipe Cucker. SIAM News, July 2013.
  182. De Moivre Revealed. Review of Abraham de Moivre: Setting the Stage for Classical Probability and its Applications by David Bellhouse. SIAM News, March 2014.
  183. Mathematics as Play. Review of Math Bytes: Google Bombs, Chocolate-Covered Pi, and Other Cool Bits in Computing, by Tim Chartier. SIAM News, June 2014.
  184. The Mathematization of America's National Sport . Review of The Sabermetric Revolution: Assessing the Growth of Analytics in Baseball, by Benjamin Baumer and Andrew Zimbalist. SIAM News, July 2014
  185. Inspiration for a Devoted Wordsmith. Review of Origins of Mathematical Words: A Comprehensive Dictionary of Latin, Greek, and Arabic Roots. By Anthony Lo Bello. SIAM News, January 2015.

Some Selected Lectures

  1. Mathematical Education: Continuous Reformation. Chauvenet Prize Remarks. Berkeley, Cal., January 28, 1963,
  2. Of Men and Mathematics: A Plea for the Historical Sense in Mathematics. Address: MAA Meeting, Annapolis, Md., April 27, 1963.
  3. Toward a Jamesian History of Mathematics. Invited address, Winter meeting of the AMS, January 1967
  4. The Raised Eyebrows of Mathematics. International Conference of Mathematical Education, 1992.
  5. Plenary Lecturer: International Commission for the Study and Improvement of Mathematics Teaching. Berlin. July 1995.
  6. Invited Lecturer: Technische Universität Vienna, December 1996.
  7. Evidence in Mathematics. First Alfred North Whitehead Lecture, Imperial College, 1998.
  8. Urania Lecturer, International Congress of Mathematicians, Berlin, August, 1998.
  9. Invited Lecturer, International Conference on War and Mathematics, Karlskrona, Sweden, August 2002.
  10. Invited Lecturer, Österreichische Gesellschaft für Geschichte der Naturwissenschaften, May 2002 and May 2004.


Interviews of and by Philip J. Davis at The History of Numerical Analysis and Scientific Computing Oral History Site
  1. Saul Abarbanel
  2. John Butcher
  3. Interview of Philip J. Davis conducted by William Kolata and Gail Corbett
  4. Walter Gautschi
  5. Paul Garabedian
  6. David Gottlieb
  7. Bertil Gustafsson
  8. Eugene Isaacson
  9. Seymour Parter
  10. Michael J. D. Powell
  11. Alfio Quarteroni
  12. Frank Stenger
  13. Hans J. Stetter
  14. Heinz Zemanek

"Phil Davis and the Mathematizing of America", Brown Alumni Monthly December 1986, pp. 18-23.

This online bibliography was assembled by Ernest Davis. Thanks to Carol Mehne for finding the articles in SIAM News, 1984-1997.