Curriculum Vitae

BOOKS:

The Mathematical Experience (National Book Award, w. Phil Davis) (Birkhauser)

Descartes’ Dream (w. Phil Davis) (Dover)

What Is Mathematics, Really? (Oxford)

18 Unconventional Essays on the Nature of Mathematics (edited) (Springer)

Loving and Hating Mathematics (w. Vera John-Steiner) (Princeton, 2011)

JOURNAL ARTICLES

Mathematical practice and life

“Mathematicians’ Proof, Established Mathematics, and Warranted Assertibility”, to appear in “From a Heuristic Point of View,” ed. E. Ippoliti, Cambridge Scholars

“Paul Cohen in 1963,” The Mathematical Intelligencer, 24 (3) 38-40, 2011

“Dialogo fra un matematico de succeso e uno studente testardo”, Archimede (Firenze, Italia) ottobre-dicembre 2010 4/2010, 202--205

“Alvin White,” Journal of Humanistic Mathematics, 2011

“Under-represented Then over-represented: A Memoir of Jews in American Mathematics,” College Mathematics Journal, January 2010, pp. 2-9

“Refuge from Misery and Suffering,” Mathematical Intelligencer, Winter, 2008, 30 (1) 22-26

“Clarence Stephens and the Potsdam Model,” Math Horizons, February 2010, pp 18-21, 29

Introduction to Indiscrete thoughts by Gian-Carlo Rota, Birkhauser, 1997

“Report on programs for minorities in mathematics” , Newsletter of SW region of MAA, 1988; Focus

Obituary of Nicholas Kazarinoff, SIAM News

“Proof is convincing and explaining,” Ed Stud in Math vol 24 pp 389-399 1993

“What is humanistic mathematics?”, Mathematics in College, 1990 49-50

“Humanistic mathematics and the real world,” in Essays in Humanistic Mathematics, MAA 1993, ed. A. White, pp. 15-18

“Szeged in 1934,” (edited from manuscripts of Edgar Lorch) Amer Math Monthly 100(3) Winner of Ford Prize

“Math lingo vs. plain English: double entendre”, Amer Math Monthly January 1997

Biographies of David Blackwell and Solomon Lefschetz, Dictionary of Mathematicians

“Mathematical menopause, or, a young man’s game?” The Mathematical Intelligencer 23(3) 2001 52-60

“Form and function in mathematical modeling,” talk at Budapest meeting of Santa Fe Institute

“The Origin of Chaos,” talk at Santa Fe Institute

“Mathematics and Ethics,” The Mathematical Intelligencer 12(3) 1990 12-15

“Ethics for Mathematicians,” in Philosophy of Math Education, P. Ernest ed., 2007

Partial differential equations

“Mixed problems in several variables,” J Math Mech 12(3) 1963

“Boundary conditions for equations of evolution,” Arch Rat Mech Anal 16(4) 1964

“On surface waves with finite and infinite speed of propagation,” Arch Rat Mech Anal 19(4) 1965

“On vibration, diffusion or equilibrium across a plane interface,” Arch Rat Mech Anal 21(5)1966

“The three-dimensional wave equation in a characteristic quarter-space,” with Y W Chen, J Math and Mech, November 1967

“Finite difference approximations for mixed initial-boundary value problems of general type,” SIAM J on Numer Anal 5(2) June 1968

“On the general theory of mixed problems,” Proc Battelle Rencontres 1968, 85-96

“Direct solution of general one-dimensional parabolic equations via an abstract Plancherel formula,” Proc Nat Acad Sci July 1969

“The method of reflection for two-sided problems of general type,” in Studies and Essays Presented to Yu-Why Chen, Math Res Center, Taipei, October 1970, pp 209-222

“A perturbation series for Cauchy’s problem for higher-order abstract parabolic equations” (with J Donaldson) Proc Nat Acad Sci vol 67 September 1970, pp 41-44

“How to classify differential polynomials,” Amer Math Monthly June-July 1973 pp 641-654

“The method of transmutations,” Lecture Notes in Mathematics, Partial Differential Equations and Related Topics, Springer-Verlag 1975, no 446, pp 264-282

“Stochastic solutions of hyperbolic equations”, ibid, pp 283-301

“Hyperbolic equations with coefficients in an enveloping algebra” (with S Steinberg) J Diff Eq 34(3) December 1979 pp 405-426

Random evolutions

“Random semigroups, Markov chains, and systems of partial differential equations” (with Richard J Griego) Proc Nat Acad Sci February 1969

“Theory of random evolutions with applications to partial differential equations” (with R J Griego) Trans Amer Math Soc vol 156 May 1971 pp 405-418

“Random evolutions are asymptotically Gaussian” (with M Pinsky) Comm Pure & Appl Math vol 25 1972 pp 33-44

“Non-commuting random evolutions, and an operator-valued Feynman-Kac formula” (with G Papanicolaou) Comm Pure & Appl Math vol 25 1972 pp 337-367

“Two limit theorems for random differential equations” (with R Cogburn) Indiana U Math J vol 22 1973 pp 1067-1089

“Random evolutions, a survey of results and problems,” Rocky Mt J Math, Summer 1974 pp 443-477

“Weyl’s theorem for certain operator-valued potentials” (with R. Griego) Indiana Univ Math J 1978 27(2) pp 195-209

“The birth of random evolutions,” The Mathematical Intelligencer 25(1) 2003 53-60

Probability

“A class of central limit theorems for convolution products of generalized functions,” Trans Amer Math Soc June 1969

“Some limit theorems for stochastic equations and applications” (with G Papanicolaou) Indiana U Math J vol 21 1972 pp 815-840

“Maxwell’s coefficients are conditional probabilities” Proc Amer Math Soc June 1974 pp 449-453

“Introduction to a special issue on stochastic differential equations,” Rocky Mt J Math Summer 1974

“Quasi-standard random variables and stochastic differentials” (with P. Greenwood) Stochastic differential equations Springer Lecture Series no 451 pp 35-62

Brownian motion and nonstandard analysis, University of New Mexico Technical Report No. 277, May 1973.

Linear operator equations

“Explicit solution of a class of abstract Cauchy problems,” J Diff Eqs vol 8 1970 570- 579

“Perturbation and approximation theory for higher-order abstract Cauchy problems” (with L Bobisud) Rocky Mt J Math vol 2 1972 pp 57-73

“On the invariance principle of scattering theory” (with J A Donaldson and A G Gibson) J Func Anal October 1973 14(2) pp131-145

“High-accuracy stable difference schemes for well-posed initial-value problems” (with T.Kato) SIAM J Numer Anal 1979 pp670-682

Pedagogy and philosophy

“Why Faulhaber Polynomials are Powers of (n + 1/2)”, College Math J., 2011

“From counting to quaternions”, Journal of Humanistic Mathematics, Vol 1, No. 1, 2011

“Mathematical Intuition: Poincare, Polya, Dewey”, in Knowledge and Logic” , Ed. C Cellucci et al., Cambridge Scholars Publishing, Newcastle on Tyne, pp. 223-242 (also at Rio de Janeiro, CLF Conference, May 2010)

“Mathematical discourse: the link from pre-mathematical to fully mathematical thinking,” (with KristinUmland) in Philosophy and Education 19 “Mathematical practice as a scientific problem,” in Proof & Other Dilemmas: Mathematics and Philosophy, ed B Gold, MAA 2008

“Definition of mathematics” in Dictionary of Scientific Terms, ed by G. Sica

“On Platonism,” Newsletter of the European Mathematical Society, June, 2008

“On von Glasersfeld’s Radical Constructivism,” Constructivist Notes, 2008

“What I would like my freshman students to know about proof”, in Teaching and Learning Proof Across the Grades, Ed. D. A. Stylianou et al., Routledge and National Council of Teachers of Mathematics, 2009

“Wings, not foundations!”, in G. Sica ed.,Essays on the foundations of mathematics and logic, Polimetrica, 2005

Foreword to New Mexico Math Contest Problem Book by L S Hahn, UNM Press 2005

“On the interdisciplinary study of mathematical practice,” in B. v. Kerkhove & J.P.v.Bendegem, Perspectives on mathematical practices, Springer, 2007

“Independent Thinking” College Math J. 34 (2) 2003

“Sines and cosines are just exponentials,” Math Rev (England) 2(4) April 1992 22-25

“The classroom encounter,” Humanistic Math Newsletter

“Reply to Martin Gardner,” The Mathematical Intelligencer 23 (1) 2001, 3-5

“The origin of geometry,” College Math J 33(3) May 2002 207-211

“A nifty derivation of Heron’s area formula by 11^th grade algebra,” Focus 22(8) 2002 p 22

“Heron’s area formula: what about a tetrahedron?” College Math J 35(2) March 2004 112-114

“A simple derivation of Heron’s area formula,” Wiskunde & Onderweis 2003

“Some proposals for reviving the philosophy of mathematics,” Advance in Mathematics 31(1) January 1979 pp 31-50

“Introducing Imre Lakatos,” Mathematical Intelligencer 1(3) 1978 pp 148-151

“Rhetoric and mathematics” (with P J Davis) in The rhetoric of the human sciences University of Wisconsin Press 1987 53-68

“Mathematics has a front and a back,” Eureka 1988, Synthese 88(2) August 1991

“Introduction to special issue,” Synthese 88(2) August 1991

“A mathematician’s perspective,” in P. Connolly and T. Vilardi, Writing to learn mathematics and science, TC Press, 1989

“Let’s teach philosophy of math!” College Math J 21(2) March 1990 105-111

“Inner knowledge, outer truth,” in Mathematics and Science, ed. R. Mickens, World Scientific, Singapore, 1990

“A visit to Hungarian mathematics,” (with V. John-Steiner) The Mathematical Intelligencer Spring 1993

“Fresh breezes in the philosophy of mathematics,” NY Acad of Sci December 2, 1993; in Amer Math Monthly and in Mathematics, Education and Philosophy ed P Ernest London 1994