Publications

First, a list of my scientific publications:

  1. Unidades de Anéis de Grupo e o Problema do Isomorfismo, M.A. dissertation, IME-USP, October 1981

  2. “Diophantine Equations and Geometry,” Bowdoin Prize expository essay on the Natural Sciences, 1987

  3. Arithmetic of p-adic Modular Forms, Ph.D. thesis, Harvard University, June 1987

  4. Arithmetic of p-adic Modular Forms, Lecture Notes in Mathematics vol. 1304, Springer-Verlag, 1988

  5. Review of Mathenauts, ed. by Rudy Rucker, Mathematical Intelligencer, 10 (1988), no. 4, p. 70

  6. Primeiros Passos p-ádicos, notes for a mini-course given at the 17o Colóquio Brasileiro de Matemática, IMPA, 1989

  7. “Pontos Racionais em Curvas Algébricas,” expository article, in Atas do 17o Colóquio Brasileiro de Matemática, 1989

  8. “Deforming Galois Representations: Controlling the Conductor,” Journal of Number Theory, 34 (1990), 95–113

  9. Introdução às Formas Modulares, notes for a mini-course given at the X Escola de Álgebra, February 1989, IMPA, 1990

  10. “Curvas Elípticas e o ‘Teorema’ de Fermat,” expository article, in Atas da X Escola de Álgebra, SBM/IMPA, 1990.

  11. “Em Busca da Demonstração Maravilhosa,” expository article for high school teachers, in Revista do Professor de Matemática, 1990

  12. “The Square-free Sieve and the Rank of Elliptic Curves,” with Barry Mazur, Journal of the A.M.S., 4 (1991), 1–23

  13. “On the Ordinary Hecke Algebra”, Journal of Number Theory, 41 (1992), 178–198

  14. “Families of Modular Eigenforms,” with Barry Mazur, Mathematics of Computation, 58 (1992), 793–805

  15. “The Square-free Sieve over Number Fields,” Journal of Number Theory, 43 (1993), 109–122

  16. Advances in Number Theory: the proceedings of the third conference of the Canadian Number Theory Association, editor, with Noriko Yui; Oxford University Press, 1993.

  17. “On the Characteristic Power Series of the U operator,” with Barry Mazur, Annales de L’Institut Fourier, 42 (1993), 301–312.

  18. p-adic Numbers: an introduction, Springer-Verlag, Berlin, 1993. A second edition has appeared, see below.

  19. “Continuity Properties of p-adic Modular Forms,” in Elliptic Curves and Related Topics, ed. by H. Kisilevsky and M. R. Murty, American Mathematical Society, 1994.

  20. “A Marvelous Proof,” American Mathematical Monthly, 101(1994), 203–222.

  21. “E2, Theta, and Overconvergence” with Robert Coleman and Naomi Jochnowitz, International Mathematics Research Notices, 1995, Number 1, 23–41.

  22. Arithmetic of Diagonal Hypersurfaces over Finite Fields, with Noriko Yui, London Mathematical Society Lecture Note Series, Cambridge University Press, 1995.

  23. “Deforming Galois Representations: a survey,” in Seminar of Fermat’s Last Theorem, CMS Conference Proceedings, vol. 17, AMS, 1995, pp. 179–207.

  24. “Searching for p-adic eigenforms,” with Barry Mazur, Mathematics Research Letters, 2(1995), 515–536.

  25. “Uma Demonstração Maravilhosa,” Matemática Universitária, 19 (December, 1995), 16–43.

  26. “Brauer Numbers of Twisted Fermat Motives,” with Noriko Yui, in Number Theory: New York Seminar, 1991–1995, ed. by D. V. Chudnosvsky, G. V. Chudnovsky, and M. B. Nathanson, Springer-Verlag, 1996.

  27. p-adic Numbers: an introduction, second edition, Springer-Verlag, Berlin, 1997.

  28. “On the Density of Modular Representations,” with Barry Mazur, in Computational Perspectives on Number Theory (Chicago, Illinois 1995), AMS/IP Studies in Advanced Mathematics, vol. 7 (1998), 127–142.

  29. “Non-ordinary forms: a story,” Experimental Mathematics, 6 (1997), 195–205.

  30. “Observations on Fermat Motives of K3-Type”, with Noriko Yui, Journal of Number Theory 71 (1998), 203–226.

  31. p-adic Numbers: an introduction, second edition, corrected second printing, Springer-Verlag, Berlin, 2000.

  32. “Where the Slopes Are,” Journal of the Ramanujan Mathematical Society, 16 (2001), 75–99.

  33. “Deformations of Galois Representations,” in Arithmetic Algebraic Geometry, ed. by Brian Conrad and Karl Rubin, American Mathematical Society, 2001, pp. 235–406. (With appendices by Mark Dickinson, Tom Weston, and Matthew Emerton.)

  34. Review of Cohomology of Number Fields, by Jürgen Neukirch, Alexander Schmidt, and Kay Wingberg. Bulletin of the American Mathematical Society, 39 (2001), 101–107.

  35. Math through the Ages: A Gentle History for Teachers and Others, with William P. Berlinghoff. Oxton House Publishers, 2002.

  36. Review of The Honors Class, by Benjamin Yandell. Science, 296 (May 3, 2002), pp. 853–854.

  37. p-adic Numbers: an introduction, second edition, corrected third printing, Springer-Verlag, Berlin, 2003.

  38. Math through the Ages, Expanded Edition: A Gentle History for Teachers and Others, with William P. Berlinghoff. Mathematical Association of America and Oxton House Publishers, 2004.

  39. “As Others See Us: Four Science-Fictional Mathematicians,” Math Horizons, April 2004.

  40. History of Mathematics, chapter 2 in Using the Mathematics Literature, ed. by Kristine Fowler, Marcel Dekker, 2004.

  41. Review of János Bolyai, Non-Euclidean Geometry, and the Nature of Space, by Jeremy J. Gray, Science, 306 (December 10, 2004), pp. 1893–1894.

  42. Review of Sherlock Holmes in Babylon and Other Tales of Mathematical History, ed. by Marlow Anderson, Victor Katz, and Robin Wilson, Aestimatio 2 (2005), 68–70.

  43. Review of Letters to a Young Mathematician, by Ian Stewart, Science and Spirit, September-October 2006

  44. “Euler’s Convincing Non-Proofs,” FOCUS, January 2007

  45. Review of A First Course in Modular Forms, by Fred Diamond and Jerry Shurman, American Mathematical Monthly, January 2007

  46. Review of Equations from God, by Daniel Cohen, First Things, December 2007

  47. “Local and Global in Number Theory,” in the Princeton Companion to Mathematics (Princeton University Press, 2008)

  48. “Numbers and Number Systems,” in the Princeton Companion to Mathematics (Princeton University Press, 2008)

  49. Review of Is God a Mathematician?, by Mario Livio. First Things, February 2009

  50. Review of Plato’s Ghost, by Jeremy Gray, Aestimatio, 6 (2009). (Actually posted July 2010.)

  51. “How to Read Mathematics”, with Shai Simonson, Hacker Monthly, October 2010, pp. 4–8. This is a shorter version of an article posted online here.

  52. Pathways from the Past I: Using History to Teach Numbers, Numerals, & Arithmetic, with William P. Berlinghoff. Oxton House, 2010.

  53. “On Books: Invation of the POD Books,” MAA Focus, December 2010–January 2011.

  54. “Was Cantor Surprised?”, American Mathematical Monthly 118, March 2011, 198–209.

  55. “Rigid Calabi-Yau Threefolds over $\mathbf{Q}$ are Modular,” with Noriko Yui, Expositiones Mathematicae 9(2011), 142–149.

  56. “Learning to Move with Dedekind”, in Mathematical Time Capsules, ed. by Dick Jardine and Amy Shell-Gallasch, Mathematical Association of America, 2011.

  57. “On Books: Could This Be The One?”, MAA Focus, February–March 2011.

  58. “On Books: Language as Barrier and Opportunity,” MAA Focus, August–September 2011.

  59. “On Books: Buy More Books!” MAA Focus, December 2011–January 2012.

  60. “Was Cantor Surprised?” (2011) was reprinted without updates in Best Writing in Mathematics 2012, ed. by Mircea Pitici, Princeton University Press, 2012.

  61. “On Books: Choosing and Using Textbooks,” MAA Focus, April–May 2012.

  62. “On Books: The Carus Mathematical Monographs: MAA’s First Books,” MAA Focus, August–September 2012.

  63. “On Books: Slow Publishing,” MAA Focus, October–Novemmber 2012.

  64. A Guide to Groups, Rings, and Fields, Mathematical Association of America, 2012.

  65. Pathways from the Past II: Using History to Teach Algebra, with William P. Berlinghoff. Oxton House, 2012.

  66. Review of Elliptic Curves, Modular Forms, and Their L-functions, by Álvaro Lozano-Robledo. American Mathematical Monthly, 20(January 2013), 84–94.

  67. “On Books: Why Buy the Book When I Have it on my iPad?” MAA Focus, April–May 2013.

  68. Além do Marquês: A Regra de L’Hospital no Contexto da História da Análise, booklet with notes for a mini-course, Sociedade Brasileira de Histíria da Matemática, 2013.

  69. “On Books: Mathematics Books of Planet Earth,” MAA Focus, June–July 2013.

  70. “On Books: The New Historian’s Bookshelf,” MAA Focus, August–September 2013.

  71. “Quadratic Twists of Rigid Calabi-Yau Threefolds over Q,” in Arithmetic and Geometry of K3 Surfaces and Calabi-Yau Threefolds, ed. by Radu Laza, Matthias Schütt and Noriko Yui, Fields Institute Communications 7, Springer, 2013, 517–533.

  72. “On Books: Lives of the Mathematicians,” MAA Focus, October–November 2013.

  73. “On Books: Chasing a Story,” MAA Focus, February–March, 2014.

  74. “On Books: Chasing a Picture,” MAA Focus, June–July, 2014.

  75. “On Books: A Bookish Guide to MAA MathFest,” MAA Focus, August–September, 2014.

  76. Review of The Man Who Knew Infinity: The Life of the Genius Ramanujan, MAA Focus, August–September, 2014. (Reprinted from MAA Reviews.)

  77. Review of A Sourcebook in the Mathematics of Medieval Europe and North Africa, ed. by Victor J. Katz, Menso Folkerts, Barnabas Hughes, Roi Wagner, and J. Lennart Berggren. CSHPM Bulletin, 60 (May, 2017), 12–14.

  78. Review of Research in the History and Philosophy of Mathematics: The CHSPM 2014 Annual Meeting in St. Catherine's, Ontario, ed. by Maria Zack and Elaine Landry. Aestimatio 13 (2016–2018), 26–29.

  79. “3890 Reviews Later: The continuing story of MAA Reviews,” MAA Focus, April/May 2019.

  80. Review of History of Nonlinear Oscillations Theory in France (1880–1940), by Jean-Marc Ginoux. Isis 110 (2019), 630–631.

  81. Review of Calculus Reordered, by David Bressoud. American Mathematical Monthly, 127 (May 2020), 470–477.

  82. “Pathways from the Past: Classroom-Ready Materials for Using History to Teach Mathematics”, with Bill Berlinghoff, Convergence May 2020. Free to download!

  83. p-adic Numbers: An Introduction, 3rd edition. Springer, June 2020.

  84. Over 400 book reviews for MAA Reviews, the online book review service of the Mathematical Association of America. These range from short notices to detailed reviews.

  85. Kurt Hensel on Common Inessential Discriminant Divisors, 1894. Fernando Q. Gouvêa and Jonathan Webster, Summer 2021. arXiv:2108.05327.

  86. Dedekind on Higher Congruences and Index Divisors, 1871 and 1878. Fernando Q. Gouvêa and Jonathan Webster, Summer 2021. arXiv:2107.08905.

  87. A Short Book on Long Sums. Preliminary notes on infinite series for calculus students, January 2021.

I’ve also published a few other things...

  1. Many reviews of books related in some way to mathematics, most of them in either MAA Reviews. I’ve listed other reviews above, but the MAA ones are too many to list here.

  2. The liner notes for the video/DVD of Fermat’s Last Tango, a musical play about the proof of Fermat’s Last Theorem. I was a consultant for the authors while they were writing the play, and ended up writing most of the booklet that comes with the video/DVD which is distributed by the Clay Mathematics Institute.

  3. I was one of the “steering advisors” for Mathematics Illuminated, a series of videos and other resources for mathematics teachers and others interested in mathematics.

  4. Many reviews of science fiction and fantasy literature, appearing in Science Fiction Review, Fantasy Review, and The New York Review of Science Fiction, among others. These were mostly some time ago, when I had more free time.

  5. Five short articles in The Evangelical Dictionary of Theology, ed. by Walter Elwell, Baker Book House, 1984.

  6. One trimester of curriculum material for Sunday School, Presbyterian Church of Brazil.

  7. Software Reviews:

Fernando Q. Gouvêa ---- fqgouvea@colby.edu