Publications
First, a list of my scientific publications:
- Unidades de Anéis de Grupo e o Problema do
Isomorfismo, M.A. dissertation, IME-USP, October 1981
- “Diophantine Equations and Geometry,” Bowdoin Prize
expository essay on the Natural Sciences, 1987
- Arithmetic of p-adic Modular Forms,
Ph.D. thesis, Harvard University, June 1987
- Arithmetic of p-adic Modular Forms, Lecture
Notes in Mathematics vol. 1304, Springer-Verlag, 1988
- Review of Mathenauts, ed. by Rudy
Rucker, Mathematical Intelligencer, 10 (1988),
no. 4, p. 70
- Primeiros Passos p-ádicos, notes for a
mini-course given at the 17^{o} Colóquio
Brasileiro de Matemática, IMPA, 1989
- “Pontos Racionais em Curvas Algébricas,”
expository article, in Atas do 17^{o}
Colóquio Brasileiro de Matemática, 1989
- “Deforming Galois Representations: Controlling the
Conductor,” Journal of Number Theory, 34
(1990), 95–113
- Introdução às Formas Modulares,
notes for a mini-course given at the X Escola de Álgebra,
February 1989, IMPA, 1990
- “Curvas Elípticas e o ‘Teorema’ de
Fermat,” expository article, in Atas da X Escola de
Álgebra, SBM/IMPA, 1990.
- “Em Busca da Demonstração
Maravilhosa,” expository article for high school
teachers, in Revista do Professor de
Matemática, 1990
- “The Square-free Sieve and the Rank of Elliptic
Curves,” with Barry Mazur, Journal of the
A.M.S., 4 (1991), 1–23
- “On the Ordinary Hecke Algebra”, Journal of
Number Theory, 41 (1992), 178–198
- “Families of Modular Eigenforms,” with Barry
Mazur, Mathematics of Computation, 58 (1992),
793–805
- “The Square-free Sieve over Number
Fields,” Journal of Number Theory, 43
(1993), 109–122
- Advances in Number Theory: the proceedings of the third
conference of the Canadian Number Theory Association,
editor, with Noriko Yui; Oxford University Press, 1993.
- “On the Characteristic Power Series of the U
operator,” with Barry Mazur, Annales de
L’Institut Fourier, 42 (1993),
301–312.
- p-adic Numbers: an introduction,
Springer-Verlag, Berlin, 1993. A second edition has
appeared, see below.
- “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.
- “A Marvelous Proof,” American Mathematical
Monthly, 101(1994), 203–222.
- “E_{2}, Theta, and Overconvergence” with
Robert Coleman and Naomi Jochnowitz, International
Mathematics Research Notices, 1995, Number 1,
23–41.
- Arithmetic of Diagonal Hypersurfaces over Finite
Fields, with Noriko Yui, London Mathematical Society
Lecture Note Series, Cambridge University Press, 1995.
- “Deforming Galois Representations: a survey,”
in Seminar of Fermat’s Last Theorem, CMS
Conference Proceedings, vol. 17, AMS, 1995,
pp. 179–207.
- “Searching for p-adic eigenforms,” with
Barry Mazur, Mathematics Research
Letters, 2(1995), 515–536.
- “Uma Demonstração Maravilhosa,”
Matemática Universitária, 19
(December, 1995), 16–43.
- “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.
- p-adic Numbers: an introduction, second edition,
Springer-Verlag, Berlin, 1997.
- “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.
- “Non-ordinary forms: a story,” Experimental
Mathematics, 6 (1997), 195–205.
- “Observations on Fermat Motives of K3-Type”,
with Noriko Yui, Journal of Number Theory 71
(1998), 203–226.
- p-adic Numbers: an introduction, second edition,
corrected second printing, Springer-Verlag, Berlin, 2000.
- “Where the Slopes Are,” Journal of the Ramanujan
Mathematical Society, 16 (2001), 75–99.
- “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.)
- Review of Cohomology of Number Fields, by Jürgen
Neukirch, Alexander Schmidt, and Kay Wingberg. Bulletin of
the American Mathematical Society, 39 (2001),
101–107.
- Math through the Ages: A Gentle History for Teachers and
Others, with William P. Berlinghoff.
Oxton House
Publishers, 2002.
- Review of The Honors Class, by Benjamin Yandell.
Science, 296 (May 3, 2002), pp. 853–854.
- p-adic Numbers: an introduction,
second edition, corrected third printing, Springer-Verlag,
Berlin, 2003.
- 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.
- “As Others See Us: Four Science-Fictional
Mathematicians,” Math Horizons, April 2004.
- History of Mathematics, chapter 2 in Using the Mathematics
Literature, ed. by Kristine Fowler, Marcel Dekker, 2004.
- Review of János Bolyai, Non-Euclidean Geometry, and
the Nature of Space, by Jeremy
J. Gray, Science, 306 (December 10, 2004),
pp. 1893–1894.
- 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.
- Review of Letters to a Young Mathematician, by Ian Stewart,
Science and Spirit, September-October 2006
- “Euler’s Convincing Non-Proofs,”
FOCUS, January 2007
- Review of A First Course in Modular Forms, by Fred
Diamond and Jerry Shurman, American Mathematical Monthly,
January 2007
- Review of Equations from God, by Daniel Cohen, First
Things, December 2007
- “Local and Global in Number Theory,” in
the Princeton Companion to Mathematics (Princeton
University Press, 2008)
- “Numbers and Number Systems,” in the Princeton
Companion to Mathematics (Princeton University Press,
2008)
- Review of Is God a Mathematician?, by Mario
Livio. First Things, February 2009
- Review
of Plato’s Ghost, by Jeremy Gray,
Aestimatio,
6 (2009). (Actually posted July 2010.)
- “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.
- Pathways from the Past I: Using History to Teach Numbers,
Numerals, & Arithmetic, with William P. Berlinghoff. Oxton
House, 2010.
- “On Books: Invation of the POD Books,” MAA Focus,
December 2010–January 2011.
- “Was Cantor Surprised?”, American Mathematical
Monthly 118, March 2011, 198–209.
- “Rigid Calabi-Yau Threefolds over $\mathbf{Q}$ are
Modular,” with Noriko Yui, Expositiones Mathematicae
9(2011), 142–149.
- “Learning to Move with Dedekind”, in Mathematical Time
Capsules, ed. by Dick Jardine and Amy Shell-Gallasch, Mathematical
Association of America, 2011.
- “On Books: Could This Be The One?”, MAA Focus,
February–March 2011.
- “On Books: Language as Barrier and Opportunity,” MAA
Focus, August–September 2011.
- “On Books: Buy More Books!” MAA Focus, December
2011–January 2012.
- “Was Cantor Surprised?” (2011) was reprinted
without updates in Best Writing in Mathematics 2012,
ed. by Mircea Pitici, Princeton University Press, 2012.
- “On Books: Choosing and Using Textbooks,” MAA
Focus, April–May 2012.
- “On Books: The Carus Mathematical Monographs: MAA’s
First Books,” MAA Focus, August–September 2012.
- “On Books: Slow Publishing,” MAA Focus,
October–Novemmber 2012.
- A Guide to Groups, Rings, and Fields, Mathematical
Association of America, 2012.
- Pathways from the Past II: Using History to Teach
Algebra, with William P. Berlinghoff. Oxton House, 2012.
- Review of Elliptic Curves, Modular Forms, and Their
L-functions, by Álvaro Lozano-Robledo. American
Mathematical Monthly, 20(January 2013), 84–94.
- “On Books: Why Buy the Book When I Have it on my iPad?”
MAA Focus, April–May 2013.
- 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.
- “On Books: Mathematics Books of Planet
Earth,” MAA Focus, June–July 2013.
- “On Books: The New Historian’s
Bookshelf,” MAA Focus, August–September 2013.
- “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.
- “On Books: Lives of the Mathematicians,” MAA
Focus, October–November 2013.
- “On Books: Chasing a Story,” MAA Focus,
February–March, 2014.
- “On Books: Chasing a Picture,” MAA Focus,
June–July, 2014.
- “On Books: A Bookish Guide to MAA MathFest,” MAA
Focus, August–September, 2014.
- Review of The Man Who Knew Infinity: The Life of the
Genius Ramanujan, MAA Focus, August–September,
2014. (Reprinted from MAA Reviews.)
- 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.
- 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.
- “3890 Reviews Later: The continuing story of MAA
Reviews,” MAA Focus, April/May 2019.
- Review of History of Nonlinear Oscillations Theory in France
(1880–1940), by Jean-Marc Ginoux. Isis 110
(2019), 630–631.
- Review of Calculus Reordered, by David
Bressoud. American Mathematical Monthly, 127 (May 2020),
470–477.
- “Pathways from the Past: Classroom-Ready Materials for
Using History to Teach Mathematics”, with Bill
Berlinghoff, Convergence
May 2020. Free to download!
- p-adic Numbers: An Introduction, 3rd edition. Springer,
June 2020.
- 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.
- Kurt Hensel on Common
Inessential Discriminant Divisors, 1894. Fernando Q. Gouvêa and
Jonathan Webster, Summer 2021. arXiv:2108.05327.
- Dedekind on
Higher Congruences and Index Divisors, 1871 and 1878. Fernando
Q. Gouvêa and Jonathan Webster, Summer 2021. arXiv:2107.08905.
- A Short Book on Long Sums. Preliminary notes on infinite
series for calculus students, January 2021.
I’ve also published a few other things...
- 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.
- 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.
- 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.
- 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.
- Five short articles in The Evangelical Dictionary of
Theology, ed. by Walter Elwell, Baker Book House, 1984.
- One trimester of curriculum material for Sunday School, Presbyterian
Church of Brazil.
- Software Reviews:
- “A Look at PARI and GP,” Notices of the
American Mathematical Society, 38 (1991),
903–904
- “Mathematica 2.0 for Windows,” Notices of the
American Mathematical Society, 39 (1992),
435–437
- “MathType for Windows,” Notices of the American
Mathematical Society, 39 (1992), 1069–1075
Fernando Q. Gouvêa ---- fqgouvea@colby.edu