(Updated November, 2018)

Book

• Euler’s Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press (2008) (Translations: Portuguese, Japanese, Korean, Chinese)
• Tales of Impossibility, to appear Fall 2019

Editorship

• I am the editor of Math Horizons, the undergraduate magazine of the Mathematical Association of America (2014–19)

Topology and Dynamical Systems

• “Entropy for symbolic dynamics with overlapping alphabets,” with Fabio Drucker (Dickinson ’11) and Jim Wiseman, Journal of Dynamics and Differential Equations 28, Issue 2 (2016), pp. 301–315
• “Spectral decomposition for topologically Anosov homeomorphisms on noncompact and non-metrizable spaces,” with Tarun Das, Keonhee Lee, and Jim Wiseman, Topology and its Applications 160 (2013), No. 1, pp. 149-158
• “Symbolic dynamics for nonhyperbolic systems,” with Jim Wiseman, Proceedings of the American Mathematical Society, 138 (2010), 4373–4385
• “Itineraries of rigid rotations and diffeomorphisms of the circle,” with Paul Winkler (Dickinson ’07) and Jim Wiseman, Theoretical Computer Science, 411 (2010), No. 1, pp. 259–265
• “Chain recurrence rates and topological entropy,” with Jim Wiseman, Topology and its Applications, 156 (2008), No. 2, 251–261
• “Positively expansive dynamical systems,” with Jim Wiseman, Topology and its Applications 154 (2007), No. 3, 604–613
• “Equivalence of expanding properties,” with Jim Wiseman, in the problem section of Topology Proceedings, 28 No. 1 (2004), 299–300
• “Topological helicity for framed links,” with Elizabeth Bouzarth (Dickinson ’03), Journal of Knot Theory and its Ramifications, 13 (2004), No. 8, 1007–1019
• “Positively expansive homeomorphisms of compact spaces,” with Jim Wiseman, International Journal of Mathematics and Mathematical Sciences, 54 (2004) 2907–2910
• “Bounded homeomorphisms of the open annulus,” with Jim Wiseman, New York Journal of Mathematics, 9 (2003), 55–68
• “A fixed point theorem for bounded dynamical systems,” with Jim Wiseman, Illinois Journal of Mathematics, 46 (Summer 2002), no. 2, 491–495, addendum, 48 (Fall 2004), No. 3, 1079–1080
• “Shift equivalence and the Conley index,” with John Franks, Transactions of the American Mathematical Society, 352 (2000), No. 7, 3305–3322
• “Connection matrix pairs,” Conley Index Theory (Warsaw, 1997), 219–232, Banach Center Publications, 47, Polish Acad. Sci., Warsaw, 1999

The History of Mathematics

• “Circular Reasoning: Who First Proved That C Divided by d Is a Constant?” The College Mathematics Journal, 46, No. 3 (May 2015), pp. 162–171 (This article will also appear in Princeton University Press’ The Best Writing on Mathematics 2016.)
• “The Japanese theorem for nonconvex polygons,” Convergence, December 2013
• “The polyhedral formula,” In Leonhard Euler: Life, Work and Legacy (R. Bradley and E. Sandifer, editors), volume 5 of the Studies in the History and Philosophy of Mathematics series. Elsevier, Amsterdam (2007) 421–439
• “The flaw in Euler’s proof of his polyhedral formula,” with Chris Francese, The American Mathematical Monthly, 114 (April 2007) 286–296

Undergraduate Mathematics and Miscellaneous Publications

• “Proof Without Words: Gregory’s Theorem” with Tom Edgar, submitted
• “I [heart] Math,“ Chalkdust Issue 08 (Autumn 2018) 15
• “Measuring Tapes for Circles and Spheres,” Mathematics Teacher 112 no. 3 (November/December 2018) 185–86
• “A-Tweeting We Will Go: Building a Professional Network with Twitter,” MAA FOCUS 37 no. 3 (June/July 2017) 18–20
• “Game, SET, Math, ”Math Horizons 25 no. 4 (April 2017) 2
  
• “A Trisectrix from a Carpenter’s Square, ”Mathematics Magazine 90 no. 1 (February 2017) 8–11
• “Sugihara’s Impossible Cylinder,” Math Horizons, 24 (September 2016) No. 1, 18–19
• “A Conversation with Timothy Gowers,” Math Horizons, 23 (September 2015) No. 1, 10–14
• “Proof without words: The maximum sum of inradii,” The College Mathematics Journal 46 (January 2015) No. 1, 23
• “Gabriel’s paper horn,” Gathering 4 Gardner 11 gift exchange
• “Letters of recommendation,” XRDS (Crossroads: the ACM Magazine for Students), 17 (Spring 2011) No. 3, 6
• “A π-less Buffon’s needle problem,” Mathematics Magazine, 79 (December 2006) No. 5, 385–389
• “Centers of the United States,” The College Mathematics Journal, 36 (November 2005) No. 5, 366–373
• “An illuminating example of the Gauss map,” The College Mathematics Journal, 35 (January 2004) No. 1, 14
• “Math goes pop: The American public succumbs to the allure of a formerly ‘uncool’ discipline,” with Cotten Seiler, Dickinson Magazine, 80, No. 4, Spring 2003
• I was “blurbed” on the dust jacket of The Universe in Zero Words: The Story of Mathematics as Told Through Equations, by Dana Mackenzie, Princeton University Press, 2012
• I was “blurbed” on the dust jacket of Mathematicians: An Outer View of an Inner World, by Mariana Cook, Princeton University Press, 2009
• I was “blurbed” on the dust jacket of How Round is Your Circle? Where Engineering and Mathematics Meet, by John Bryant and Chris Sangwin, Princeton University Press, 2008

Book Reviews

• Review of Journey Through Genius, by William Dunham, Math Horizons, April 2014
• Review of The Survival of a Mathematician: From Tenure Track to Emeritus, by Steven G. Krantz, American Mathematical Society, 2009, for MAA Reviews, (March 30, 2009)
• Review of Five-Minute Mathematics, by Ehrhard Behrends, American Mathematical Society, 2008, for MAA Reviews, (July 6, 2008)
• Review of  Hesiod’s Anvil: Falling and Spinning Through Heaven and Earth, by Andrew J. Simoson, The Mathematical Association of America, Washington D.C., 2006, for Read This! The MAA Online Book Review Column, (February 18, 2008)
• Review of Topology and its Applications, by William F. Basener, Wiley, 2006, for MAA Reviews, (January 12, 2007)
• Review of Topology Now!, by Robert Messer and Philip Straffin, The Mathematical Association of America, Washington D.C., 2006, for Read This! The MAA Online Book Review Column, (April 8, 2006)

Translations

• “Solution of a geometric problem about lunes formed from circles,” 2013 translation (w/ Chris Francese and Travis Ramsey (Dickinson ‘13)) of Leonhard Euler’s paper “Solutio Problematis geometrici circa lunulas a circulis formatas,” Commentarii academiae scientiarum Petropolitanae 9 (1744) 207–221 (available online at the Euler Archive)
• “On n-gons, n-sided figures, and polyhedra,” 2006 translation (w/Anne Maiale) of pages 20–22 of Karl Georg Christian von Staudt’s book Geometrie der Lage, Nürnberg, 1847
• “Addition to Euler’s Polyhedral Theorem,” 2006 translation (w/Anne Maiale) of J. F. Hessel’s paper “Nachtrag zu dem Euler’schen Lehrsatz von Polyedern,” Journal für die Reine und Angewandte mathematik 8 (1832), 13–20
• “Easier proof of a stereometric theorem of Euler,” 2006 translation (w/Anne Maiale) of Jacob Steiner’s paper, “Leichter Beweis eines stereometrischen Satzes von Euler,” Journal für die reine und angewandte Mathematik 1 (1826), 364–367
• “Proof of some notable properties with which solids enclosed by plane faces are endowed,” 2004 translation (w/ Chris Francese) of Leonhard Euler’s paper “Demonstratio nonnullarum insignium proprietatum quibus solida hedris planis inclusa sunt praedita,” Novi Commentarii Academiae Scientiarum Petropolitanae, 4 (1752), 94–108 (available online at the Euler Archive)