(Updated February 21, 2023)

Books

• Tales of Impossibility: The 2000-Year Quest to Solve the Mathematical Problems of Antiquity, Princeton University Press (2019) (Translations: Chinese, Turkish)
• Euler’s Gem: The Polyhedron Formula and the Birth of Topology, Princeton University Press (2008) (Translations: Portuguese, Japanese, Korean, Russian)
• Euler’s Gem: The Polyhedron Formula and the Birth of Topology (with a New Preface by the Author), Princeton Science Library Series, Princeton University Press (2019)

Articles 

• “Horseshoe,” Math Horizons, 30 no. 2 (November 2022) 20–23
• “Why mathematicians study knots,” Quanta Magazine, October 31, 2022
• “The sordid past of the cubic formula,” Quanta Magazine, June 30, 2022
• “How we can make sense of chaos,” Quanta Magazine, March 2, 2022 
• “The journey to define dimension,” Quanta Magazine, September 13, 2021 (Reprinted as “A mathematician’s guided tour through higher dimensions,” Wired, September 19, 2021)
• “Paper spheres,” Math Horizons 29 no. 1 (September 2021) 16–19
• “Presenting in class,” Math Horizons 28 no. 3 (April 2021) 18–19
• “Topology 101: The hole truth,” Quanta Magazine, January 26, 2021
• “When math gets impossibly hard: Mathematicians have long grappled with the reality that some problems just don’t have solutions,” Quanta Magazine, September 14, 2020
• “Squaring the circle in a mirror,” Math Horizons 27 no. 4 (April 2020) 21–23
• “Communicating mathematics using social media“ Notices of the American Mathematical Society 67 no. 2 (February 2020) 182–184
• “A visual proof of Gregory’s theorem” with Tom Edgar (Dickinson ‘02), Mathematics Magazine 92 no. 5 (December 2019) 384–386
• “Aftermath: It’s just notation” with Jeff Forrester, Math Horizons 27 no. 2 (November 2019) 34
• “Beware of Cranks: Misguided attempts to solve impossible mathematical problems,” Lapham’s Quarterly, October 8, 2019
• “No upper bound: A conversation with Corrin Yap,” Math Horizons 27 no. 1 (September 2019) 15–17
• “A’tweeting we will go: Building a professional network with Twitter,” MAA FOCUS 37 no. 3 (June/July 2017) 18–20
• “I heart cardioids,” proceedings of the Gathering 4 Gardner 13 conference (April 2018)
• “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 no. 1 (September 2016) 18–19 (Also appeared on the August 3 page of the American Mathematical Society’s 2020 Page-a-Day mathematics calendar, created by Evelyn Lamb.)
• “Entropy for symbolic dynamics with overlapping alphabets,” with Fabio Drucker (Dickinson ‘11) and Jim Wiseman, Journal of Dynamics and Differential Equations 28 no. 2 (2016) 301–315 
• “A conversation with Timothy Gowers,” Math Horizons 23 no. 1 (September 2015) 10–14
• “Circular reasoning: Who first proved that c divided by d Is a constant?“ The College Mathematics Journal 46 no. 3 (May 2015) 162–171 (This article also appears in Princeton University Press’ The Best Writing on Mathematics 2016 anthology.)
• “Gabriel’s paper horn,” proceedings of the Gathering 4 Gardner 11 conference (April 2014)
• “The Japanese theorem for nonconvex polygons,” Convergence, December 2013
• “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 no. 1 (2013) 149–158
• “Letters of recommendation,” XRDS (Crossroads: the ACM Magazine for Students) 17 no. 3 (Spring 2011) 6
• “Symbolic dynamics for nonhyperbolic systems,” with Jim Wiseman, Proceedings of the American Mathematical Society138 no. 12 (December 2010), 4373–4385 
• “Itineraries of rigid rotations and diffeomorphisms of the circle,” with Paul Winkler (Dickinson ‘07) and Jim Wiseman, Theoretical Computer Science 411 no. 1 (2010) 259–265 
• “Chain recurrence rates and topological entropy,” with Jim Wiseman, Topology and its Applications 156 no. 2 (2008) 251–261 
• “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 Monthly114 no. 4 (April 2007) 286–296
• “Positively expansive dynamical systems,” with Jim Wiseman, Topology and its Applications 154 no. 3 (2007) 604–613 
• “A π-less Buffon’s needle problem,” Mathematics Magazine 79 no. 5 (December 2006) 385–389 
• “Centers of the United States,” The College Mathematics Journal 36 no. 5 (November 2005) 366–373 
• “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 no. 8 (2004) 1007–1019 
• “Positively expansive homeomorphisms of compact spaces,” with Jim Wiseman, International Journal of Mathematics and Mathematical Sciences 2004 no. 54 (2004) 2907–2910 
• “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)
• “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 no. 2(Summer 2002) 491–495, addendum, 48 no. 3 (Fall 2004) 1079–1080 
• “Shift equivalence and the Conley index,” with John Franks, Transactions of the American Mathematical Society352 no. 7 (2000) 3305–3322 
• “Connection matrix pairs,” Conley Index Theory (Warsaw, 1997), 219–232, Banach Center Publications 47, Polish Acad. Sci., Warsaw, 1999 

Book Reviews 

• “The best books for mathematics enthusiasts,” Shepherd.com, April 4, 2022
• Review of Calculus Reordered: A History of the Big Ideas by David Bressoud; Change Is the Only Constant: The Wisdom of Calculus in a Madcap World by Ben Orlin; and Infinite Powers: How Calculus Reveals the Secrets of the Universe by Steven Strogatz, The College Mathematics Journal 50 no. 4 (October 2019) 307–312
• Review of Math with Bad Drawings, by Ben Orlin, Math Horizons, 26 no. 4 (April 2019) 28
• Review of The Art and Craft of Geometric Origami, by Mark Bolitho, Math Horizons, 25 no. 4 (April 2018) 28
• Review of Journey Through Genius, by William Dunham, Math Horizons, 21 no. 4 (April 2014) 22
• 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) 
•  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) 

Odds and Ends 

• “Mary Gertrude Haseman,” Wikipedia entry (created), 2022
• “Off on a tangent” (crossword puzzle), MAA FOCUS 40 no. 5 (October/November 2020) 14–15
• “By the numbers,” (a crossword puzzle with numbers rather than letters) The College Mathematics Journal 50 no. 4 (September 2019) 286–287
• “Measuring tapes for circles and spheres,” Mathematics Teacher 112 no. 3 (November/December 2018) 185–86
• “I [heart] maths,” Chalkdust, Issue 08 (Autumn 2018) 15
• “Proof without words: The maximum sum of inradii,” The College Mathematics Journal 46 no. 1 (January 2015) 23
• “An illuminating example of the Gauss map,” The College Mathematics Journal 35 no. 1 (January 2004) 14

Translations 

• “Solution of a geometric problem about lunes formed from circles,” 2013 translation, with 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, with Anne Maiale (Dickinson ‘08), 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, with Anne Maiale (Dickinson ‘08), of J. F. Hessel’s paper “Nachtrag zu dem Euler’schen Lehrsatz von Polyedern,” Journal für die Reine und Angewandte mathematik8 (1832), 13–20 
• “Easier proof of a stereometric theorem of Euler,” 2006 translation, with Anne Maiale (Dickinson ‘08), 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, with 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) 

Videos 

I have a YouTube channel where I have posted some instructional videos for students (not connected to any class), videos connected to some of my publications, and videos of general mathematical interest. Here’s a selection.

• “Proving that functions are injective and surjective (one-to-one and onto),” December 23, 2020
• “A quick introduction to LaTeX,” July 8, 2020
• “The magnificent Möbius band,” March 25, 2020
• “Three takes on the circle square illusion,” July 29, 2019
• “Make your own Pythagorean cup: A practical joke drinking vessel,” December 28, 2018
• “Make your own impossible cylinder,” August 29, 2016
• “Through one hole or two: A topological magic trick,” February 1, 2008