Article Series in Convergence

In addition to stand-alone articles, Convergence encourages submissions for series providing information, resources, and classroom-ready materials suitable for teaching mathematics through its history. Series that have appeared in Convergence are listed below:

Historically Speaking

Selections from the short columns on historical mathematics that ran in NCTM’s Mathematics Teacher between 1953 and 1969, with new commentary placing the history and mathematics into context.

Series Introduction, by Betty Mayfield
The Quadrature of the Parabola: An Ancient Theorem in Modern Form, by Carl Boyer with commentary by William Dunham

HOM SIGMAA Student Contest Winning Papers

2022: First place – First place: Rye Ledford (University of Missouri – Kansas City), "The Assumptive Attitudes of Western Scholars Regarding the Contributions of Mathematics from India: Assessing yukti-s from the Yuktibhāṣā of Jyeṣṭhadeva"; Second place – Sarah Szafranski (University of Redlands), "Estimations of \(\pi\): The Kerala School of Astronomy and Mathematics, The Gregory-Leibniz Series, and the Eurocentrism of Math History."
2021: Megan Ferguson (Adelphi University), “The Suan shu shu and the Nine Chapters on the Mathematical Art: A Comparison.”
2020: Jeffrey Powers (Grand Rapids Community College), “Did Archimedes Do Calculus?”
2019: Amanda Nethington (University of Missouri – Kansas City), "Achieving Philosophical Perfection: Omar Khayyam's Successful Replacement of Euclid's Parallel Postulate."
2018: First place – Callie Lane (University of Missouri – Kansas City), "Race to Refraction: The Repeated Discovery of Snell's Law"; Second place – Christen Peters (Lee University), "The Reality of the Complex: The Discovery and Development of Imaginary Numbers," and Rachel Talmadge (University of Missouri – Kansas City), "François Viète Uses Geometry to Solve Three Problems."
2017: Co-winners – Amanda Akin (Lee University), “To Infinity and Beyond: A Historical Journey on Contemplating the Infinite,” Johann Gaebler (Harvard University), “Traditionalism: 1894 to 1925,” and Nathan Otten (University of Missouri – Kansas City), “Huygens and The Value of all Chances in Games of Fortune.”
2016: Co-winners – Brittany Anne Carlson (Salt Lake Community College), “A Latent Element of Alice’s Agency in Wonderland: Conservative Victorian Mathematics,” and William Cole (Lee University), “The Evolution of the Circle Method in Additive Prime Number Theory.”
2015: Co-winners – Samuel Patterson (University of Missouri – Kansas City), “Bernard Bolzano, a Genius Unnoticed in His Time,” and Briana Yankie (Lee University), “Examining Disproved Mathematical Ideas through the Lens of Philosophy.”
2014: First place – Jenna Miller (University of Missouri – Kansas City), "Casting Light on the Statistical Life of Florence Nightingale," and Anna Riffe (University of Missouri – Kansas City), "The Impossible Proof: An Analysis of Adrien-Marie Legendre's Attempts to Prove Euclid's Fifth Postulate"; Second place – Paul Ayers (University of Missouri – Kansas City), “Gabriel Cramer: Over 260 Years of Crushing the Unknowns," and Mary Ruff (Colorado State University – Pueblo), "Probability to 1750."
2013: Matthew Shives (Hood College), "Paradigms and Mathematics: A Creative Perspective."
2012: First place – Jesse Hamer (University of Missouri – Kansas City), “Indivisibles and the Cycloid in the Early 17th Century”; Second place – Kevin L. Wininger (Otterbein University), “On the Foundations of X-Ray Computed Tomography in Medicine: A Fundamental Review of the 'Radon transform' and a Tribute to Johann Radon.”
2011: First place – Paul Stahl (University of Missouri – Kansas City), “Kepler's Development of Mathematical Astronomy”; Second place – Sarah Costrell (Brandeis University), “Mathematics and Mathematical Thought in the Quadrivium of Isidore of Seville,” and Rick Hill (University of Missouri – Kansas City), “Thomas Harriot's Artis Analyticae Praxis and the Roots of Modern Algebra.”
2010: Co-winners – Jennifer Nielsen (University of Missouri – Kansas City), “The Heart is a Dust Board: Abu’l Wafa Al-Buzjani, Dissection, Construction, and the Dialog Between Art and Mathematics in Medieval Islamic Culture,” Palmer Rampell (Phillips Academy and Harvard University), “The Use of Similarity in Old Babylonian Mathematics,” and Stefanie Streck (Pacific Lutheran University), “The Fermat Problem.”
2009: First place – Nathan McLaughlin (University of Montana), “The Mathematical Optics of Sir William Hamilton: Conical Refraction and Quaternions”; Second place – Tim Chalberg (Pacific Lutheran University), “Regression Analysis: A Powerful Tool and Riveting Drama”; Honorable Mention – Amy Buchmann (Chapman University), “A Brief History of Quaternions and the Theory of Holomorphic Functions of Quaternionic Variables.”
2008: First place – Mame Maloney (University of Chicago), “Constructivism: A Realistic Approach to Math?”; Second place – Woody Burchett (Georgetown College), “Thinking Inside the Box: Geometric Interpretation of Quadratic Problems in BM 13901,” and Cole McGee (Colorado State University – Pueblo), “Jean Le Rond D'Alembert: Biography of a Mathematician, Philosophe, and a Man of Letters”; Honorable mention – Mame Maloney (University of Chicago), “Pathological Functions in the 18th and 19th Centuries.”
2007: Co-winners – Rory Plante, “The Libra Astronomica and its Mathematics,” and Douglas Smith (Miami University, Ohio), “Lucas’s theorem: A Great Theorem.”
2006: Co-winners – Jennifer Wiegert, “The Sagacity of Circles: A History of the Isoperimetric Problem,” and Samantha Reynolds (University of Missouri – Kansas City), “Maria Gaetana Agnesi: Female Mathematician and Brilliant Expositor of the 18^th Century.”
2005: First place – Newlyn Walkup (University of Missouri – Kansas City), “Eratosthenes and the Mystery of the Stades”; Second place – James Collingwood (Drake University), “Rigor in Analysis: From Newton to Cauchy.”
2004: Co-winners – Mark Walters, “It Appears That Four Colors Suffice: A Historical Overview of the Four-Color Theorem,” and Heath Yates (University of Missouri – Kansas City), “An Emanji Temple Tablet.”

HoM Toolbox, or Historiography and Methodology for Mathematicians

A series that guides readers through the basic principles and theoretical approaches for researching and writing the history of mathematics.

Series Purpose and Structure, by Amy Ackerberg-Hastings
Introduction to Historiography and Methodology, by Amy Ackerberg-Hastings

Keys to Mathematical Treasure Chests

A series that offers examples of how online databases of mathematical objects can be mined to unlock the collections that they preserve for use in research and teaching.

Series Introduction, by Peggy Aldrich Kidwell
19th-century String Models, by Peggy Aldrich Kidwell
Andean Khipus, by Manuel Medrano

Math Origins

Erik R. Tou explores how concepts, definitions, and theorems familiar to today's students of mathematics were developed over time.

Quotations in Context

Michael Molinsky explores the origins and meanings of various quotations about mathematics and mathematicians.

Reprints from NCTM’s Mathematics Teacher

Patricia R. Allaire and Robert E. Bradley, “Geometric Approaches to Quadratic Equations from Other Times and Places,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 308–313, 319.
David M. Bressoud, "Historical Reflections on Teaching Trigonometry," Mathematics Teacher, Vol. 104, No. 2 (September 2010), pp. 106–112, plus three supplementary sections, "Hipparchus," "Euclid," and "Ptolemy."
Richard M. Davitt, “The Evolutionary Character of Mathematics,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 692–694.
Keith Devlin, "The Pascal-Fermat Correspondence: How Mathematics Is Really Done," Mathematics Teacher, Vol. 103, No. 8 (April 2010), pp. 578–582.
Jennifer Horn, Amy Zamierowski and Rita Barger, “Correspondence from Mathematicians," Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 688–691.
Po-Hung Liu, “Do Teachers Need to Incorporate the History of Mathematics in Their Teaching?”, Mathematics Teacher, Vol. 96, No. 6 (September 2003), pp. 416–421.
Seán P. Madden, Jocelyne M. Comstock, and James P. Downing, “Poles, Parking Lots, & Mount Piton: Classroom Activities that Combine Astronomy, History, and Mathematics,” Mathematics Teacher, Vol. 100, No. 2 (September 2006), pp. 94–99.
Peter N. Oliver, “Pierre Varignon and the Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 4 (April 2001), pp. 316–319.
Peter N. Oliver, “Consequences of the Varignon Parallelogram Theorem,” Mathematics Teacher, Vol. 94, No. 5 (May 2001), pp. 406–408.
Robert Reys and Barbara Reys, “The High School Mathematics Curriculum—What Can We Learn from History?”, Mathematics Teacher, Vol. 105, No. 1 (August 2011), pp. 9–11.
Rheta N. Rubenstein and Randy K. Schwartz, “Word Histories: Melding Mathematics and Meanings,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 664–669.
Shai Simonson, “The Mathematics of Levi ben Gershon,” Mathematics Teacher, Vol. 93, No. 8 (November 2000), pp. 659–663.
Frank Swetz, “The ‘Piling Up of Squares’ in Ancient China,” Mathematics Teacher, Vol. 73, No. 1 (January 1977), pp. 72–79.