Editor: Janet Beery
Associate Editors: Amy Ackerberg-Hastings, Janet Barnett, Kathleen Clark, Lawrence D'Antonio, Douglas Ensley, Victor Katz, Daniel Otero, Randy Schwartz, Lee Stemkoski, Frank Swetz
Founding Editors: Victor Katz, Frank Swetz
An Investigation of Subtraction Algorithms from the 18th and 19th Centuries, by Nicole M. Wessman-Enzinger
This survey of four subtraction algorithms used in North America includes as sources both handwritten "cyphering books" and printed arithmetic texts.
Connecting Greek Ladders and Continued Fractions, by Kurt Herzinger and Robert Wisner
An exploration of two historical techniques for estimating irrational numbers and a link between them
Did Euler Know Quadratic Reciprocity?: New Insights from a Forgotten Work, by Paul Bialek and Dominic W. Klyve
The authors use their newly translated paper of Leonhard Euler to answer their title question.
Cubes, Conic Sections, and Crockett Johnson, by Stephanie Cawthorne and Judy Green
Author and illustrator Johnson, author of Harold and the Purple Crayon, posed a question about Euclid, cubes, and conic sections, and painted an answer!
When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox, by Robert Bradley and Lee Stemkoski
Interactive graphics illustrate the seeming paradox that 9 points should determine a curve of order 3, yet two curves of order 3 can intersect in up to 9 distinct points.
David Hilbert's Radio Address, by James T. Smith
Read and listen to this famous 1930 address, with its dramatic conclusion: "Wir müssen wissen; wir werden wissen." ("We must know; we will know.")
Read winning student papers on the statistics of Florence Nightingale and on Legendre's attempts to prove Euclid's Fifth Postulate.
Celebrating a Mathematical Miracle: Logarithms Turn 400, by Glen Van Brummelen
Why John Napier's invention of logarithms in 1614 was hailed as a miracle by astronomers and mathematicians
Wibold's Ludus Regularis, a 10th Century Board Game, by Richard Pulskamp and Daniel Otero
Players competed for virtues in this dice game for clerics.
How to Improve a Math History Assignment, by Christopher Goff
Moving college students' original source mathematics history projects beyond "reporting" to "engagement"
Historical Activities for the Calculus Classroom, by Gabriela R. Sanchis
History and mathematics of curve sketching, tangent lines, and optimization, explored using interactive applets
A Pair of Articles on the Parallelogram Theorem of Pierre Varignon, by Peter N. Oliver
Mathematical life of Varignon, plus ideas for classroom activities and extensions of his famous theorem
Unreasonable Effectiveness of Knot Theory, by Mario Livio
Knot theory has become surprisingly useful in explaining string theory.
Proofs Without Words and Beyond, by Tim Doyle, Lauren Kutler, Robin Miller, and Albert Schueller
History and philosophy of visual proofs, together with dynamic, interactive "proofs without words 2.0"
Van Schooten's Ruler Constructions, by C. Edward Sandifer
Translation of and commentary on Frans van Schooten's work on constructions using only a straightedge -- and a postulate that allows the copying of one line segment onto another.
Led Astray by a Right Triangle: Misconception, Epiphany, and Redemption, by Frank J. Swetz
A well-known historian initially erred in his study of ancient Chinese mathematics.
Euclid21: Euclid's Elements for the 21st Century, by Eugene Boman, Alexandra Milbrand, Tyler Brown, Siddharth Dahiya, Joseph Roberge, and Mary Boman
A dynamic, interactive Euclid's Elements organized as a directed graph via its logical structure
Online Museum Collections in the Mathematics Classroom, by Amy Ackerberg-Hastings and Amy Shell-Gellasch
The Smithsonian Institution's National Museum of American History website features dozens of object groups, collections of digitized object images and detailed catalog records, related to mathematics. View sample objects and read suggestions for using these resources in your teaching.
Mathematical Treasures from the National Museum of American History, Smithsonian Institution, by Amy Ackerberg-Hastings, Judy Green, Peggy Kidwell, and Amy Shell-Gellasch
Ishango Bone (20000-25000 years ago, Congo)
Old Babylonian Area Calculation (circa 1800-1600 BCE)
Ptolemy's Almagest (1515 edition of 2nd century work)
The Arithmetic of Boethius (circa 500 CE)
Zhu Shijie’s Introduction to Mathematical Studies (1299, China)
Sacrobosco's 13th Century Astronomy (1484 copy)
Sacrobosco's 13th Century Arithmetic (1490 copy)
Al-Banna's Lifting of the Veil in the Operations of Calculation (c. 1300, North Africa)
Islamic Astronomical Chart (15th century)
Piero della Francesca's illustrated Works of Archimedes (late 1450s, Italy)
Italian Arithmetica Pratica (1575 manuscript)
Al-‘Amili's Quintessence of Calculation (circa 1600, Persia)
Ricci's and Xu's Theory of Surveying (circa 1610)
Edmund Gunter's Measuring Instruments (1624/1636)
Thomas Harriot's Algebra (1631)
William Oughtred's Clavis Mathematicae (1631/1667)
Daniel Schwenter’s Delicia (1636 and 1651)
Galileo's Collected Works (1656)
Isaac Barrow on Mathematics Education (1685/1734)
De Moivre's Doctrine of Chances (1711/1756)
Logic for American Independence (1748/1811)
Playfair on Teaching Geometry (1795/1832)
Lagrange's Theorie des Fonctions Analytiques (1797/1813)
Lazare Carnot's Geometry (1803)
Monge on Differential Geometry (1807/1809)
Jeremiah Day's Introduction to Algebra (1814/1834)
Bolzano's Three Problems (1817)
Cauchy's Cours d'Analyse (1821)
Poncelet's Projective Geometry (1822/1865)
Davies' American Textbooks (1826-1840)
Babbage's Tables of Logarithms (1827/1872)
Julius Plucker on Geometry (1835 and 1839)
Salmon's Treatise on Conic Sections (1848/1869)
Michel Chasles’ Higher Geometry (1852/1880)
George Boole’s Differential Equations (1859/1877)
Klein's Non-Euclidean Geometry (1892-1893)
Poincaré on Probability (1907/1912)
Review of Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander. Reviewed by Frank J. Swetz.
How 17th century European proponents of indivisibles and infinitesimals clashed with Thomas Hobbes, Christopher Clavius, and the Catholic Church