*Editors:* Janet Beery, Kathleen Clark

### Articles

Algebraic Formalism within the Works of Servois and Its Influence on the Development of Linear Operator Theory, by Anthony Del Latto and Salvatore Petrilli

This article describes how Servois’ failed attempt to construct a foundation for the calculus nevertheless may have helped shape modern mathematics.

Teaching the Fundamental Theorem of Calculus: A Historical Reflection, by Jorge López Fernández and Omar Hernández Rodríguez

The authors argue that the teaching of elementary integration should better reflect its historical development.

Georg Cantor at the Dawn of Point Set Topology, by Nicholas Scoville

How the history of analysis, and in particular that of Fourier series, can be used to motivate the study of point-set topology

When a Number System Loses Uniqueness: The Case of the Maya, by Amy Shell-Gellasch and Pedro J. Freitas

Considering non-unique representation of Maya calendar numbers may help your students understand their own number system better.

HOM SIGMAA 2012 Student Paper Contest Winners, featuring essays by Jesse Hamer and Kevin Wininger

Download the two winning essays to learn about the history of using indivisibles to find the area under an arch of the cycloid in the 17th century and of the Radon transform and its use in x-ray tomography in the 20th century.

Servois’ 1813 Perpetual Calendar, with an English Translation, by Salvatore J. Petrilli, Jr.

An image of an early 19th century perpetual calendar, together with a translation and explanation of its creator’s instructions for its use

Maya Cycles of Time, by Sandra Monteferrante

Maya calendars as they were developed over time and the Maya modified base 20 number system used in the calendars

“He Advanced Him 200 Lambs of Gold”: The Pamiers Manuscript, by Randy Schwartz

A discussion of the context and content of the 15^{th} century Pamiers manuscript, with translations of its problems, including one for which negative solutions were acceptable

An Analysis of the First Proofs of the Heine-Borel Theorem, by Nicole Andre, Susannah Engdahl, and Adam Parker

A comparison of five circa-1900 proofs of the famous theorem with a view toward improving student understanding of compactness

Learning Geometry in Georgian England, by Benjamin Wardhaugh

A comparison of the geometry found in two 18th century copybooks written with two very different purposes

### Features

Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection, by Janet Beery and Carol Mead

The well-known mathematician took most of these 343 photos of mathematicians from the 1950s through the 1980s. We welcome you to provide additional information about the photo subjects, including fond memories and interesting stories. This article was an expanding feature throughout 2012 (and through March of 2013), with new photos added every week throughout the year.

Mathematical Treasures, by Frank J. Swetz

Index to Mathematical Treasures Collection: Images of historical texts and objects from libraries, museums, and individuals around the world for use in your classroom!

Mathematical Treasures added during 2012:

- Mesopotamian Accounting Tokens: Mesopotamian accounting evolved from simple clay token counters to a number-recording system that included depictions of these tokens on clay tablets.
- The Best Known Old Babylonian Tablet?: YBC 7289, though written by a scribal student, contains an excellent estimate of the square root of 2 and shows how to use it to obtain the length of the hypotenuse of any isosceles right triangle.
- Problems from the
*Zibaldone da Canal:* Colorful images from a 14th century 'notebook' of arithmetic and other practical information
- Ratdolt's Euclid's
*Elements**:* Images of the first printed edition of Euclid's *Elements* (1482)
- Cuthbert Tunstall's
*De arte supputandi:* Images from a 1529 edition of the first arithmetic book published in England
- Oronce Fine's
*Protomathesis:* Fine presented arithmetic, geometry, trigonometry, instrument-making, and astronomy in this 1532 compendium.
- Copernicus'
*De revolutionibus:* Images from the book in which Copernicus presented his heliocentric theory, arguing that the planets, including the Earth, rotated about the Sun
*Stratioticos, *by Leonard and Thomas Digges: Images from the 1579 manual (in English) on the mathematics of war
- Robert Tanner's
*A Mirror for Mathematiques:* Images from a 16th century text about the astrolabe and its uses
- George Waymouth's
*Jewell of Artes* (1604): Images from a beautifully illustrated book of practical mathematics designed to impress King James I of England
*Specula mathematica* of Roger Bacon: A 1614 collection of Roger Bacon's 13th century writings on applications of mathematics
*Arithmetica Logarithmica* of Henry Briggs: Images from the 1624 work in which Briggs presented his base 10 logarithms, along with many examples of their use in geometry
- Edward Cocker's
*Arithmetick:* Image of the title page of the second volume (1685) of the most popular arithmetic book in England from its publication in 1673 through the 18th century
- Mary Serjant's Copybook (1688): Images from the handwritten copybook of a 15-year-old girl learning penmanship and arithmetic
- Matthew Wood's Copybook (1699): Images from a handwritten copybook presenting counting and arithmetic needed by merchants

### Reviews

*In Pursuit of the Traveling Salesman, *by William J. Cook. Reviewed by Christopher Thompson.

Author William Cook recounts the history of and computational progress on the traveling salesman problem, emphasizing connections within mathematics and with other disciplines.

*The Man of Numbers: Fibonacci's Arithmetic Revolution*, by Keith Devlin. Reviewed by Frank J. Swetz.

Author Keith Devlin brings to life the impact of the Pisan merchant and his Arabic numbers on medieval Europe.

*Mathematics Emerging: A Sourcebook 1540–1900*, by Jacqueline Stedall. Reviewed by Frank J. Swetz.

Our reviewer praises the selection of excerpts, the use of facsimiles rather than transcriptions, and the commentary and English translation in this collection.

*The Lost Millennium: History's Timeline under Siege,* by Forin Diacu. Reviewed by Branden Anglin.

This book suggests that the accepted historical chronology is fundamentally flawed.

*A Remarkable Collection of Babylonian Mathematical Texts,* by Jöran Friberg. Reviewed by Frank J. Swetz.

Our reviewer finds this collection of translations of Babylonian mathematical texts to be both "remarkable" and accessible.