Perfect numbers like perfect men are very rare.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.
What's in Convergence?
Annual Volumes and Regular Features
Articles, Announcements, and Reviews are divided into annual volumes:
The following Regular Features also can be accessed from the Convergence homepage:
Mathematics History Calendar: Upcoming mathematics history conferences and events
On This Day … what happened in mathematics history?
Collections for Classroom Use:
Images for Classroom Use
Use these images of mathematical objects, texts, and people in your classroom!
Mathematical Treasures: Images of historical objects and texts from the Columbia University Library.
The Quipu: A collection of images of Inca quipus, with references to their earliest descriptions.
Counting Boards: Two photos of a rare and fine example of a counting table the author found in a French museum.
Paul R. Halmos Photograph Collection: Photos of mathematicians from the 1950s through the 1990s.
Contents of Volume 1 - 2004
Editors: Victor J. Katz, Frank J. Swetz
Using Problems from the History of Mathematics, by Frank Swetz
Why should we use historical problems in today's classroom? This article answers that question and serves as an introduction to the problems on this website.
Can You Really Derive Conic Formulae from a Cone?, by Gary S. Stoudt
As is the case with a great deal of interesting mathematics, the conic sections are believed to have been discovered in an attempt to solve a problem, a problem that on the surface seems to have nothing to do with conic sections.
Benjamin Banneker's Trigonometry Puzzle, by Florence Fasanelli, Graham Jagger, and Bea Lumpkin
Benjamin Banneker solved some trigonometry problems in his extant notebooks. One of them is discussed here. The authors have also discovered the probable source of Banneker's trigonometry table.
Euler's Analysis of the Genoese Lottery, by Robert E. Bradley
In the middle of the 18th century, King Frederick the Great of Prussia became interested in creating a lottery to raise money. As was his custom when mathematical matters were involved, he called upon Leonhard Euler for counsel.
Van Schooten's Ruler Constructions, by C. Edward Sandifer
A translation of and commentary on Frans van Schooten's work on constructions using only a straightedge. Van Schooten's postulates for use of the straightedge, however, allow the copying of one line segment onto another.
Measuring the Globe: An Historical Activity, by Barnabas Hughes
Eratosthenes' measurement of the earth, in a form that's easy for teachers to use.
A Euclidean Approach to the FTC, by Andrew Leahy
The Fundamental Theorem of Calculus is presented in the version of Scottish mathematician James Gregory -- without the use of limits.
The Right and Lawful Rood, by Peter Ransom
The "rood", a linear measure dating from many centuries ago, is calculated anew in today's classrooms.
Using Historical Problems in the Middle School, by Karen Michalowicz and Robert McGee
Historical problems can be used to enliven any mathematics class. Here are some examples from medieval times, from a 19th century American textbook, and from a 19th century Armenian textbook, among other sources.
Alien Encounters, by Gavin Hitchcock
A dramatization, in two Acts, of the struggles of European mathematicians of the seventeenth and eighteenth centuries to come to terms with the newly admitted negative numbers.
Mathematics as the Science of Patterns, by Michael N. Fried
Mathematics is often referred to today as the "science of patterns." But has this always been true historically, or is this something that happened in recent times? The question is discussed here with reference to the work of Euclid and Jacob Steiner.
Counting Boards, by Chris Weeks
The author finds a rare and fine example of a counting table in Strasbourg. Article contains two photos of this table.
Teaching Leonardo: An Integrated Approach, by Rick Faloon
The work of the great Renaissance artist/scientist Leonardo da Vinci can be taught in secondary schools through an integrated approach of several disciplines. This article explores the approach of the Ross School.
Sherlock Holmes in Babylon, edited by Marlow Anderson, Victor Katz and Robin Wilson. Reviewed by Frank J. Swetz
A collection of articles in the history of mathematics that appeared in journals of the Mathematical Association of America over the past 90 years.
Famous Problems and Their Mathematicians, by Art Johnson. Reviewed by Frank J. Swetz
This resource consists of a series of 61 worksheets, each focused on a particular problem and related to a particular historical mathematical personality.
Stamping Through Mathematics, by Robin Wilson. Reviewed by Tim Keenan
The author takes us on a historical tour of mathematics through postage stamps of the world that display mathematicians and mathematics.
St. Andrews History of Mathematics Archive Website Reviewed by Barnabas Hughes
This website offers a collection of biographies of mathematicians and a variety of resources on the development of various branches of mathematics. It is an extremely rich and extensive site.
Statisticians of the Centuries, edited by C. C. Heyde and E. Seneta. Reviewed by Winston Richards
Thumbnail sketches of statisticians throughout history.
Historical Connections in Mathematics, by Wilbert Reimer and Luetta Reimer. Reviewed by Frank J. Swetz
Brief biographies of mathematicians with mathematical activities based on their work.
Multicultural Classroom Posters Sets 3 & 4 Reviewed by by Vincent Corrado
These posters illustrate aspects of the history of mathematics in countries from Babylonia to Ireland.
Celebrating Women in Mathematics and Science, by Miriam P. Cooney. Reviewed by Erica Voolich
This unique and beautiful book features the biographies of twenty-two notable female mathematicians and scientists, showing how their determination, creativity, and intellectual passion helped them excel in their fields.
Agnesi to Zeno, by Sanderson Smith. Reviewed by Linda Shuey
Short biographies of mathematicians with mathematical activities.
Euler: The Master of Us All, by William Dunham. Reviewed by Clifford Wagner
A small selection of Euler's works, explained by a master expositor.
Mathematics Elsewhere, by Marcia Ascher. Reviewed by Lawrence Shirley
A compilation of ethnomathematical ideas from around the world.
Four Colors Suffice, by Robin Wilson. Reviewed by Frank J. Swetz
The history of the four color problem with sketches of the attempted proofs in the nineteenth century and an outline of the computer proof of the twentieth century.
Historical Topics for the Mathematics Classroom, edited by J.K. Baumgart, D.E. Deal, B.R. Vogeli, and A.E. Hallerberg. Reviewed by Tim Keenan
This 1989 revision of the 1969 NCTM yearbook still provides wonderful suggestions for using the history of mathematics in the classroom.
The Art of the Infinite, by Robert Kaplan and Ellen Kaplan. Reviewed by Albert Briggs
This book is a collection of mathematical ideas organized around the themes of infinity and the illumination of the nature of mathematical thought.
Number from Ahmes to Cantor, by Midhat Gazalé. Reviewed by Frank J. Swetz
A lively history of number systems and number theory from earliest times up to the notion of "infinity".
Milestones of Mathematics Posters Reviewed by Lynn Godshall
Two posters illustrating the major milestones in the history of mathematics, from the first ideas of "number" to the proof of Fermat's Last Theorem.
The Nothing That Is, by Robert Kaplan. Reviewed by Austin Lobo
A history of the concept of zero from as far back as the Babylonian period, with philosophical excursions into the meaning of "nothing".
The Saga of Mathematics, by Marty Lewinter and William Widulski. Reviewed by Jim Kiernan
A brief history of mathematics aimed at college students with little technical knowledge of mathematics.
Multicultural Classroom Posters Sets 1 & 2 Reviewed by Lynn Godshall
Posters illustrating mathematics concepts in such places as China, Japan, India, and the Americas.
Historic Women of Mathematics Poster Reviewed by Karen Michalowicz
Poster picturing five famous women, from Hypatia to Grace Hopper.
Benjamin Banneker Poster Reviewed by Karen Michalowicz
Poster of Banneker, with a brief description of his life and work.
Consortium's Historical Notes Reviewed by Jim Kiernan
Collection of historical articles that appeared in Consortium, the newsletter of COMAP.
Remarkable Mathematicians, by Ioan James. Reviewed by Jim Kiernan
A collection of biographies of sixty mathematicians from the eighteenth century to the twentieth.
Colorful Characters of Mathematics Posters, by Isaac Asimov. Reviewed by Art Johnson
Whimsical posters of fifteen mathematicians with brief biographies.
The Pioneers of Calculus Posters, by Bruce White. Reviewed by Art Johnson
A collection of sixteen posters of contributors to calculus, with brief biographical sketches.
Great Ideas of Mathematics Posters Reviewed by Sylvia Lazarnick
A set of four posters dealing with the Pythagorean Theorem, infinity, prime numbers, and the history of pi.
Speaking of Mathematics Posters Reviewed by Lynn Godshall
A collection of 24 mini-posters, each containing a quotation about mathematics.
Archimedes: What Did He Do Besides Cry Eureka?, by Sherman Stein. Reviewed by Tim Keenan
Archimedes' work, The Method, explained, along with many other important ideas of the great Greek geometer.
A History of Analysis, edited by Hans Niels Jahnke. Reviewed by Jeff Suzuki
A superb collection of articles by experts on various areas of the history of analysis, from the Greeks to modern times.
Readings in the History of Mathematics Education, by James K. Bidwell and Robert G. Clason. Reviewed by Lynn Godshall
This collection of readings gives details on the history of mathematics education in the U.S. from 1828 to 1959.
Mathematical Evolutions, edited by Abe Shenitzer and John Stillwell. Reviewed by Lang Moore
A collection of articles from the American Mathematical Monthly by experts on the evolution of various fields of mathematics.
The Mathematical Century, by Piergiorgio Odifreddi. Reviewed by Gary Stoudt
The development of 30 important mathematics subjects during the twentieth century made understandable to undergraduate mathematics majors.
The Story of Mathematics, by Richard Mankiewicz. Reviewed by Anne Loesch
A wonderful survey of the history of mathematics, emphasizing its relationship with the ambient culture.
Great Moments in Mathematics Before 1650, by Howard Eves. Reviewed by Jon Choate
A collection of short lectures by Howard Eves giving details on 20 important happenings in the history of mathematics before 1650.
Cogwheels of the Mind: The Story of Venn Diagrams, by A. W. F. Edwards. Reviewed by Jim Kiernan
An introduction to the work of Venn as well as the work of the author in extending some of Venn's results.
Abel's Proof, by Peter Pesic. Reviewed by by Lynn Godshall
A discussion of the meaning of mathematical unsolvability in the context of the history of Abel's proof of the unsolvability of the quintic equation in terms of radicals.
Math and the Mona Lisa, by Bűlent Atalay. Reviewed by Frank J. Swetz
The author makes the case for Leonardo da Vinci as the first modern scientist, as he discusses Leonardo's mathematics and science.
Pascal's Arithmetical Triangle, by A. W. F. Edwards. Reviewed by Richard M. Davitt
A history of the development of Pascal's triangle in its various manifestations.
Contents of Volume 2 - 2005
Editors: Victor J. Katz, Frank J. Swetz
The Magic Squares of Manuel Moschopoulos, by P. G. Brown
This is a translation from the original Greek of a manuscript on magic squares by the Byzantine scholar Manuel Moschopoulos, written about 1315.
Benjamin Banneker's Inscribed Equilateral Triangle, by John F. Mahoney
An interesting problem from Banneker's notebook as well as other problems to use with students.
Completing the Square, by Barnabas Hughes
Explain the geometric basis of "completing the square," the original method of solving quadratic equations, to your students.
American Pi, by Larry Lesser
A song for Pi Day.
Thomas Simpson and Maxima and Minima, by Michel Helfgott
Simpson's methods for finding maxima and minima are explored by using examples from his "Doctrine and Application of Fluxions". Many of his techniques could be used in today's classroom.
Leonardo of Pisa: Bunny Rabbits to Bull Markets, by Sandra Monteferrante
The Fibonacci numbers and applications to areas such as plant growth and stock market predictions.
Archimedes' Method for Computing Areas and Volumes, by Gabriela R. Sanchis
Archimedes' use of the Law of the Lever to compute areas and volumes in The Method is discussed. Classroom ready examples are presented.
Euler's Investigations on the Roots of Equations, by Todd Doucet
This is a translation of an article of Leonhard Euler in which he attempts to prove the fundamental theorem of algebra. In addition, he discusses in detail his understanding of the nature of complex numbers.
Eratosthenes and the Mystery of the Stades, by Newlyn Walkup
In this article, which won the 2005 HOM SIGMAA Student Paper Contest, the author discusses Eratosthenes' argument to determine the size of the earth as well as possibilities for the size which Eratosthenes found (in modern measures).
Websites to Visit: Plus Magazine and National Curve Bank, by Victor J. Katz and Frank J. Swetz
There are a number of wonderful mathematics websites that readers of Convergence should be aware of. We describe two of them here, Plus Magazine and the National Curve Bank.
The Nodding Sphere and the Bird's Beak: D'Alembert's Dispute with Euler, by Robert E. Bradley
An introduction to the priority dispute between Euler and D'Alembert relating to several mathematical ideas that both worked on in the 1740s and 1750s.
This will be the fifth meeting of this kind, which brings together mathematics educators and researchers to share their teaching ideas and classroom experience in teaching mathematics based on historical, epistemological and cultural approaches.
A History of Mathematics: Brief Version, by Victor J. Katz. Reviewed by Robert McGee.
A brief version of the author's well-known history of mathematics text.
Fibonacci's Liber Abaci: Leonardo Pisano’s Book of Calculation, by Laurence Sigler. Reviewed by Frank J. Swetz.
A translation of one of the earliest European mathematical texts to use the Hindu-Arabic number system.
Everything and More: A Compact History of ∞, by David Foster Wallace. Reviewed by Gabriela Sanchis.
A survey of concepts of infinite sets over the centuries.
Science and Mathematics in Ancient Greek Culture, edited by C. J. Tuplin and T. E. Rhill. Reviewed by Barnabas Hughes.
Essays on various aspects of Greek science and mathematics, which help give a context for those aspects of Greek culture.
The Mystery of Numbers, by Marc-Alain Quaknin. Reviewed by Art Johnson.
A journey through numbers from their earliest beginning in India to the proof of Fermat's Last Theorem by Wiles.
Companion Encyclopedia of History of Math Sciences, edited by I. Grattan-Guinness. Reviewed by Frank J. Swetz.
The paperback reprint of this large collection of articles by experts on all aspects of the history and philosophy of mathematics.
The Calculus Gallery, by William Dunham. Reviewed by Gary Stoudt.
A gallery of episodes from the history of calculus.
Pi: A Biography of the World's Most Mysterious Number, by Alfred S. Posamentier and Ingmar Lehman. Reviewed by Frank J. Swetz.
A discussion not only of the mathematics of pi, but of its applications through the centuries.
A Discourse Concerning Algebra, by Jacqueline Stedall. Reviewed by Kathleen Acker.
A study of the rise of English algebra from the Medieval period to the end of the seventeenth century.
When Least is Best: How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible, by Paul J. Nahin. Reviewed by Clifford Wagner.
A survey of techniques of minimizing and maximizing over the centuries.
Musings of the Masters, edited by Raymond G. Ayoub. Reviewed by Jeff Suzuki.
Essays on various aspects of mathematical thought by prominent mathematicians of the past century.
Gauss: Titan of Science, by G. Waldo Dunnington. Reviewed by Jon Choate.
Reprint of a classic biography of Gauss, with a new foreward by Jeremy Gray.
History of Mathematical Symbolism and Terminology Website, by Jeff Miller. Reviewed by Anthony Piccolino.
Website containing much information on mathematical symbolism and terminology, as well as portraits of mathematicians from postage stamps.
The Greate Invention of Algebra, by Jacqueline Stedall. Reviewed by Frank J. Swetz.
Jacqueline Stedall has uncovered the numerous algebraic ideas of Thomas Harriot from the early 17th century and has organized them into a readable treatise.
Architecture and Mathematics in Ancient Egypt, by Corinna Rossi. Reviewed by Dorothee Jane Blum.
A study of the nature of architecture in ancient Egypt and its relationship to Egyptian mathematics.
David Joyce's Website Reviewed by Jim Kiernan.
This website contains a complete version of Euclid's Elements, with all the proofs.
Kepler's Conjecture, by George Z. Szpiro. Reviewed by Jonathan Choate.
A survey of the attempts to prove Kepler's conjecture over the past 400 years.
Trigonometric Delights, by Eli Maor. Reviewed by Dorothee Jane Blum.
A delightful survey of the history of trigonometry, along with discussions of its uses, both ancient and modern.
Math Archives: History of Mathematics Website Reviewed by Laura Smith.
A website with links to information about numerous topics in the history of mathematics.
Historical Modules for the Teaching and Learning of Mathematics, edited by Victor Katz and Karen Dee Michalowicz. Reviewed by by Lynn Godshall, David Lutz, and Neil Via.
A CD with eleven modules, each containing numerous activities designed to help secondary teachers use the history of mathematics to teach mathematics.
Complexities: Women in Mathematics, edited by Bettye Anne Case and Anne M. Leggett. Reviewed by Erica Voolich.
A collection of articles about historical and contemporary women in mathematics.
Classics of Mathematics, edited by Ronald Calinger. Reviewed by Gary Stoudt.
A sourcebook of original materials in the history of mathematics from ancient times to the early twentieth century.
History of Mathematics - Mesopotamia to Modernity, by Luke Hodgkin. Reviewed by T. M. Mills.
A new history of mathematics text that asks lots of questions about the history and the mathematics.
It's About Time, by N. David Mermin. Reviewed by James Callahan.
A great book from which to learn and teach the subject of relativity.
Contents of Volume 3 - 2006
Editors: Victor J. Katz, Frank J. Swetz
The Rule of False Position and Geometric Problems, by Vicente Meavilla Segui and Alfinio Flores
This article contains examples of the use of the rule of false position in the solution of geometric problems as found in the work of Simon Stevin. We discuss the benefits for future teachers and their students.
Approximate Construction of Regular Polygons: Two Renaissance Artists, by Raul A. Simon
Leonardo da Vinci and Albrecht Durer both offered approximate constructions of regular pentagons for the use of artists. This article explains these constructions.
John Napier: His Life, His Logs, and His Bones, by Michael J. Caulfield
A brief introduction to the life of John Napier, along with an animation of calculations using Napier's bones.
The Sagacity of Circles: A History of the Isoperimetric Problem, by Jennifer Wiegert
A summary of the history of the problem of finding the region of greatest area bounded by a given perimeter. This essay was a winner of the HOM SIGMAA Student Paper Contest in 2006.
Gerbert d'Aurillac and the March of Spain: A Convergence of Cultures, by Betty Mayfield
The story of Gerbert, who became Pope Sylvester II in 999, and his mathematics.
Dear Professor Greitzer, by Joe Richards and Don Crossfield
A letter to Sam Greitzer, late editor of Arbelos, discussing the derivation of two formulas for calculating pi.
The Quadrature of the Circle and Hippocrates’ Lunes, by Daniel E. Otero
A study of some elements of Greek geometry, as part of a course for liberal arts undergraduates dealing with basic concepts of the calculus.
An Investigation of Historical Geometric Constructions, by Suzanne Harper and Shannon Driskell
Dynamic geometry software is used to demonstrate early Greek attempts at the trisection of an angle and the squaring of a circle.
The Great Calculation According to the Indians of Maximus Planudes, by Peter G. Brown
A translation of part of a thirteenth century work by the Byzantine monk Maximus Planudes on the Hindu-Arabic numerals and the algorithms for calculation.
Fibonacci and Square Numbers, by Patrick Headley
A discussion of aspects of Leonardo of Pisa's Book of Squares.
Leonard Euler’s Solution to the Konigsberg Bridge Problem, by Teo Paoletti
A survey of the famous Konigsberg Bridge Problem and its connection to graph theory.
A Plague of Ratios, by Benjamin Wardhaugh
The story of Nicolaus Mercator, music, and logarithms.
Student Reports: A Rewarding Undertaking, by Frank J. Swetz
Some ideas on using student reports when you teach a course in the history of mathematics
How Tartaglia Solved the Cubic Equation, by Friedrich Katscher
The method of Tartaglia for solving cubics, that he eventually explained to Cardano.
Who Was Tartaglia Really?, by Friedrich Katscher
In many sources, we see that Tartaglia has the surname Fontana. According to the author of this article, the co-discoverer of the cubic formula did not ever use that name.
Karen Dee Michalowicz, by Victor J. Katz
We sadly announce the untimely death of one of Convergence's editorial board members.
From the Editors, by Victor J. Katz and Frank Swetz
The editors invite contributions, participation, and feedback from Convergence readers.
From Calculus to Computers: Using the Last 200 Years of Mathematics History in the Classroom, edited by Amy Shell-Gellasch and Dick Jardine. Reviewed by Jim Kiernan.
A collection of articles on using the history of mathematics of the past 200 years in the undergraduate classroom.
The Joy of Pi, by David Blatner. Reviewed by Frank J. Swetz.
A highly recommended new book on the history and applications of pi.
Joy of Pi Website Reviewed by Jon Choate.
This website is connected to the book, The Joy of Pi. It has numerous interesting facts about pi, with links to additional sites.
Negative Math: How Mathematical Rules Can Be Positively Bent, by Alberto A. Martinez. Reviewed by Karen Michalowicz.
The story of the negative numbers.
The Archimedes Website Reviewed by Marcus Barnes.
This website devoted to miscellanea about Archimedes contains much interesting material about his life and times.
The Equation that Couldn't Be Solved, by Mario Livio. Reviewed by Doris Schattschneider.
A history of attempts to solve cubic and higher degree polynomial equations, including the notions of group theory and their relationship to the idea of symmetry.
The Square Root of 2: A Dialogue Concerning a Number and a Sequence, by David Flannery. Reviewed by Barnabas Hughes.
A wonderful book about the square root of 2, beginning with the search for the side of a square double a given square.
A Contextual History of Mathematics, by Ronald Calinger. Reviewed by Frank J. Swetz.
An overly ambitious textbook on the history of mathematics.
The Prince of Mathematics: Carl Friedrich Gauss, by M. B. W. Tent. Reviewed by Linda Y. Shuey.
A biography of Gauss designed for high school students.
The History of Mathematics: A Brief Course, by Roger Cooke. Reviewed by Gary Stoudt.
A new edition of a brief history text, arranged topically rather than chronologically.
Awakening of Geometrical Thought in Early Culture, by Paulus Gerdes. Reviewed by Lawrence Shirley.
How does geometry begin? This work explores the origins of geometry in the work of artisans.
The Honors Class: Hilbert’s Problems and Their Solvers, by Ben H. Yandell. Reviewed by Frank J. Swetz.
This work discusses the people who solved some of Hilbert's problems from 1900, as well as the mathematics involved in the solutions.
Math Forum Website Reviewed by Gail Kaplan.
A description of this well-regarded website.
Math Pages Website Reviewed by Laura Smith.
A general mathematics website with much information on the history of mathematics.
Ancient Mathematics, by Serafina Cuomo. Reviewed by Barnabas Hughes.
A new history of Greek mathematics, taking into account the latest research.
History of Mathematics Archive Website Reviewed by Don Crossfield.
A wide-ranging site with links to many sources in the history of mathematics.
ABOUT Website on History of Mathematics Reviewed by Lawrence Shirley.
A section of a much larger website, dealing with some random topics in the history of mathematics.
Mathematics and The Historian’s Craft: The Kenneth O. May Lectures, edited by G. Van Brummelen and M. Kinyon. Reviewed by Jon Choate.
A collection of the Kenneth May lectures in the history of mathematics given at meetings of the Canadian Society for the History and Philosophy of Mathematics.
Thinking about Mathematics: The Philosophy of Mathematics, by Stewart Shapiro. Reviewed by Frank J. Swetz.
An excellent book surveying the history of the philosophy of mathematics from the time of Plato to the nineteenth and early twentieth centuries.
Contents of Volume 4 - 2007
Editors: Victor J. Katz, Frank J. Swetz
Euler Squares, by Elaine Young
An elementary introduction to Euler squares
Maya Cycles of Time, by Sandra Monteferrante
Explorations of the Mayan calendar
Abel on Elliptic Integrals: A Translation, by Marcus Emmanuel Barnes
A translation of one of the seminal papers in the field of elliptic integrals, but one that can be read by an undergraduate.
Limit Points and Connected Sets in the Plane, by David R. Hill and David E. Zitarelli
A study of Mullikan's Nautilus, using movies to illustrate the important ideas
Historical Activities for the Calculus Classroom, by Gabriela R. Sanchis
Several historical ideas of calculus, including curve sketching and optimization, explored using interactive applets and Geometers Sketchpad.
Proportionality in Similar Triangles: A Cross-Cultural Comparison, by Jerry Lodder
A comparison of the Greek and Chinese approach to the idea of similarity.
The Unique Effects of Including History in College Algebra, by G. W. Hagerty, S. Smith, D. Goodwin
Using the history of mathematics in a college algebra class has had significant positive effects on student learning.
Episodes in the History of Geometry through Models in Dynamic Geometry, by Eduardo Veloso and Rita Bastos
Four episodes in the history of geometry are discussed, where dynamic geometry helps in understanding the ideas.
Euler Tercentenary Year, by Victor J. Katz
2007 marks the three hundredth anniversary of the birth of Leonhard Euler, the most prolific mathematician of all time. There are numerous events throughout the world celebrating this anniversary, many of which are listed here.
2008 Joint Mathematics Meetings, by Victor J. Katz
There are numerous mathematics history events at the upcoming AMS-MAA Joint Mathematics Meetings in San Diego, CA.
Great Feuds in Mathematics, by Hal Hellman. Reviewed by Jim Kiernan.
A lively description of ten of the greatest feuds in mathematics.
History of Mathematics, by Charles Boyer and Uta Merzbach. Reviewed by Kathleen Acker.
Boyer's classic text, as revised by Uta Merzbach, is still worth having.
A Concise History of Mathematics, by Dirk J. Struik. Reviewed by Barnabas Hughes.
The classic work by Dirk Struik is still worth reading, especially for its attention to the social context of the development of mathematical ideas
God Created the Integers: Mathematical Breakthroughs that Changed History, edited by Stephen Hawking. Reviewed by Eugene Boman.
Original source material from seventeen mathematicians, with commentary by Stephen Hawking
Pioneers in Mathematics, by Michael J. Bradley. Reviewed by Linda Y. Shuey.
A five volume set of biographies of mathematicians from ancient times to the twentieth century, aimed at secondary students.
Arthur Cayley: Mathematician Laureate of the Victorian Age, by Tony Crilly. Reviewed by Kathleen M. Clark.
A biography of Arthur Cayley, the outstanding mathematician of Victorian Britain
King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, by Siobhan Roberts. Reviewed by Jonathan Choate.
A biography of the geometer Donald Coxeter.
A Radical Approach to Real Analysis, by David Bressoud. Reviewed by James Callahan.
A historically minded textbook designed to teach real analysis by considering some of the problems faced by 19th century mathematicians.
Unknown Quantity; A Real and Imaginary History of Algebra, by John Derbyshire. Reviewed by Don Crossfield.
A history of algebra from its early beginnings to the twentieth century.
Equations from God: Pure Mathematics and Victorian Faith, by Daniel J. Cohen. Reviewed by Barnabas Hughes.
A study of Victorian idealism and its relation to religion, as exemplified in the work of three 19th century British mathematicians.
An Introduction to the History of Mathematics, by Howard Eves. Reviewed by Gary Stoudt.
Howard Eves' sixth edition is still worth considering for a textbook.
The Secret Life of Numbers, by George G. Szpiro. Reviewed by Edith Prentice Mendez.
Short sketches on how mathematicians work and think.
Prime Numbers: The Most Mysterious Figures in Math, by David Wells. Reviewed by Gabriela R. Sanchis.
An introduction to the prime numbers in many of their aspects.
Jewish Mathematician in a Victorian World, by Karen Hunger Parshall. Reviewed by Gail Kaplan.
The first detailed biography of James Joseph Sylvester.
Yearning for the Impossible: The Surprising Truths of Mathematics, by John Stillwell. Reviewed by Lynn Godshall.
This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress.
The Early Mathematics of Leonhard Euler, by C. Edward Sandifer
The Genius of Euler: Reflections on his Life and Work, edited by William Dunham
Reviewed by Frank J. Swetz
Two excellent volumes on Euler in honor of his three hundredth birthday.
Unexpected Links between Egyptian and Babylonian Mathematics, by Jöran Friberg. Reviewed by Lawrence Shirley.
This book demonstrates the relationship between the mathematics in some recently discovered Babylonian tablets and some standard problems from Egyptian mathematics.
Measuring America, by Andro Linklater. Reviewed by Frank J. Swetz.
The beginnings of land measurement in the early United States and how this affected American democracy.
The Life of Numbers, written by Alberto Manguel, Antonio Duran and George Ifrah; illustrated by Sean Macksouli, Natalia Pintado, and Javier Pagola. Reviewed by Frank J. Swetz.
A creative expression combining text, design and illustrations, originally designed for the International Congress of Mathematicians in Madrid.
Amazing Traces of a Babylonian Origin in Greek Mathematics, by Jöran Friberg. Reviewed by Barnabas Hughes.
Aspects of classical Greek mathematics are compared with areas of Babylonian mathematics.
The Poincare Conjecture: In Search of the Shape of the Universe, by Donal O’Shea. Reviewed by Eugene Boman.
The history of the Poincare conjecture up to its recent proof by Grigori Perelman.
Euler Tercentenary Volume 3:
How Euler Did It, by C. Edward Sandifer. Reviewed by Frank J. Swetz.
A collection of short pieces each detailing how Euler solved a particular mathematics problem.
A History of Mathematics, by Jeff Suzuki. Reviewed by Gary Stoudt.
A solid history of mathematics text that any instructor of a history course should consider.
The Development of Mathematics in Medieval Europe, by Menso Folkerts. Reviewed by Frank J. Swetz.
A collection of articles on mathematics in Europe from the twelfth to the fifteenth century.
The Pythagorean Theorem: A 4,000 Year History, by Eli Maor. Reviewed by Jim Kiernan.
A survey of this theorem's 4000 year history, with applications to many fields.
Mathematics: Powerful Patterns in Nature and Society, by Harry Henderson. Reviewed by Linda Y. Shuey.
The work of ten scientists who thought deeply about patterns.
The Mathematics of Egypt, Mesopotamia, China, India and Islam, edited by Victor J. Katz. Reviewed by Barnabas Hughes.
A new collection of original source materials in the mathematics of five civilizations.
Calculus Gems: Brief Lives and Memorable Moments, by George F. Simmons Reviewed by Kathleen M. Clark.
A collection of short biographical sketches of people involved in the development of calculus, as well as brief descriptions of important events in that development.
Euler and Modern Science, edited by N.N. Bogolyubov, G.K. Mikhailov, and A.P. Yushkevich
Euler at 300: An Appreciation, edited by Robert Bradley, Lawrence D’Antonio, and C. Edward Sandifer
Reviewed by Frank J. Swetz
The two final volumes of the MAA tercentenary series on Euler present numerous papers on various aspects of Euler's life and work.
The Mathematician's Brain, by David Ruelle. Reviewed by Kathleen Acker.
A book delving into the working of the mathematical mind.
How Mathematics Happened: The First 50,000 Years, by Peter S. Rudman. Reviewed by Gail Kaplan.
A popular history of ancient mathematics, dealing with the mathematics of ancient Egypt and Babylonia.
Math for Mystics: From the Fibonacci Sequence to Luna's Labyrinth to the Golden Section and Other Secrets of Sacred Geometry, by Renna Shesso. Reviewed by Edith Prentice Mendez.
A book connecting mathematics to mysticism, but not recommended.
Numbers at Work: A Cultural Perspective, by Rudolf Taschner. Reviewed by Jonathan Choate.
Essays on how number has been critical to the work of scientists through the ages.
Hypatia of Alexandria: Mathematician and Martyr, by Michael A. B. Deakin. Reviewed by Eugene Boman.
A biography of Hypatia in her times that carefully distinguishes between the known facts of her life and the many speculations about her.
Contents of Volume 5 - 2008 (Loci - Volume 1)
Editors: Victor J. Katz, Frank J. Swetz
Apollonius's Ellipse and Evolute Revisited, by Frederick Hartmann and Robert Jantzen
Apollonius found how to draw normals to an ellipse from points in the ellipse by using hyperbolas. A modern version is presented here.
What is 0^0?, by Michael Huber and V. Frederick Rickey
The expression 0^0 is usually called an indeterminate form. This article details the history of the meaning of this expression and concludes that, in some cases, we should evaluate it as 1.
Leonardo da Vinci’s Geometric Sketches, by Frank J. Swetz
Leonardo da Vinci illustrated Luca Pacioli’s 1509 De divina proportione. Several of his illustrations are shown here.
Mathematics Education at West Point: The First Hundred Years, by V. Frederick Rickey and Amy Shell-Gellasch
A survey of the mathematics education of cadets in the first century after the founding of the U.S. Military Academy.
HOM SIGMAA Student Paper Contest Winners, by Victor J. Katz
There are four winners of the HOM SIGMAA Student Paper Contest for 2008. The winning papers may be accessed here.
A discussion of a collaborative effort in Italy to produce materials enabling secondary school teachers to use the history of mathematics in the classroom.
Triangles in the Sky: Trigonometry and Early Theories of Planetary Motion, by Sandra M. Caravella
A survey of early theories of planetary motion, with dynamic figures to help in understanding these motions.
Apportioning Representatives in the United States Congress, by Michael J. Caulfield
The history of apportionment of representatives in the U.S. Congress, from the 1790s until today, along with a discussion of the mathematics involved in the various methods.
The Quipu, by Frank J. Swetz
A collection of illustrations of Inca quipus, with references to their earliest descriptions.
A discussion of why we use "e" to represent the base of the natural logarithm system.
The quadrennial meeting of the International Study Group on the Relations between History and Pedagogy of Mathematics will be in Mexico City, July 14-18, 2008.
Benjamin Franklin's Numbers: An Unsung Mathematical Odyssey, by Paul C. Pasles. Reviewed by Eugene Boman.
A thorough study of Benjamin Franklin's mathematical accomplishments, in particular his work on magic squares.
Hands on History, A Resource for Teaching Math, edited by Amy Shell-Gellasch. Reviewed by Don Crossfield.
A collection of articles about mathematical models and objects and how they can be used in teaching.
A History of Abstract Algebra, by Israel Kleiner. Reviewed by Ueli Daepp.
A history of the various algebraic structures that came together to give us "abstract algebra" by early in the twentieth century.
The World of Maria Gaetana Agnesi, Mathematician of God, by Massimo Mazzotti. Reviewed by Kathleen Ambruso Acker.
A biography stressing Agnesi's deep commitment to help those in need.
Museum of the History of Science, Oxford. Reviewed by Frank J. Swetz.
There is much to see in this museum related to the history of mathematics.
A Biography of Maria Gaetana Agnesi, by Antonella Cupillari. Reviewed by Edith Prentice Mendez.
A biography of the 18th century author of an early calculus text, with some translations from the text.
Tools of American Mathematics Teaching, 1800-2000, by Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts. Reviewed by Don Crossfield.
A survey of the use of technology in American mathematics teaching over the past 200 years.
Sacred Mathematics: Japanese Temple Geometry, by Fukagawa Hidetoshi and Tony Rothman. Reviewed by Frank J. Swetz.
This book describes some of the so-called temple geometry problems that Japanese mathematicians posed and solved beginning in the seventeenth century.
Mathematical Expeditions: Chronicles by the Explorers, by Reinhard Laubenbacher and David Pengelley. Reviewed by Jim Kiernan.
A collection of original texts to help students learn some important areas of mathematics.
Mathematics in Ancient Iraq: A Social History, by Eleanor Robson. Reviewed by Frank J. Swetz.
A new history of mathematics in ancient Mesopotamia, concentrating on its social aspects.
Contents of Volume 6 - 2009 (Loci - Volume 1)
Editors: Victor J. Katz, Frank J. Swetz, Janet Beery, Kathleen Clark
James Gregory and the Pappus-Guldin Theorem, by Andrew Leahy
An analysis of James Gregory's proof of the Pappus-Guldin Theorem, along with the original documents in both Latin and English.
A Locally Compact REU in the History of Mathematics: Involving Undergraduates in Research, by Betty Mayfield and Kimberly Tysdal
A description of a Research Experience for Undergraduates conducted in 2007 at Hood College.
Sums of Powers of Positive Integers, by Janet Beery
A history of attempts to develop formulas expressing the sums of powers of the first n positive integers from the Pythagoreans to Jakob Bernoulli.
Investigating Euler's Polyhedral Formula Using Original Sources, by Lee Stemkoski
The works of Leonhard Euler are particularly accessible to readers as his papers usually contain many examples as well as a gradual progression of ideas. The author shows how teachers can use Euler's original works in the classroom to explore the polyhedral formula and related results.
HOM SIGMAA 2009 Award Winners, by Amy Shell-Gellasch
These are the winning papers from the annual History of Mathematics Special Interest Group of the MAA (HOM SIGMAA) 2009 Student Paper Contest.
A Modern Vision of the Work of Cardano and Ferrari on Quartics, by Harald Helfgott and Michel Helfgott
A study of the solution of quartic equations in Cardano's Ars Magna and in the work of Euler and Descartes.
The Classic Greek Ladder and Newton’s Method, by Robert J. Wisner
Greek ladders for approximating square roots may be more ancient than the ancient Greeks. Students at any level can appreciate their beauty and simplicity. Those who have studied calculus can compare them with Newton’s Method for approximating roots.
After completing this assignment on Simon Stevin's treatment of decimal numbers in his 1585 De Thiende, the author's preservice mathematics teachers understood why our usual procedure for multiplying such numbers works.
The Mayan and Other Ancient Calendars, by Geoff Stray. Reviewed by Lawrence Shirley.
A detailed study of the cycles of the Mayan calendar, along with some other ancient calendars.
Euler's Gem: The Polyhedron Formula and the Birth of Topology, by David S. Richeson. Reviewed by Clifford Wagner.
A sketch of the history of topology, beginning with the polyhedron formula and continuing up to the present.
Mathematics in India, by Kim Plofker. Reviewed by Frank J. Swetz.
A survey of over two thousand years of the history of mathematics on the Indian subcontinent.
The Mathematics of the Heavens and the Earth: the Early History of Trigonometry, by Glen Van Brummelen. Reviewed by Frank J. Swetz.
A comprehensive history of trigonometry from ancient times to the Renaissance.
Mathematical Works Printed in the Americas, 1554-1700, by Bruce Stanley Burdick. Reviewed by Frank J. Swetz.
A bibliographical reference to mathematics books printed in the New World before 1700.
Mathematicians: An Outer View of the Inner World, by Mariana Cook. Reviewed by Frank J. Swetz.
Portraits of 92 living mathematicians, with autobiographical comments.
Pythagoras' Revenge: A Mathematical Mystery, by Arturo Sangalli. Reviewed by James F. Kiernan.
A fictionalized account of Pythagoras and Pythagorean beliefs.
Euclidean and Non-Euclidean Geometries: Development and History, by Marvin Jay Greenberg. Reviewed by Eugene Boman.
This textbook seamlessly combines the history of non-Euclidean geometry with the mathematical ideas.
Contents of Volume 7 - 2010 (Loci - Volume 2)
Editors: Janet Beery, Kathleen Clark
Discovering the Beauty of Science, by Christine Latulippe and Joe Latulippe
The authors' math history class visited the "Beautiful Science" exhibit at the Huntington Library in Southern California. Find actual math history texts and artifacts near you and virtual ones online to share with your students.
Images from Kepler’s 1609 New Astronomy.
The Geometry of Rene Descartes, by Frank J. Swetz
Images from a 1659 Latin edition of Descartes’ Geometria, originally published in 1637 in French as La géométrie.
The author uses her poem, "The Enigmatic Number e," to show how poetry about the history of mathematics can be used to enrich and enliven mathematics instruction.
Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation, by Robert E. Bradley and Salvatore J. Petrilli, Jr.
The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.
HOM SIGMAA 2010 Student Paper Contest Winners, featuring essays by Jennifer Nielsen, Palmer Rampell, and Stefanie Streck
Download the three winning essays from the 2010 HOM SIGMAA Student Paper Contest to learn about medieval Islamic dust boards, Old Babylonian similarity, and the Fermat Problem.
Extracting Square Roots Made Easy: A Little Known Medieval Method, by Friedrich Katscher
A method for extracting square roots used in Italy through the 18th century was introduced in a manuscript by the 12th century mathematician al-Hassar.
Logarithms: The Early History of a Familiar Function, by Kathleen Clark and Clemency Montelle
The authors recount the ‘great tale’ of Napier’s and Burgi’s parallel development of logarithms and urge you to use it in class.
François-Joseph Servois: Priest, Artillery Officer, and Professor of Mathematics, by Salvatore J. Petrilli, Jr.
This biography reveals that, during his life as a military officer and mathematician, Servois fought for Paris and for the foundations of calculus.
A Disquisition on the Square Root of Three, by Robert J. Wisner
The author compares Greek ladder, continued fraction, and Newton's Method approximations, pointing out that the Greek ladder easily produces both of Archimedes' famous bounds.
The author presents five modules based on mathematics from medieval Islamic cultures for use in a variety of high school and college mathematics courses.
Maya Calendar Conversions, by Ximena Catepillan and Waclaw Szymanski
Students learn about Maya calendar systems, including how to convert Maya Long Count dates to Calendar Round (Tzolkin and Haab calendar) dates, on a trip to the Yucatan.
Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation, by Robert E. Bradley and Salvatore J. Petrilli, Jr.
A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange
The Music of Pythagoras, by Kitty Ferguson. Reviewed by Gail Kaplan.
Subtitled How an Ancient Brotherhood Cracked the Code of the Universe and Lit the Path from Antiquity to Outer Space, this is a book of entertaining stories more so than scholarly research.
Routes of Learning: Highways, Pathways, and Byways in the History of Mathematics, by Ivor Grattan-Guinness. Reviewed by Frank J. Swetz.
In this collection of essays on modern trends and issues in the history of mathematics, consideration of mathematics history in the classroom is often more theoretical than practical.
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics, by Clifford A. Pickover. Reviewed by Frank J. Swetz.
In this fascinating and accessible book, the author devotes one page of lively and informative text and one striking, full-page illustration to each milestone.
Agora, directed by Alejandro Amenábar, written by Amenábar and Mateo Gil. Reviewed by Shirley Gray.
Our reviewer reports that the movie, Agora, about the mathematician Hypatia of Alexandria (c. 400 AD), is spectacular and intriguing but that Hypatia could and should have been portrayed as the heroine she truly was.
The Babylonian Theorem: The Mathematical Journey to Pythagoras and Euclid, by Peter S. Rudman. Reviewed by Frank J. Swetz.
The author constructs a possible and plausible path from the mathematics of the ancient Babylonians of 2000-1600 BCE to that of Pythagoras, Euclid, and the ancient Greeks of 600-300 BCE.
Nine examples of using mathematics history in the mathematics classroom -- for those who read French!
Contents of Volume 8 - 2011 (Loci - Volume 3)
Editors: Janet Beery, Kathleen Clark
SMURCHOM: Providing Opportunities for Undergraduate Research in the History of Mathematics, by Sloan Evans Despeaux
This article describes an MAA Regional Undergraduate Mathematics Conference (RUMC) featuring history of mathematics, and offers great ideas for getting students in your mathematics history course started on their research papers and projects.
Peano on Wronskians: A Translation, by Susannah M. Engdahl and Adam E. Parker
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Teaching and Research with Original Sources from the Euler Archive, by Dominic Klyve, Lee Stemkoski, and Erik Tou
How faculty and students can use and contribute to the MAA Euler Archive!
HOM SIGMAA 2011 Student Paper Contest Winners, featuring essays by Paul Stahl, Sarah Costrell, and Rick Hill
Download the three winning essays to learn about Kepler's mathematical astronomy, the roots of modern algebra, and the Quadrivium of Isidore of Seville.
Extending al-Karaji’s Work on Sums of Odd Powers of Integers, by Hasan Unal and Hakan Kursat Oral
The authors share their discovery of an 1867 article in a Turkish scientific journal that extends al-Karaji's famous formula for the sum of the cubes to sums of higher odd powers.
Kepler: The Volume of a Wine Barrel, by Roberto Cardil
In his analysis of volumes of wine barrels, Kepler used ideas that would become important in differential and integral calculus. This article provides you with visual imagery, much of it animated, to help share Kepler's ideas with your students.
When Nine Points Are Worth But Eight: Euler's Resolution of Cramer's Paradox, by Robert E. Bradley and Lee Stemkoski
How Euler resolved the paradox first noted by Maclaurin that nine points should determine a curve of order three, yet two such curves can intersect in nine points. Includes a translation of Euler's 'lost' letter to Cramer on this subject.
Eratosthenes' Geography, by Duane W. Roller. Reviewed by Frederick Sakon.
Subtitled Fragments collected and translated, with commentary and additional material, this book provides the first English translation of Eratosthenes' Geography and includes "On the Measurement of the Earth."
The Chinese Roots of Linear Algebra, by Roger Hart. Reviewed by Frank Swetz.
An excellent, careful, and penetrating study of matrix methods for solving systems of linear equations in first century China.
The Genesis of Science: The Story of Greek Imagination, by Stephen Bertman. Reviewed by Angelina Kuleshova.
Review of Bertram's text on the history of Greek science.
L’algèbre au temps de Babylone: Quand les mathématiques s’écrivaient sur de l’argile, by Jens Høyrup. Reviewed by Marc Moyon.
Revised and expanded French translation of the author's original 1998 book for Danish high school teachers. The title in English is Algebra in the Time of Babylon: When Mathematics Were Written on Clay.
Contents of Volume 9 - 2012 (Loci - Volume 4)
Editors: Janet Beery, Kathleen Clark
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 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
Considering non-unique representation of Maya calendar numbers may help your students understand their own number system better.
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.
An image of an early 19th century perpetual calendar, together with a translation and explanation of its creator’s instructions for its use
Maya calendars as they were developed over time and the Maya modified base 20 number system used in the calendars
A discussion of the context and content of the 15th century Pamiers manuscript, with translations of its problems, including one for which negative solutions were acceptable
A comparison of five circa-1900 proofs of the famous theorem with a view toward improving student understanding of compactness
A comparison of the geometry found in two 18th century copybooks written with two very different purposes
Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection, by Janet Beery and Carol Mead
An expanding and interactive feature with new photos every week throughout the year and the opportunity for you to provide additional information about them
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.
This book suggests that the accepted historical chronology is fundamentally flawed.
Our reviewer finds this collection of translations of Babylonian mathematical texts to be both "remarkable" and accessible.
Contents of Volume 10 - 2013 (Loci - Volume 4, continued)
Editors: Janet Beery, Kathleen Clark
Who's That Mathematician? Images from the Paul R. Halmos Photograph Collection, by Janet Beery and Carol Mead
An expanding and interactive feature with new photos every week through early March of 2013 and the opportunity for you to provide additional information about them