I am acutely aware of the fact that the marriage between mathematics and physics, which was so enormously fruitful in past centuries, has recently ended in divorce.
Missed Opportunities, 1972
Discovering the Beauty of Science
The Huntington Library, Art Collections, and Botanical Gardens are located in San Marino, California, about a 30 minute drive east of downtown Los Angeles. The Huntington is home to many literary and artistic treasures such as a Gutenberg Bible, an Ellesmere manuscript of Chaucer’s Canterbury Tales, Gainsborough’s Blue Boy, and Lawrence’s Pinkie to name a few. Although these items deserve special attention, and a day could be spent in the gardens alone, we are particularly interested in the new exhibit found in the Dibner Hall of the History of Science, “Beautiful Science: Ideas that Changed the World.” In Spring 2009 we visited the Huntington with students enrolled in a graduate level history of mathematics course at Cal Poly Pomona. This article describes the Beautiful Science exhibit, some background on the course, and some suggestions for creating your own math history field trip.
Figure 1. An exhibit on early telescopes in the Astronomy Gallery of the Beautiful Science exhibit (© The Huntington Library)
Beautiful Science at the Huntington Library
Opened in Fall 2008, “Beautiful Science: Ideas that Changed the World” is now part of the permanent exhibitions at the Huntington Library. The aptly named exhibit showcases four areas to discover and explore: astronomy, light, medicine, and natural history. Not only is the material accessible to those less familiar with the sciences, it also includes some real gems for those who have a deep appreciation for the sciences, including mathematics. Of particular interest to mathematically minded visitors may be the appearance of familiar names from the history of mathematics in multiple areas of the exhibit. For example, works by Sir Isaac Newton and Johannes Kepler appear in both the astronomy and light sections; Rene Descartes’ works are in both medicine and light. The Beautiful Science exhibit helps to highlight the broad-ranging capabilities of these prolific mathematicians, and also the pervasiveness of mathematical ideas throughout the sciences.
Figure 2. The Light Gallery in the Beautiful Science exhibit (© The Huntington Library)
Visitors are invited to tour the four rooms of the Beautiful Science exhibit at their own pace, viewing original books and documents including:
The astronomy exhibit contains a replica of Galileo’s refracting telescope through which you can get a view of “the moon” at a scale and quality similar to that at which Galileo saw it. The optics area includes prisms and mirrors for experimentation. In each room there are stations where visitors can hear portions of classic texts read aloud; in the medicine section, guests can touch and smell medicinal herbs, some of which can be found while walking the over 207 acres of the Huntington Botanical Gardens. After our field trip to the Huntington Library, one student reflected that he “found it exciting to watch some of the children playing with the demonstrations with a parent, asking questions and developing a curiosity for science.”
Figure 3. In the Medicine Gallery, apothecary jars are filled with the medicinal herbs chamomile, rosemary, bay leaf, and lavender. (© The Huntington Library)
One hall in the Beautiful Science area includes overstuffed chairs and a wall of bookshelves with old and new books where visitors can sit and discover the beauty of science. One example is the Encyclopedia, or a systematic dictionary of the sciences, arts, and crafts, by Denis Diderot (1765). Readers may gently peruse the volume on display (one of 35 volumes), which includes diagrams and sketches of mathematical ideas, terms, and tools (see Figure 5, below).
Figure 4. The Reading Room in the Beautiful Science exhibit (© The Huntington Library)
One student reflected that “the exhibits had a well-balanced amount of material, which kept my interest. The audio interactions, coupled with the interactive exhibits such as Galileo’s telescope replica, the microscope, the computers, and books, made the experience memorable.” Another commented that the “layout reflects strategy and organization by the exhibit’s designers; Beautiful Science contains a lot of information, yet it is not overwhelming.”
Figure 5. Diagrams of conic sections in Denis Diderot's 1765 Encyclopedia
Historic Texts at the Huntington Library
In addition to exploring the beauty of science, visitors to the Huntington Library can admire the detail and opulence of historic texts and documents including fonts, colors, illustrations, fold-outs, and “pop-ups” that any graphic designer or layman will appreciate. As an example, the Munger Research Center at the Huntington holds a 1570 copy of Billingsley’s edition of Euclid’s Elements that contains pop-ups of three-dimensional geometric objects such as pyramids and perpendicular planes. Within the Beautiful Science exhibit, Isaac Newton’s "An Account of a New Kind of Telescope, invented by Mr. Isaac Newton" in the 1672 Philosophical Transactions contains a page that folds out to reveal a larger diagram than the regular page size will allow (see Figure 6, below). These special bookmaking effects can only truly be appreciated when viewing a manuscript in person; photographs don’t do justice to the sight, smell, and feel of authentic historical documents.
For a truly memorable experience, the 90,000 square foot Munger Research Center at the Huntington Library allows university faculty and scholars access to its documents and resources by appointment. Details can be found at the Huntington web site. This is an opportunity to view firsthand these scientific and artistic treasures in their original state. The Huntington’s science collections include the recently acquired 67,000 volume Burndy Library from the Dibner family of Connecticut, which consists of an extensive collection in the history of science and technology. After touring the Beautiful Science exhibit, we spent some time with the library’s Dibner Curator of the History of Science and Technology, Daniel Lewis, and were able to see some specific texts like a copy of Billingsley’s 1570 “pop-up” edition of Euclid’s Elements. This special experience was exciting for students and a nice culmination to our classroom and museum exploration of texts that allow us to understand the history of mathematics. As one student reflected, “It was amazing… [to be] one of the rare people to see these valuable books so closely.”
The History of Mathematics Course
Our visit to the Huntington was part of a graduate level history of mathematics course at Cal Poly Pomona. Throughout the ten-week quarter students read and discussed original mathematical works from Jacqueline Stedall’s Mathematics Emerging: A Sourcebook 1540-1900, learning about the mathematics and mathematicians of the Age of Enlightenment. Mathematics Emerging provides some historical narrative, but is primarily a collection of facsimiles of mathematical texts alongside their modern translations. The balance between reading, writing and arithmetic throughout the quarter left students feeling that “the materials from the course, extra readings, and class activities made the Huntington Library exhibit an impressive and memorable experience.”
For each seminar-style class meeting, students read and analyzed topics ranging from Euclid’s definitions and Descartes’ notation through Euler’s definition of a function and the calculus of Newton and Leibniz. Throughout the quarter, students submitted weekly written reflections on the readings and class discussions. Students were encouraged to investigate external resources while reading, in order to answer their own questions and to stimulate in-class discussion. As a group, we were not always able to answer our reading questions in a satisfactory manner, and in our meeting with Curator Lewis at the Huntington, we were pleased to have one of our unanswered questions answered. In many of the texts shown in Mathematics Emerging, there is a word or two in the bottom right corner of a page that repeats at the top of the next page (see, for instance, Figure 7, below). Lewis explained to us that this is called a “catch phrase” and helps to aid in flow when reading and smooth the transition between pages.
Figure 7. Moon drawings from Galileo Galilei’s 1610 Sidereus Nuncius (Starry Messenger) (photo by Christine Latulippe)
Before our field trip, each student researched and presented biographies of two eighteenth century mathematicians highlighted in Mathematics Emerging, including Abraham deMoivre, the Bernoullis, Jean Fourier, and Joseph Lagrange; as a class, we created a biography of Isaac Newton. The fact that one of the students had researched and presented a biography of DeMoivre added to the excitement of being in the same room with a first edition of his Doctrine of Chance when we met with the curator at the Huntington.
The Beautiful Science exhibit is accompanied by an interactive web site allowing for further investigation of the interrelated nature of people and ideas. The timelines provided on the Beautiful Science web site present a clear picture of the key players in each of the four highlighted areas of the exhibit, astronomy, light, medicine, and natural history. Although the web site complements the actual exhibit, there is no feeling of redundancy; we visited the web site as part of our preparation for our trip to the Huntington.
Figure 8. A proposition on ellipses in a section on conic sections in a first edition of Isaac Newton's Principia Mathematica (Mathematical Principles), 1687 (© The Huntington Library)
As additional preparation for our visit to the Huntington Library, we devoted two weeks to ideas related to Galileo and astronomy (including watching PBS NOVA’s “Galileo’s Battle for the Heavens”) and to Chapter 5 of Stedall’s Mathematics Emerging, which focuses on Book I of Newton’s Principia. As with our other course readings, students worked through Newton’s definitions and proofs independently and in class, working to understand the context and mathematics involved in Book I of the Principia. Students were able to view one copy of the Principia within the Beautiful Science Exhibit and a second copy during our time with the curator (see Figure 8, above).
While exploring the mathematics and mathematicians of (roughly) the eighteenth century, we considered historical texts and artifacts and the resources we have today that allow us to study the history of mathematics. This emphasis began with the choice of Stedall’s text, which allowed students to see facsimiles of historical texts, and culminated in our Huntington trip, which allowed students to see original copies of historical texts. Other resources utilized include the PBS NOVA film, “Infinite Secrets: The Genius of Archimedes,” which is a captivating introduction to the recent discovery and restoration of Archimedes’ work, The Method. Students were also assigned to read a recent article in the Wall Street Journal (Alter 2009) that describes the process of digital preservation of manuscripts and includes links to digital archives and resources like the Archimedes Palimpsest Project.
Virtual Tours and Field Trips Near You
Although we encourage you to visit the Beautiful Science exhibit, we recognize that not everyone is within field trip distance of the Huntington Library in San Marino, California. However, there are many resources about the history of mathematics that are only a mouseclick away. If we’ve piqued your interest, but you are too far away to visit the Beautiful Science exhibit at the Huntington Library, here are two online resources directly related to it:
Additionally, past Convergence articles contain links to many online resources that can be used to enhance the teaching and learning of the history of mathematics. The Columbia University Library contains many “Mathematical Treasures” that can be accessed through an article by Frank Swetz and Victor Katz. These are high quality images and descriptions of pages from over 100 historical texts.
Expanding from texts to mathematics artifacts, the photographs of quipus in the Convergence article, “The Quipu,” by Frank Swetz were taken during an MAA Mathematical Study tour to Peru.
For more artifacts, and a truly virtual field trip related to the history of teaching mathematics, visit the Smithsonian Institute site, “Slates, Slide Rules, and Software: Teaching Math in America.”
Also in the category of virtual museums is the web site of the Museum of the History of Science in Oxford, England. The “Online Exhibits” section of the web site includes the text from within the section panels of many exhibits, in addition to images from the exhibits. This web site can also be accessed through Frank Swetz’s review of the Museum of the History of Science in Convergence. Much like the Smithsonian Institute site, this site gives not only images of mathematics texts and artifacts, but also narrative that completes the pictures and enhances their usefulness.
For a more hands-on field trip, historical mathematics resources and resources related to the history of mathematics can be found in a variety of places very near to you. Many university libraries house small collections of old mathematics texts and textbooks that provide an engaging perspective on early math resources. For example, at Cal Poly Pomona, we have found school math textbooks from the 1950s and a 1930 edition of Pappus’ commentary on Book X of Euclid’s Elements. Our library also holds four different editions of Descartes’ Discourse on Method, including a 1934 edition in French and a 1937 English translation, providing a great opportunity for students to compare and contrast.
Many Morrill Land Grant universities own mathematics texts dating back to at least the 1860s. For example, at Montana State University in Bozeman, there are geometry textbooks from the 1880s and an 1893 edition of Ball’s A Short Account of the History of Mathematics. At the University of Wisconsin, Madison, there are microforms of mathematics texts extending back to 1487 and a copy of a 1545 Italian edition of Euclid’s Elements. Sometimes larger libraries’ special collections will also contain historical mathematics artifacts, such as the Mesopotamian cuneiform tablets found at Florida State University, Catholic University of America, University of Pennsylvania, and Brown University.
You and your students may be surprised at the local treasures you are able to find that can be used to enhance your teaching of mathematics and the history of mathematics. Whether online or at a local museum, university, or library, we encourage you to find resources that are readily available in your neighborhood. It’s time for a field trip, so get those permission slips ready ….
A. Alter, “The Next Age of Discovery,” Wall Street Journal, May 8, 2009,
Archimedes Palimpsest Project, Walters Art Museum, Baltimore, http://www.archimedespalimpsest.org/
Huntington Library, Art Collections, and Gardens, “Beautiful Science: Ideas that Changed the World,” http://www.huntington.org/thehuntington_full02.aspx?id=3000
Museum of the History of Science, Oxford, England, “Online Exhibits,” http://www.mhs.ox.ac.uk/exhibits/
National Curve Bank, “Deposit #93: A History of Math Class Visits the Huntington Library,” California State University, Los Angeles, http://curvebank.calstatela.edu/visit/visit.htm
PBS NOVA, “Galileo’s Battle for the Heavens,” WGBH Studios, Boston, MA, 2002, http://www.pbs.org/wgbh/nova/galileo/
PBS NOVA, “Infinite Secrets: The Genius of Archimedes,” WGBH Studios, Boston, MA, 2003, http://www.pbs.org/wgbh/nova/archimedes/
Smithsonian National Museum of American History, “Slates, Slide Rules, and Software: Teaching Math in America,” http://americanhistory.si.edu/teachingmath/
J. Stedall, Mathematics Emerging: A Sourcebook 1540-1900, Oxford University Press, 2008
F. Swetz and V. Katz, “Mathematical Treasures,” Convergence, http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2591
F. Swetz, “The Quipu,” Convergence (December 2008), DOI: 10.4169/loci003206, http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3206
F. Swetz, “Review of Museum of the History of Science, Oxford,” Convergence,http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=2581
About the Authors
Christine Latulippe is Assistant Professor of Mathematics Education at Cal Poly Pomona; Joe Latulippe is Assistant Professor of Mathematics at Cal Poly Pomona. Since first meeting in an undergraduate multivariable calculus course, they have shared many mathematical adventures including being 2007-2008 Project NExT Fellows. To exercise the other half of their brains, the Latulippes enjoy painting, reading, and taking field trips.