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Mathematical Treasure: A Number Line Owned by Andrew Gleason

Peggy A. Kidwell (National Museum of American History, Smithsonian Institution)

Number line previously owned by Andrew Gleason.

Number Line, about 1972, Smithsonian Institution negative number JN2012-0821.

Mathematicians, mathematics educators, engineers, students and diverse other numerate people long relied on printed charts and tables. These not only conveniently listed numerical information, but sometimes illustrated mathematical ideas.

From the time of Descartes (1596–1650), mathematicians have described positive and negative integers as evenly-spaced points on a line, now called the number line, extending infinitely in both directions. This usage had made it into some school textbooks by the early 20th century. Particularly at the time of the development of the New Math in the 1950s and 1960s, number lines became part of the school classroom. This chart showing a number line was developed by Loraine McMillan and sold by Houghton Mifflin Company to accompany the 1972 edition of the textbook Modern School Mathematics. McMillan also published a leaflet that described the use of the object.

First of eleven cards in McMillan's number line.

The number line was made of eleven plastic-coated cards, with the first ten numbered from 0 to 100 (the eleventh card was blank). The first of the cards is shown.

This example of McMillan’s number line was owned by Andrew Gleason (1921–2008), a professor of mathematics at Harvard University who took considerable interest in school mathematics teaching.

To find more information about mathematical charts and tables in the collections of the Smithsonian’s National Museum of American History, see the website For examples of books of tables, consult the catalog of Smithsonian Institution Libraries.

Index of Mathematical Treasures

Index of Mathematical Objects

Peggy A. Kidwell (National Museum of American History, Smithsonian Institution), "Mathematical Treasure: A Number Line Owned by Andrew Gleason," Convergence (October 2014)

Mathematical Treasures: Smithsonian National Museum of American History Object Groups