### Introduction

An innovator in mathematics education, particularly in the teaching of geometry, Irish-born Oliver Byrne (1810-1880) lived in England and the United States at a time of prejudice against the Irish. Byrne faced physical and financial hardship and ridicule from his contemporaries for his mathematical and pedagogical innovations. His wife, Eleanor Rugg Byrne, published articles and books in meteorology at a time when women were discouraged from scientific and mathematical pursuits. This most comprehensive biography of Oliver Byrne to date discusses both Oliver's and Eleanor's accomplishments and highlights Oliver’s pedagogical philosophy, emphasizing his most innovative, famous, and visually stunning mathematical work on Euclidean geometry, *The First Six Books of the Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners *(1847). We will conclude with a discussion of how Byrne's *Euclid,* and his pedagogical views, might be used in geometry, mathematics education, and mathematics history classes.

**Figure 1.** Lithograph of Oliver Byrne (from the original in the collection of Gerald L. Alexanderson, Michael and Elizabeth Valeriote Professor in Science at Santa Clara University.) The caption reads as follows:

OLIVER BYRNE.

LATE PROFESSOR OF MATHEMATICS, COLLEGE FOR CIVIL ENGINEERS.

Author of

*“The New and Improved System of Logarithms.”_“The Doctrine of Proportion.”_“The Practical,*

Complete, and Correct Gager.”_“The Elements of Euclid by Colours.”_“A Practical,

Treatise on Spherical Trigonometry.”_“How to Measure the Length of a

Degree on the Earth's Surface by the assistance of Railroads."

&c., _&c.,_&c.

Inventor of

*“The Patent Calculating Instruments.”~“The System of Facilitating the Acquirement of Geometry, &*

of other Linear Arts and Sciences by Colours, &c.”~“Proposer of the New Theory of

the Earth, which accounts for many Astronomical, Geographical, and

Geological Phenomena, hitherto unaccounted for.”