*The Continued Exercise of Reason: Public Addresses by George Boole* edited by Brendan Dooley is a collection of lectures, some of which have never been published, that gives the reader further insights to the early thinking of this mathematician. George Boole (1815–1864) is remembered by history as the developer of algebraic logic and can be considered one of the pioneers of the information age.

Boole’s ideas are the fundamental to the internal logic of a programmable computer. Boole never saw a computer, of course, but without his ideas, we would have no computer technology. Formally, Boole “algebraized” mathematical logic. According to Bertrand Russell, “pure mathematics was discovered by Boole.” In his lectures, Boole interpreted for a general audience recent discoveries and debates in a wide range of fields. In this book, Dooley offers us a collection of eight lectures:

- On the Genius and Discoveries of Sir Isaac Newton
- On the Character and Origin of the Ancient Mythologies
- On the Question: Are the Planets Inhabited?
- A Plea for Freedom
- The Right Use of Leisure
- On Education
- The Claims of Science
- The Social Aspect of Intellectual Culture

As pointed out in the introduction, few of Boole’s actual lectures survice. Those few are occasionally citied but almost never read. Dating from his years in Lincoln, England, “On the Character and Origin of the Ancient Mythologies,” “On the Question: Are the Planets Inhabited?,” “A Plea for Freedom,” and “On Education” are published here for the first time. “On the Genius and Discoveries of Sir Isaac Newton” and “The Right Use of Leisure” are printed for the first time in 180 years. “The Claims of Science,” ast appeared in a rare edition in 1952 and “The Social Aspect of Intellectual Culture” was reprinted for the first time since 1855. These lectures, delivered in various venues, reveal the ways and means of popular education in the age of John Stuart Mill, a great contemporary with whom Boole shared not only an interest in logical reasoning but also in social improvement.

I enjoyed reading the lectures as they pointed out the thinking of a man in the 19th century: a journey back in time. In the lecture “On the Question: Are the Planets Inhabited?” on page 119, Boole summarizes his results, which contain the highest application of mathematics:

- One planet revolving around one central sun, through space, void of resistance, would constitute an undisturbed and permanent system. The planet would revolve in the same orbit, and with the same relations of distance and velocity forever.
- One or more planets revolving under the same conditions around a central sun, would constitute a disturbed but permanent system… If the orbit of the planet is at one period dilating, as is now the case with the earth’s orbit, it will subsequently contract. If the inclination of the orbit’s plane to the plane of the equator is diminishing, and such is the condition of the earth’s now, such diminution will be followed by increase… The unassisted intellect of man has achieved no higher triumph than in establishing this great principle of the economy of the universe.
- Planets revolving around a central sun through a resisting medium cannot constitute a permanent system.

In the lecture “On Education” among other points, Boole discusses the study of languages on pages 155–156 and how modern languages are easier to learn than ancient languages.

For mathematics historians, this book offers the reader a deeper appreciation of Boole, his thinking, his passions, and his beliefs in education. While there is a substantial introduction offering a biographical outline of Boole, a novice should perhaps read a different book, discussing Boole’s life, before reading this book.

Peter Olszewski is a Mathematics Lecturer at The Pennsylvania State University, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Chapter Advisor of the Pennsylvania Alpha Beta Chapter of Pi Mu Epsilon. His research fields are mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks. He can be reached at pto2@psu.edu. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar and bass, reading, gardening, traveling, and painting landscapes.