Category Archives: Mathematics

George Boole at 200: The Emotion Behind the Logic

Today is the 200th anniversary of George Boole’s birth, and he certainly merits a big celebration at University College Cork, where he was the first professor of mathematics, and even that rare honor: a Google Doodle. The focus has been on his technical breakthroughs, since his brilliant advances in mathematics and logic formed the foundation of modern computing.

But on this bicentennial it’s also worth looking at the emotional motivation behind Boole’s supposedly dispassionate technical work—and at ourselves in the mirror. As I wrote in my book Equations from God: Pure Mathematics and Victorian Faith, Boole lived in a time of painful polarization, unfortunately not so dissimilar to ours. While his attention was on religion rather than politics (although those were intertwined, as they are in our day), Boole found the divisiveness unrelenting and sorely lacking in compassion.

My thesis, documented in his notebooks and letters home, and in his published articles and books—his Laws of Thought includes as much about social and philosophical concerns as it does mathematics—is that Boole saw his logic as a way to transcend the overwrought differences of his time to find an ecumenical way to work together toward divine truth. Boole hated that it had become so hard for opposing sides to talk to each other about many issues, and that even minor distinctions were amplified by the modes of discourse and by everyone’s quick jumps to strong opinion and judgment.

Boole’s contemporary and fellow mathematical logician Augustus De Morgan summarized the problem when he wrote that if you asked someone if the craters were larger on the dark side of the moon than on the side we can see, “The odds are, that though he has never thought of the question, he has a pretty stiff opinion in three seconds.” To counter this dogmatism, Boole and De Morgan not only created symbolic logic, but also through their generous interactions with those of many sects and faiths, tried to be true to the spirit of their work.

So today let us honor George Boole the mathematician, but also George Boole the human being. His entreaties to respect all sides, to be charitable with those with whom you disagree, to not jump to conclusions but instead to pause and think carefully first, to try to find a way bridge divides—these are all too rare qualities in our age as well as his.

Equations from God

“On September 23, 1846, the Berlin astronomer Johann Gottfried Galle scanned the night sky with a telescope and found what he was looking for—the faint light of the planet Neptune. Excitement about the discovery of an eighth planet quickly spread across Europe and America, generating a wave of effusive front-page headlines…Neptune was the first heavenly body found by mathematical prediction. Without peering into the sky at all, two mathematicians independently calculated the location of the planet through geometrical analysis and the laws of gravitation [after noticing] Uranus’s orbital irregularities [and told Galle where to look]…This remarkable aspect of the discovery of Neptune was not lost upon contemporaries. To many it signaled a new era of human knowledge [in which mathematicians were] potent sorcerers who conjured and commanded the supreme realm of Truth.” So begins Equations from God, my new book. I’ve been careful on this blog to stay on topic, i.e., only discuss digital matters, but as many of you know I also do work that is very much analog. And since one only comes out with a book once in a while, I’m taking the liberty of using the blog today as a platform to tell you why you might want to pick up a copy of Equations from God and read it.

Beginning with Plato and ending on the eve of the twentieth century, Equations from God tells the story of how and why so many Europeans and Americans came to see mathematics as a divine language, a way to ascend above the petty differences of mankind and commune with the mind of the Deity. Although it focuses on an ostensibly technical topic, it is written in a plainspoken way that makes the world of the mathematician accessible to a general audience, and it contextualizes that world within the religious, social, and political upheaval of the Victorian era. And it reveals surprising ideas from many unpublished works such as diaries, notebooks, sermons, and letters—ideas that remain remarkably relevant in today’s world. I think it also provides a good introduction to the intellectual and cultural debates and tensions of the nineteenth century.

Readers of this blog will likely find chapters and sections of interest, such as…

…the tale of George Boole, the brilliant, meek creator of the logic that runs our computers and our searches, who left England in his early thirties to teach mathematics in Ireland, only to find himself under siege during the Great Famine and the outbreak of Irish nationalism…

…the life of the greatest American mathematician of the nineteenth century, the pompous and cantankerous Harvard professor Benjamin Peirce, who refused to teach students who were insufficiently smart and who would end his math classes by exclaiming, “Gentlemen, there must be a God!”…

…the strange world of circle-squarers—amateur mathematicians who believed that pi was not what professional mathematicians said it was, and thought they had found its true value through mystical means…

…rare books such as The Lady’s Diary, a combination of astronomical knowledge, riddles, and math problems “designed for the use and diversion of the fair sex”…

…and much more. The book has been out for a few weeks now and so should be on bookshelves near you. While the list price is more for the “academic market,” as university presses like to call it (i.e., it’s listed at $50), through the power of the Internet you can find it for much less by looking at PriceGrabber or your favorite comparison site, or by going straight to A1 Books ($30), Barnes and Noble ($40 or $36 for members), or get it directly from The Johns Hopkins University Press ($40 with this special discount from the author).