Many years ago, when I was in graduate school, I was writing a paper on the origins of the calculus when I came across a strange complaint by a seventeenth-century Italian mathematician. Stefano degli Angeli, as he was called, was a fierce advocate of “the method of indivisibles,” an early form of the calculus, but he was facing some stiff opposition. Everyone, he wrote in frustration, accepted the new method, except for one group: The Jesuits. And because the Jesuits were the most powerful Catholic order of the day, and because they ran the largest and best educational system in the world, and because they counted among their members some of the most distinguished mathematicians in all of Europe, their opposition counted for much. As long as the Jesuits continued their opposition, Angeli feared, the new mathematics will always be under threat.
I didn’t do much with Angeli and his complaint at the time. I finished my paper and moved on to other things, and eventually I made my way to The Planetary Society, where I wrote many articles about space exploration. But in all those years Angeli’s grievance kept nagging at me, raising questions to which I had no answer. The Jesuits, after all, were a religious order with a religious mission – to save souls and battle “heretics,” especially Protestants. Why would they care about mathematics? And why would they possibly take a position on technical method like indivisibles? Why, in short, did the Jesuits object to the calculus?
Three years ago I finally sat down to solve this riddle, and what I found amazed me. The Jesuits didn’t just object to the early calculus; rather, they fought a systematic campaign against it that lasted for half a century and put an end to the brilliant Italian mathematical tradition. And they weren’t alone either: all across Europe the battle over indivisibles raged, drawing in not just Christian orders, but famous philosophers and scientists, religious reformers, cardinals, and even Popes. Untangling the story took me from the courts of kings and Emperors to secretive Vatican conclaves, and from the bustling cities of Italy to the battlefields of Europe’s religious wars. In the end I came to understand that the fight was really between two very different visions of the modern world. Those who believed that only a strict uncontestable hierarchy and a single unchallengeable truth can preserve the peace detested the early calculus; those who believed in a future that allowed for dissent and a plurality of voices championed the new method and its promise. It was a story, I knew, that needed to be told.
Academics usually publish in specialized journals and academic presses, which means that most of the people who read their work are other academics, and in their very own field. But my years at The Planetary Society taught me that it didn’t have to be this way. There is a huge public out there, I learned – intelligent, well-informed, often highly-trained in their field, and excited about all aspects of science. Those are the people who read my stories about SETI and exoplanets, and who read every word of Emily Lakdawalla’s blogs and listen to Bruce Betts’ lectures. And those are the people, I decided, that I want to reach with the story of the battle over indivisibles.
Those people are you, and it is with you in mind that I wrote Infinitesimal. I hope you enjoy it.