Math in/as History

Mathematics and history make strange bedfellows. Practitioners of the former claim to study universals, “pure” logic, and transcendent conclusions; practitioners of the latter often emphasize particulars and contingencies, and are suspicious of sweeping, universal claims. Yet, both disciplines focus on the difficult process of moving from the granular to the synthetic, are compelled by the idiosyncratic and the counterintuitive, and make general claims about the world we live in. Certainly there have been times in which historians explicitly embraced mathematics, and mathematicians embraced history, as a way of deepening their understanding of their work.

From about 1961 to his death in 1974, the Hungarian philosopher and mathematician Imre Lakatos introduced a historical dimension to mathematicians’ understanding of proofs. By analyzing the historical twists and turns, the dead ends and past contingent decisions of mathematicians, he aimed to provide a general account of the nature of mathematical knowledge, not as a steady accumulation of irrefutable facts, but as a series of creative solutions to practical problems. Over almost precisely the same period, some historians of American slavery began embracing mathematics as a method of challenging assumptions about the economics of antebellum America. This version of the so-called “cliometric revolution” culminated--in some ways--in the 1974 publication of Robert Fogel and Stanley Engerman’s Time on the Cross. The ensuing debates focused on the limitations and possibilities of what Fogel and Engerman claimed was the reconstruction of the “entire history of American economic development on a sound quantitative basis” (6).  Despite their many differences, these two developments revealed new possibilities for mathematics in history and history in mathematics emerged. By considering this crucial period, I hope to contribute to a more general discussion about the nature of cross-disciplinary and inter-disciplinary approaches within historical inquiry.