Equations from God: Pure Mathematics and Victorian Faith

CHAPTER ONE: Heavenly Symbols: Sources of Victorian Mathematical Idealism

I think God’s thoughts after him. —Johannes Kepler Victorian intellectuals seeking philosophical support for a grand characterization of mathematics did not have to look far afield. One ally was the prominent contemporary philosopher William Whewell (1794–1866), the master of Trinity College, Cambridge, in the 1840s and 1850s.1 Although Whewell wrote on topics ranging from education, ethics, and the classics, to political economy and literature, he originally made his name in pure mathematics and associated topics in physics.2 As a young tutor he was an early champion of the Continental system of the calculus, which blossomed among a group of his friends later known as the Cambridge Analytical Society . Whewell’s most important work, The Philosophy of the Inductive Sciences Founded Upon Their History (1840; 2nd ed. 1847), thus unsurprisingly contained numerous laudatory chapters on pure mathematics. He proclaimed that mathematical notation, concepts, and reasoning were of such great importance that they rightly stood at the head of all “intellectual progress” in the history of mankind.3 Although Whewell witnessed and even participated in revolutionary advances in modern mathematics, he nevertheless thought that this lofty understanding of the discipline was as old as Western thought and believed that it was absolutely essential to understand the mathematical conceptions of certain ancient and medieval predecessors. To this end he included long digressions in The Philosophy of the Inductive Sciences on critical philosophers such as Plato,4 and he sprinkled the text with exclamations from the classics that buttressed his own arguments. For instance, Whewell cited the Roman naturalist Pliny the Elder, who declared upon the mathematical pre14 chapter one Heavenly Symbols Sources of Victorian Mathematical Idealism diction of an eclipse, “‘Great men! elevated above the common standard of human nature, [have] discover[ed] the laws which celestial occurrences obey.’”5 In addition to the luminaries of Greco-Roman thought, Whewell included equally long chapters on lesser-known medieval figures such as Ramon Llull.6 Spaced throughout the history of the West, Whewell portrayed these characters as apostles who sought to spread the gospel of mathematics . The ancient Greek Plato, the Roman Pliny, and the medieval Spaniard Llull had all come to the same conclusion, though separated by the centuries —they looked upon mathematics as a discipline that communed with the highest elements of the cosmos. To them, mathematics was neither a vocation nor an avocation; rather, it was a calling. Like Whewell, other Victorian mathematical idealists looked to these older sources for intellectual support, justification, and inspiration. Indeed, mid-nineteenth-century British and American mathematicians, especially those interested in pure mathematics, had an unusually strong sense of the history of their discipline. Simply put, they were fanatical bibliophiles. Their keen interest in the portrayal of mathematics through the ages was apparent in the rare tomes on their bookshelves and in the importance they gave to the conceptualization of mathematics above and beyond proofs and formulas . Augustus De Morgan could have been mistaken for a librarian; the list he compiled of ancient, medieval, and Renaissance mathematics books remains a useful bibliography. De Morgan also wrote biographies of premodern mathematicians for a number of encyclopedias. Similarly, John Herschel recounted the ideas of ancient Greece in a monograph for the Cabinet Cyclopædia.7 George Boole and the American educator Thomas Hill (a central figure in chapter 2) both cited the Renaissance Neoplatonist John Dee as a crucial antecedent to their own thought.8 William Rowan Hamilton went so far as to read Plato in the original Greek, and connected his own theories to Pythagorean conceptions that had influenced Plato.9 Because these Victorian mathematicians saw their work as the culmination of a lengthy and privileged Western intellectual lineage, the contents of their personal libraries provide an extremely useful entrée into the AngloAmerican ideology of mathematics in the early nineteenth century. In these volumes, ancient, medieval, and early modern philosophers and mathematicians posited a universe divided into two planes—the sacred realm of the ideal and the profane realm of matter—with mathematics as a courier between the two. The discipline was in a unique position: available to great minds in this world, yet part of the invisible, divine sphere. Like the Victo15 heavenly symbols and victorian mathematical idealism rians, many of the authors of these works yearned to transcend the fault lines of their age through mathematics. Plato, Platonism, and Mathematics Alfred North Whitehead may...