Equations from God: Pure Mathematics and Victorian Faith

CHAPTER FOUR: Augustus De Morgan and the Logic of Relations

An insignia designed by Augustus De Morgan for the nascent London Mathematical Society perhaps typifies the ecumenism of pure mathematicians in the Victorian age better than George Boole’s poetry or Benjamin Peirce’s prose. De Morgan inscribed a symmetric figure of concentric arcs and triangles with the name of the organization, the Latin motto Vis unita fortior (a united force is stronger), and three numbers: 1865, 5625, and 1281. The first number was probably the most obvious to contemporaries, being the year in which De Morgan, his son George, and a handful of other British mathematicians founded the institution. More precisely, 1865 was the year of the Society’s founding based on the Christian calendar, for the other two dates were the year based on Jewish and Muslim reckoning. The motto ampli fied this interfaith overture, as De Morgan explicitly added it to highlight the “union of races and nations as well as of individuals” under the banner of mathematics.1 Indeed, he further reinforced this idealistic unification through the symmetry of the figure, which De Morgan borrowed from the first chapter of the first book of Euclid’s Elements. As he recorded in his notebook , this diagram represented the opening of the mathematical science to Jews, Christians, and Muslims alike.2 De Morgan therefore felt he had created in the London Mathematical Society insignia an icon for the perfect and symbiotic whole of mathematics, humanity, and faith. This spirit lent one of De Morgan’s technical phrases, “the logic of relations,” a certain double entendre: it seemed logical to the mathematician to relate to people from all religious traditions.3 De Morgan’s grittier side also gave his insignia for the London Mathematical Society a second, less spiritual meaning. The motto Vis unita fortior signified that mathematicians could enhance their authority by joining together in a professional organization such as the London Mathematical So106 chapter four Augustus De Morgan and the Logic of Relations ciety. In the early part of the nineteenth century, mathematical research comprised a loose federation of interested parties who approached somewhat nebulous topics by using a panoply of individual methods and symbols . By the end of the century, however, mathematics had become a far more centralized discipline, with numerous well-defined subjects of research and a standardized notation. Rather than often being a physicist, astronomer , or philosopher with a strong interest in mathematics, a “mathematician ” was a distinct professional specializing in a circumscribed area. The London Mathematical Society was one of the first professional organizations specifically devoted to mathematics and helped to accelerate these changes. In the three decades after its founding, similar institutions spread across Europe and America. The sense of that impending professionalization of mathematical work is apparent in the London Mathematical Society insignia, uneasily coexisting with its loftier ecumenical sentiment. To understand the professionalization of mathematics in the second half of the nineteenth century, we must examine how mathematicians portrayed their discipline in concert with their broader social concerns. In this context , the rise of modern, professional mathematics in large measure developed out of a strong desire among mathematicians like Augustus De Morgan to set their discipline apart from other spheres of Victorian society. “Gus! Gus! At ’em a’round!” was Augustus De Morgan’s favorite anagram of his name, and he thought it a proper motto for his stand against the divisive nature of nineteenth-century religion, education, and intellectual life.4 De Morgan protected and advanced the mathematical science by defining it, like the anagram, against what he saw around him. Where religious sects constantly bickered, mathematicians would discuss matters peacefully; where polemical fanatics overstated their cases, mathematicians would be cautious in their proclamations; where amateur mathematicians and arrogant metaphysicians discussed grand notions, professional mathematicians would limit their purview; where the evils of dogma and the religious establishment smothered nonconformity, mathematicians would be open to the new and different—as long as dogma and religion were not involved . In the setting of an extremely divisive culture, mathematicians would be active yet unified, progressive yet unassuming. Appealing to a conception of the “scientific method” that simultaneously embodied Pauline humility and professional ambition, mathematicians like De Morgan would distinguish themselves and their discipline. To achieve this contradiction of Victorian culture and establish a pro107 augustus de morgan and the logic of relations fessional realm for themselves, however, mathematicians would have to...