Math geek/lit profUCI English professor explores intersection of Victorian mathematics and culture
by Annabel Adams
The idea that STEM and the humanities are distant disciplines is a more recent development than we often realize. In fact, still in the mid-nineteenth century, scientists considered themselves artists and artists considered themselves scientists. Andrea Henderson, professor of English at the University of California, Irvine, is passionate about finding and exploring connections between these disciplines. In her book, Algebraic Art: Mathematical Formalism and Victorian Culture (Oxford University Press, 2018), Henderson investigates how innovations in science and mathematics influenced Victorian culture. Below, she discusses the genesis of her book and what she hopes readers will take away from it.
Q. Until more recently, little has been written about the influence of Victorian mathematics on Victorian aesthetics (how people create and appreciate art and beauty). What inspired you to take on this topic?
A. My previous books focused on early-nineteenth-century culture, and I got it in my head that I wanted to do something with poet Samuel Taylor Coleridge’s comments on mathematics. Then I found that the most innovative work in British mathematics was done in the latter part of the century, so I shifted forward chronologically and wrote a piece on Flatland—a Victorian novel in which the characters are geometrical shapes. That led me to look into non-Euclidean geometry and symbolic algebra, and, later, to study symbolic logic and field theory in physics. Often, I would read works I didn’t expect to write on—like James Clark Maxwell’s early essays on electricity—and discover connections I didn’t anticipate, like those between Maxwell’s analogical method and Algernon Charles Swinburne’s poetic principles. I ultimately realized that what I was noticing was a general movement towards formal abstraction, even in scientists and artists who were committed to describing the physical world.
Q. Your book focuses on a crucial shift in mathematical thinking during the mid-19th-century; how would you characterize that shift? Did it impact other disciplines?
A. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay less in its capacity to describe the world than in its internal coherence. This turn to “pure” mathematics produced a convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wavelike stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland, and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or the particulars associated with the realist novel. Victorian mathematics thus not only redefined itself as a field but also all the disciplines around it: inquiry centered on facts and data was increasingly considered less important than the study of the general laws that structured those facts. This emphasis on forms, structures, and laws rendered even very different disciplines analogous. Victorian philosopher of science William Whewell’s coinage of the word “scientist” reflects this fact: “We need very much a name to describe a cultivator of science in general. I should incline to call him a Scientist. Thus we might say, that as an Artist is a Musician, Painter, or Poet, a Scientist is a Mathematician, Physicist, or Naturalist.”
Q. Did focus on the form rather than on content itself reverberate to the political and legal sphere?
A. Indeed, the cultural prestige of scientific formalism shaped contemporary party politics, most obviously in the case of the Reform Bills, which took for granted that political improvement could stem from changes in formal procedure alone. Liberal politicians, eager to present themselves as forward-looking and rational, proudly spoke of formal regularity as inherently “scientific.” At the same time, the nineteenth century saw the consolidation of legal formalism, which produced its own version of rationalist reform, as did the project of codifying existing laws. The Social Science Association was established in 1857, and in 1870 Edward Denison spoke of the felt need for “a Social Science policy . . . the day of expedients is passed, and the reign of principles begun.” This legal regularity sustained, in turn, capitalist economic organization.
Q. What do you hope readers will take away from Algebraic Art?
A. One of the things that impresses me most about the work of Victorian mathematicians and physicists is the way they constantly struggle, not just to produce sound theories, but also to consider the implications of such theories for their conceptions of knowledge, ethics, and social life. That is, they didn’t regard their scientific pursuits as separate from other aspects of human life. Quirky as he was, Lewis Carroll wasn’t alone in being interested in multiple disciplines: a professor of mathematics, he not only wrote children’s books and practiced photography but also developed his own system of symbolic logic and drew up plans for improving election design. Maxwell was trained in philosophy, took an interest in visual phenomena and art, and wrote poetry. The advances he made in electromagnetic theory sprang in part from his capacity to synthesize a wide range of physical, visual, and mathematical conceptions of the phenomena he studied, while constantly testing those conceptions against each other. Today we tend to silo our knowledge into separate disciplines. (Still worse, we often leave thinking about science to specialists; this has many practical advantages given the complexities of our technologies, but it also leaves scientific argument itself at risk of appearing to be no more than a matter of presumed authority. We have seen how this can
backfire in the case of claims that climate change is simply a fabrication.) There is more to be learned from Victorian thinkers than simply what we find in their essays, novels, and poems: there is also a habit of mind, a wide-ranging and versatile curiosity.
Q. Do you think it is important for humanists to engage with STEM disciplines? What challenges and rewards did you encounter by doing so?
A. I don’t think all humanists need to do research on science, but I do think there’s much to be learned by putting different models of the world in dialogue with each other. In the past I’ve explored the connections between literature and other arts, but scientific paradigms are also imaginative human constructs, with philosophical, social, and aesthetic implications. Moreover, scientific methods shape what we do across the university, either explicitly or implicitly, so understanding the history of those methods also illuminates the larger project in which we’re all engaged. For me personally, thinking about math in relation to nineteenth-century literature and art was excitingly new. That said, it’s certainly true that taking on such topics is daunting for a non-mathematician. I have to do more than simple “research” for any given paper I write; I have to teach myself about whatever mathematical subfield I’m discussing, and that takes a lot of time.