To gain insight into the connections between antebellum school mathematics, on the one hand, and the debates on how most speedily to abolish slavery, on the other, it is invaluable to research databases of antebellum publications. This includes, for instance, Readex’s Early American Newspapers, African American Newspapers, and Caribbean Newspapers. As long as one bears in mind that this research does not give the full picture of antebellum abolitionist activity—for instance, written documents may not have survived, and not all outspoken abolitionists had access to newspaper printing[1]—it is productive to scour the databases and to build clusters, patterns, and hypotheses.
One critical question is that of who had access to arithmetic and other fields of school mathematics. Generally speaking, antebellum school mathematics came with an economic edge. This is best illustrated by the hundreds of newspaper advertisements for the sale of new arithmetic books found in eighteenth- and nineteenth-century Anglophone publications in the United States as well as other regions subsumed under the New World. The United States saw a slow shift from imported (and often, translated) textbooks towards an increasing percentage of Anglophone books authored by Americans. A prominent author among them, Massachusetts-based Warren Colburn, advocated the intellectual advancement of the individual future arithmetician rather than rote learning. However, evaluating exactly which individuals, old and young, had access to these arithmetic books is a more complex matter. Some educated guesses about disenfranchised subjects can be made via detours. For instance, “Reward” advertisements in pre-emancipation newspapers often described an enslaved person who managed to escape into (at least, temporary) freedom. Occasionally, such advertisements would go beyond the person’s appearance and make mention of their skills, including, rather rarely, a reference to their abilities in arithmetic and keeping accounts. More frequent are papers from the northern states in which arithmetic is mentioned as a subject of schools like the African Free School (founded in New York in 1787) and the Institute for Colored Youth (founded in Philadelphia in 1837). These day and evening schools advertised their classes in abolitionist newspapers. They announced job openings and reported on school exhibitions, i.e., events during which pupils were asked to publicly present knowledge acquired, sometimes linked to prizes bestowed upon the most talented reckoner or most original essayist.
Researching these newspaper databases is also an important step towards an analysis of school arithmetic’s position in the panoply of rhetorical images used by African American and white abolitionists in their speeches and writings. For instance, a particularly concise use of metaphorical arithmetic to address slavery, this “[all-absorbing] test question in American politics,” is offered in an 1859 speech by William J. Watkins. Watkins was a journalist, activist, and skillful public speaker. In the speech, published in the Weekly Anglo-African of September 24 under the title “The Issue Plainly Stated,” he aims to rally abolitionists to join him in shaping the Republican Party from within. At the same time, Watkins does not stop short of criticizing the very same party for its repeated failure to take a proper stance. Watkins’s rhetoric is well-versed, generally speaking; it offers Shakespeare quotes and allusions to the Bible, and it repeatedly evokes animal narratives.[2] Perhaps the central image, however, can be found at the point in the speech where the central argument is presented. Watkins reasons that abolitionists will be successful in outnumbering slaveholders and pro-slavery lobbyists on all political levels—provided they make good use of their skills. This he shows with reiterated reference to logic as such; he repeatedly demonstrates the form of the sound argument that should guide the audience “from premise to conclusion.”
But practical philosophy asks for political action, too, Watkins reminds his audience. In addition to logic, then, abolitionists must apply their “arithmetic” in a sound manner; ultimately, this is a question of “the rule of three.” In other words, if uncompromising stances can persuade local crowds, as Watkins recounts having experienced during his lecture tours, then certainly this phenomenon should now be upscaled. The entire problem’s seeming complexity is deceptive; its solution may be “as clearly demonstrated as the plainest mathematical problem,” Watkins concludes.
Less than a year later, a speech by Beriah Green implicitly took up Watkins’s imagery and amplified his criticism against a tame Republican Party that appeared to cower before Southern slaveholders. The speech had been given at the 1860 annual meeting of the American Anti-Slavery Society. The same issue of The Liberator that included the transcript (June 1, 1860) also included five other abolitionist speeches held at the same meeting, and practically all of them started out by emphasizing the use of sound logic for persuading others of the atrocity of slavery.
Green’s text, the last one presented in the issue, goes the extra mile. Green makes use of a mathematical simile when dissecting William H. Seward’s senatorial address from earlier in the same year. Green’s biting criticism extends over a series of steps. To begin with, Seward started out with an entirely “false position” regarding his views on the U.S. Constitution; this view was what then lead him to defend the indivisibility of the union even at the expense of a proper denunciation of slavery—contrary to what he, Seward, had himself promised in previous speeches. By this leniency, Green states, Seward proved willfully blind towards several axioms and conventions Christian ethics was based upon, only to uphold his personal reading of the U.S. Constitution. Without certain axioms and conventions of human dignity, Green concludes, the entire sphere of ethics is bound to deflate.
Green here compares Seward’s obstinacy with a reinvention of Indo-Arabic numerals. If three out of our nine non-zero digits are replaced by zeros, “the entire sphere of arithmetic” collapses as a consequence. Furthermore, Green’s simile that evokes the “boys at school” here connects with his pun from earlier in the speech: when describing Seward’s erroneous assumptions, Green speaks of his “false position” and thus alludes to a method taught in antebellum algebra schoolbooks. And the simile also looks ahead to a later passage in which Green, defending the memory of John Brown, prompts all audiences to remember their “horn-book” years and to recall how they were taught the foundations of justice.
Watkins and Green were not the only abolitionists to use such imagery. In the early years of American abolitionist newspapers, a writer in Freedom’s Journal wrote that any person arriving from the outside could “see [by] the force of mathematical demonstration” the necessity to abolish slavery (1827, April 27). A similar example is to be found in an 1838 text from the Colored American. An anonymous contributor (April 5; originally published in the Pennsylvania Freeman, March 29) here defended the fight for immediate emancipation and against racist prejudice. The text’s author did so by deriding the colonialist Dr. David M. Reese, whom he or she described as having used alternate logic and created nothing but “silli-gism[s]” in his repeated attacks against said fight. A comparable critique was launched by William Lloyd Garrison (Thoughts of African Colonization, 1832, later quoted in abolitionist newspapers), who sarcastically asked why the “philanthropic arithmeticians” were always enthusiastic to subsidize the colonialist project but consistently failed to properly care about the well-being of Black and Native American communities in North America itself.
In 1845 (December 25), the National Anti-Slavery Standard equally warned against attempts to undermine the fundamental axioms of ethics. The “new arithmetic” this would create, the paper’s authors argued, was to undermine almost every principle of human interaction. Exactly ten years later, in 1855 (December 1), the newspaper used the same imagery against an application of erroneous methods when analyzing slavery. As the writer opined, to “transfer the subject[] [...] from ethical grounds to the compass of history [was] just as false as, in mathematics, to attempt the solution of a geometrical problem by pure arithmetical computation, or to answer a question in the Rule of Three by the demonstration of Pythagoras.” And in 1862 (January 4), the same National Anti-Slavery Standard described the 28th National Anti-Slavery Subscription Anniversary and illustrated its continued right to exist some nine months into the Civil War: emancipation had yet to be obtained, slavery yet to be eradicated. Certain things ought to be regarded as axiomatic “in morals [the same way this takes place] in mathematics,” the author wrote—and named the abolition of slavery as the prime example.
The evident goal of such immediatist abolitionists was to drive home the rebuttal of any compromises with slaveholders and pro-slavery politicians; with increasing prominence as of the 1840s, this included a dismantling of colonization, too. The authors showed that such rebuttals and dismantling were logical necessities. The texts often deployed the imagery of school mathematics, and present-day historians can now dissect the nuances of these choices. The imagery may have served a twofold rhetorical purpose. On the one hand, the reference to numbers illustrated the orator’s responsibility, sophistication, and wisdom: as numbers and statistics had grown ubiquitous in antebellum life,[3] so had politicians’ use of exemplary calculations for argumentative purposes in their speeches. On the other hand, the reference to the schoolroom implied an invitation even for beginners to join the cause of abolitionism: understanding the ethical grounds was not so difficult, after all, and it was implied that everybody in the audience who could read an introductory arithmetic was sufficiently versed to see why compromises with slaveholders were wrong. (Both aspects, the politician’s arithmetic as well as the pupil’s, ultimately raise the old question of who in the antebellum era was allowed schooling in the first place.) Accessing large digitized newspaper collections is critical for an extension of such dissections. It helps us group certain rhetorical examples into patterns; collect non-editorial contents such as arithmetic advertisements; and sketch out forms of educational disenfranchisement. Ultimately, it may bring us closer to understanding how arithmetic learning relates to eighteenth- and nineteenth-century systems of power in North America and the Caribbean, and to a glimpse at forms of resistance against and subversion of this power.
Footnotes:
[1] See Graham Russell Gao Hodges’s David Ruggles: A Radical Black Abolitionist and the Underground Railroad in New York City (2010), 70-72.
[2] See also The Black Abolitionist Papers, edited by C. Peter Ripley et al. (1992), Volume V, 33-34.
[3] See Patricia Cline Cohen’s A Calculating People: The Spread of Numeracy in Early America (1999).
