John Wallis at 400:
A Workshop on Science, Mathematics, and Religion in Seventeenth-Century England
Jackman Humanities Building, University of Toronto
2 November 2016
Session 1 (1:00-2:00): Wallis’s Algebra and Its Legacy (JHB 616)
Amir Alexander, “Experimental Algebra: How John Wallis Saved Mathematics for the Royal
Society”
Abram Kaplan, “Reshaping the Algebra of Conic Sections: Newton Reads Wallis”
Coffee break (2:00-2:10)
Session 2 (2:10-3:30): IHPST Colloquium (JHB 100a)
Douglas Jesseph, “Wallis vs. Hobbes: Mathematics, Politics, and Theology”
Coffee break (3:30-3:45)
Session 3 (3:45-5:15): Science and Religion in Wallis’s Works (JHB 100a)
Louisiane Ferlier, “John Wallis’s World of Ink: From Manuscripts to Library”
Jason Rampelt, “John Wallis’s Ecclesiology”
Adam Richter, “John Wallis and the Catholics”
Closing remarks (5:15-5:30)
John Wallis at 400:
Abstracts
Amir Alexander, History, UCLA: “Experimental Algebra: How John Wallis Saved
Mathematics for the Royal Society”
To the Royal Society in its early years mathematics posed an uncomfortable dilemma. Founded
in the wake of the Civil War, the Society advocated public experimentation, reasoned debate,
and ultimate consensus as a substitute for the uncompromising dogmas that had driven the
conflict. What then was one to do with mathematics, a field that prided itself on its absolute
certainty and irrefutable results? John Wallis, the only mathematician among the Society’s
founders, believed he had the answer. While his unorthodox approach rankled traditional
mathematicians, it allowed the Royal Society to embrace this crucial field.
Louisiane Ferlier, Royal Society of London: “John Wallis’s World of Ink: From
Manuscripts to Library”
“Thus I have, in a Long Letter, given you a Short Account of my Methods (used, in such cases,
with good Success;) which to do at Large, would require a Book.”
(John Wallis, “A Letter of Dr. John Wallis, [Geom. Prof. Oxon, and F. R. S.] to Mr. Thoma’s
Beverly; Concerning His Method for Instructing Persons Deaf and Dumb” Philosophical
Transactions, [245, 20] pp.353-360; p. 359.)
John Wallis’s encyclopaedic endeavours were built on a mountain of ink and paper. To consider
Wallis’ work in the making, I will first draw his portrait as a reader and book collector. Keeper
of the Oxford University archives, he secured donations for the Bodleian and Savilian libraries
and consulted obsessively old and new publications, manuscript or printed texts to build and
defend his own work. To reveal the interconnections between his contributions to theology,
cryptography, linguistics, music and mathematics, this paper will then focus on Wallis’s
methodical construction of his personal ‘inkscape’. Wallis’s passionate obsession with the
preservation and dissemination of his thought in print will be considered alongside the research
he only consigned in manuscript form, through correspondence and notes. This reconstruction of
John Wallis’s libraries will therefore provide us with an overview of the erudite’s contested
achievements, as well as a panorama of contemporary scholarly practices.
Douglas Jesseph, Philosophy, University of South Florida: “Wallis vs. Hobbes:
Mathematics, Politics, and Theology”
This talk seeks to explain what was at stake in the long-running dispute between John Wallis and
Thomas Hobbes. I argue that Wallis’s original motivations for attacking Hobbes are closely
connected with important political and theological issues in England in the 1650s. However, as
the dispute unfolded, these issues faded into the background. Through it all, a number of
significant mathematical topics remained front and center, specifically the criteria for rigorous
demonstration, the nature of ratios, and the relationship between algebra and geometry. In the
end there is no question that Wallis emerged victorious from this dispute, but his victory failed to
achieve his broader goal of discrediting Hobbesian politics, religion, and methodology.
Abram Kaplan, History, Columbia University: “Reshaping the Algebra of Conic Sections:
Newton Reads Wallis”
In his 1685 Treatise of Algebra, John Wallis defended his 1655 study On conic sections against
earlier critiques of mid-century geometers like Pierre de Fermat. Wallis claimed to have treated
the conic sections abstractly, “without the embranglings of the Cone.” In this paper, I discuss the
techniques through which Wallis released the sections from their geometric setting. I place these
techniques in the context of Wallis’ historical treatment of Greek geometry. In defending the
primacy of arithmetic, Wallis developed a theory to explain how fundamental arithmetical
properties became “embrangled” in geometry to begin with. I argue that around the time of the
Treatise of Algebra, Isaac Newton was also reading of Wallis’ On conic sections. Newton’s
reading, reflected in manuscripts from the 1680s and 1690s, was surprising. He reversed Wallis’
key techniques of decontextualization in order to replace the algebraic treatment of curves into
what he saw as their proper, geometrical context. Newton mathematical-philological
investigations both motivated and enabled his reversal of Wallis, a reversal that employed
cutting-edge philological tools. Visions of mathematical progress and views about the status of
algebra were themselves embrangled with historical and sociological arguments about the
relevance of geometry and the nature of expertise.
Jason Rampelt, History and Philosophy of Science, University of Pittsburgh: “John
Wallis’s Ecclesiology”
John Wallis was Savilian Professor of Geometry in Oxford for the second half of the seventeenth
century, advancing research and teaching in mathematics, and was a productive member of the
Royal Society. In both areas, Wallis was involved in debates (such as his 20 year wrangle with
Thomas Hobbes) which often stretched beyond the boundaries of scientific concerns into broader
social, political, and religious domains. During his lifetime, success in one area was often
contingent on security in the other. Wallis was criticized by some of his contemporaries, and is
known by historians today for his numerous political and ecclesiastical allegiances. Wallis
survived the tumult of the English Civil Wars professionally unscathed and some see this as
evidence that he simply changed his mind on debated issues at his convenience. For example,
his ecclesiastical service ranged from his role as scribe to the Westminster Assembly, to chaplain
to the restored monarch Charles II.
This paper will focus on his ecclesiology, that is, his theological commitments with
respect to church polity and ceremonial practice, as a way of understanding his broader
philosophy undergirding his research and teaching in natural philosophy. Published and
unpublished theological tracts and correspondence offer ample evidence for his views on church
government, the sacraments, and prayer in public worship. An attempt will be made to answer
the question if, in fact, Wallis did change his position on these issues throughout his life, or if
there is another explanation for the appearance of having done so. An answer to this question
may help us better understand his motives for other debates and projects during his career.
Adam Richter, IHPST, University of Toronto: “John Wallis and the Catholics”
Despite his correspondence with numerous Catholic scholars and his favourable reception of
their work, Wallis’s texts are peppered with suspicions about Catholic plots in England and
derision of Catholic theology. This paper considers the role of anti-Catholic sentiment in
Wallis’s thought. I argue that Wallis’s anti-Catholic position motivates his acceptance or
rejection of certain ideas about nature or mathematics, depending on whether he considers them
to support or to challenge Catholic interests. This is evident beginning in his earliest publication,
Truth Tried, as Wallis adopts a metaphysical position regarding time and space that makes
transubstantiation impossible. In addition, I suggest that anti-Catholic sentiment helps to explain
why Wallis produced a Latin translation of Francis Potter’s Interpretation of the Number 666, a
work that uses mathematical calculations to interpret biblical prophecy, a subject in which Wallis
normally shows no interest. Finally, I will reconsider Wallis’s well-known criticism of Descartes
as a plagiarist of Thomas Harriot’s algebra, a dubious claim that might have been motivated in
part by theological differences.