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John Wallis, a founding member of the Royal Society, theologian and churchman, participated in the leading ecclesiastical conferences in England from the beginning of the English Civil War to the Restoration. His allegiance across governments, both civil and ecclesiastical, has provoked criticism. Close investigation into his position on key church issues, however, reveals a deeper philosophical unity binding together his natural philosophy, mathematics and views on church polity and liturgy. [ABSTRACT FROM AUTHOR]

The dispute that raged between Thomas Hobbes and John Wallis from 1655 until Hobbes's death in 1679 was one of the most intense of the 'battles of the books' in seventeenth-century intellectual life. The dispute was principally centered on geometric questions (most notably Hobbes's many failed attempts to square the circle), but it also involved questions of religion and politics. This paper investigates the origins of the dispute and argues that Wallis's primary motivation was not so much to refute Hobbes's geometry as to demolish his reputation as an authority in political, philosophical, and religious matters. It also highlights the very different conceptions of geometrical methodology employed by the two disputants. In the end, I argue that, although Wallis was successful in showing the inadequacies of Hobbes's geometric endeavours, he failed in his quest to discredit the Hobbesian philosophy in toto. [ABSTRACT FROM AUTHOR]

Emulating the Greek geometers, Newton used synthetic demonstration to present the groundbreaking arguments of the Principia. This paper argues that we can better understand Newton's reasons for using geometry by considering John Wallis's interpretation of synthetic demonstration. Wallis condemned demonstration for failing to explain the mathematical truths it presented. He opposed to it a presentation that combined symbolic analysis with a documented account of discovery. In preferring symbols, Wallis was motivated both by the nascent tradition of symbolic analysis and by contemporary interest in artificial languages. Newton maintained Wallis's characterization of Greek demonstration as adapted to common understanding rather than as strictly elucidating, but he inverted the values Wallis associated with synthesis and analysis. In Newton's new account, synthetic demonstration was preferable precisely because it could address inexpert readers without exposing them to the complications of symbols-based analysis. Newton advanced his arguments on behalf of geometry through portraits of ancient mathematicians: Archimedes and Pythagoras. [ABSTRACT FROM AUTHOR]

John Wallis's encyclopaedic endeavours were built on a mountain of ink and paper. To consider Wallis's work in the making, this article will draw his portrait as a reader and book collector. Keeper of the University of Oxford archives, he secured donations for the Bodleian and Savilian libraries and obsessively consulted old and new publications, manuscript and printed texts to build and defend his own work. Revealing interconnections between his contributions to theology, cryptography, linguistics, music and mathematics, this paper will focus on Wallis's methodical construction of his personal 'inkscape'. His 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 érudit's contested achievements, as well as a panorama of contemporary scholarly practices. [ABSTRACT FROM AUTHOR]

In his posthumously published work Chartham News (1669), the antiquary William Somner tentatively sought to link the discovery of fossilized remains near Canterbury to the prehistoric existence of an isthmus connecting Britain and France, before calling on natural philosophers to pursue his explanation further. This call was eventually heeded by the Oxford mathematician John Wallis, but only after more than thirty years had elapsed. The arrival in England of a catalogue of questions concerning the geology of the Channel led to the republication of Chartham News in the Philosophical Transactions, prompting Wallis to develop a physical explanation based on his intimate knowledge of the Kent coastline. Unbeknown to Wallis at the time, that catalogue had been sent by G. W. Leibniz, who had in turn received it from G. D. Schmidt, the former Resident of Brunswick-Lüneburg in Sweden. Wallis's explanation, based on the principle of establishing physical causes both for the rupturing of the isthmus and for the origin of fossils, placed him in a camp opposed by Newtonian authors such as John Harris at a time when the priority dispute over the discovery of the calculus led to the severing of his ties with the German mathematician and philosopher Leibniz. [ABSTRACT FROM AUTHOR]

This paper explores Wallis's role as editor of Newton's mathematical work. My objective is to understand how two mathematicians who held different views concerning mathematical method could nonetheless cooperate with one another quite effectively. Most notably, Wallis and Newton pursued different policies as far as the printing of algebra is concerned. In the 1690s Newton held the view that algebra is a heuristic method 'not worthy of publication™. Wallis, instead, for all his life was keen on making algebraic methods explicit in print. As the analysis of the correspondence between Wallis, Collins and Newton reveals, the methodological tension between Wallis and Newton was resolved in such a way that Newton agreed to print his heuristic methods in Wallis's English Algebra (1685) and Latin Opera (1693-99). Newton wished to guarantee his priority rights on discoveries in algebra and calculus, yet he also sought to avoid any tight authorial commitment towards them. Wallis, in contrast, received from Newton material that turned out to be useful for the fulfilment of a nationalistic programme aimed at eulogizing British mathematicians as well as his own work. [ABSTRACT FROM AUTHOR]