Call for abstracts | Mathematical Thought in the Renaissance and the Genesis of Modern Mathematics

edited by Riccardo Bellé and Beatrice Sisana

Submission deadlines: 15 March 2025 (abstract) | 15 November 2025 (article)
Publication date: April 2026

Journal section: Focus [read the section policies | submit]

How did the modern mathematics of Descartes and Leibniz take shape? What connections tie this new mathematics to the humanistic recovery of classical traditions and the advances in algebra developed in abacus schools? How did the mathematical pathways of the 15th and 16th centuries shape Galileo’s new science?

The Renaissance, often celebrated as an era of artistic and cultural rebirth, also witnessed profound transformations in mathematical thought, laying the groundwork for modern science. Historiography, shaped by figures like Pierre Duhem and Marshall Clagett, has frequently framed the Renaissance as a mere interlude between the medieval calculatores and the grand achievements of the 17th century. In contrast, Paul L. Rose, in The Italian Renaissance of Mathematics, argued that the recovery of Greek mathematics and science directly preceded the Galilean turning point. These opposing views have sparked extensive debate throughout the latter half of the 20th century and they still find some credence to this day, even as the historiographical landscape has evolved dramatically since 1967, when Carlo Maccagni underscored the need to recover the scientific legacy of the 15th and 16th centuries to properly assess Galilean science and the so-called scientific revolution.

But the time seems ripe for a reassessment of this legacy.

Recent decades have indeed seen significant studies and critical editions emerge, focusing on key figures of 16th-century mathematics — Commandino, Maurolico, Guidobaldo Dal Monte, Benedetti, Valerio, Galileo. The studies on the Italian algebra of Tartaglia, Cardano, and Bombelli, and its diffusion beyond the Alps, have been profoundly renewed, not to mention those on the crucial innovations introduced by Viète’s ars analytica. These developments highlight the interconnectedness of mathematical traditions across Europe and invite further reflection on the transnational nature of Renaissance science.

This call invites a focused exploration of the role of Renaissance mathematics in the transition to modernity: did its contributions to geometry and algebra represent blind alleys or revolutionary insights? How did the recovery of Greek mathematics intertwine with arithmetic and algebraic practices that had, for centuries, underpinned the mathematical education of Renaissance elites? How did reflections on the fundamental concepts at the core of the theory of proportions shape natural philosophy, influencing Galileo — and others— in their attempts to geometrise physical reality?

In the context of the 16th century Francesco Maurolico emerges as a particularly significant figure. Studies related to the National Edition (http://maurolico.it) of his mathematical work reveal that Maurolico’s approach to ancient texts led him to a revision of the fundamentals of classical mathematical heritage. In his effort to create a comprehensive system of mathematical knowledge, Maurolico developed profound ideas on subjects that later became central to 17th-century mathematics. This process of intellectual renewal was not limited to Maurolico but spanned the broader mathematical landscape of the 16th century. These developments, which reshaped the boundaries of mathematics, may perhaps reflect a deeper intellectual current flowing from the 16th century towards the dawn of modern mathematics. The aim of this focus is to explore these developments and currents.

Topics may include, but are not limited to:
- The rediscovery and translation of Greek mathematical texts and their impact on Renaissance innovation;
- The interaction of classical, medieval, and practical mathematical traditions in the Renaissance;
- The development of algebra: from Italian roots to its blossoming beyond the Alps;
- The influence of classical geometry on Galilean science;
- Francesco Maurolico and the reorganization of mathematical knowledge;
- Francesco Maurolico and the use of classical and medieval sources for a renewed mathematics.

Abstracts must include the author’s/co-authors’ name(s), affiliation(s), and email address(es), in addition to a brief CV.

Authors are expected to submit 300-word abstracts in English by 15 March 2025 to Riccardo Bellé (belle@mat.uniroma2.it) and Beatrice Sisana (beatrice.sisana@uniroma2.it). Proposals will be assessed by the journal’s editorial committee and by the editors of the focus.

Selected contributors will be notified by 1 April 2025.

Authors are expected to submit their articles in English by 15 November 2025 via the journal website at gal-studies.museogalileo.it.