Mathematics in the Spanish press: a case study of the 18th century journal *Semanario de Salamanca*

The paper investigates how mathematics and mathematics education appeared and were disseminated in the Spanish press during the 18th century, focusing on the weekly journal Semanario erudito y curioso de Salamanca (Semanario de Salamanca). The research question centers on identifying and classifying the mathematical contents present in this non-specialist periodical to understand informal aspects of mathematics and its teaching: what knowledge readers had, which topics interested them, and how the press served as a platform for dissemination. Contextually, 18th-century Spain saw Bourbon-driven modernization efforts, promotion of science and technology, and evolving educational landscapes with diminished Jesuit dominance and growth of civil and military institutions requiring mathematics teachers. University mathematics professorships were founded or renewed, with curricular reforms encouraging updated mathematics teaching. The century was also the age of the press in Spain, with journals becoming vehicles for spreading scientific knowledge despite fluctuating official support. Prior studies on Spanish press and mathematics are relatively scarce, motivating this case study. Semanario de Salamanca (1793–1798; 20 volumes; 586 issues, often biweekly) reflected Salamanca’s cultural revival and had a broad readership; contributors often used pseudonyms. The study aims to shed light on the presence, nature, and reception of mathematics content in this influential Enlightenment-era periodical.

The authors situate their work within research on the history of mathematics and mathematics education that often relies on historical books and textbooks (Schubring, 1987). Examples include analyses of arithmetic texts for King James VI (Craik, 2015), the transmission of Lacroix and Legendre to Colombia and Venezuela (Oliveira & Schubring, 2021), and textbook approaches in Dutch Realistic Mathematics Education (Van Zanten & Van den Heuvel-Panhuizen, 2021). Beyond books, journals have served as vehicles for mathematical content, e.g., late-19th-century American recreational columns (Zelbo, 2019), a European journal on history of mathematics and physics (Fiocca, 2017), British university-affiliated journals (Despeaux, 2007), and the Spanish Miscelánea Turolense (Meavilla & Oller-Marcén, 2018). In Spain, specific periodical studies include Semanario Literario y Curioso de Cartagena (Madrid & López-Esteban, 2018) and mathematics problems in Barcelona and Madrid dailies (Oller-Marcén, 2019, 2020). Broader historical context on Spanish mathematics books and teachers includes works on Tosca’s Compendio Mathematico (Oller-Marcén & Muñoz-Escolano, 2019), Cerdá’s Liciones de Matemáticas (Maz & Rico, 2009), and calculus teaching in Spain and France (Blanco, 2013). The press’s role in disseminating science in Hispano-America is also noted (Clément, 2017). This literature supports examining the Spanish press as a source for understanding historical mathematics dissemination.

Design: Qualitative, descriptive, ex post facto study using content analysis, following prior journal analyses. Corpus and sources: Issues of Semanario de Salamanca located via the Hispanic Digital Library (Spanish National Library) and the Spanish Digital Library of Historical Press. Available and analyzed issues: 1–447 and 475–586 (published 1793–1798), approximately 560 issues. The journal had variant titles; the study refers to the collection as Semanario de Salamanca. Unit of analysis: Any journal entry containing content related to mathematics or mathematics education. Procedure: Units were read, analyzed, and categorized using a previously designed form (Madrid et al., 2021, 2022). Recorded elements included issue data, publication date, and author(s) when provided. Coding categories for type of mathematical content:

• Mathematical problems in various knowledge areas and contexts.
• Solutions, methods of resolution, and proofs.
• Expository texts on mathematics or mathematics education.
• Texts expressing opinions, attitudes, or beliefs about mathematics or mathematics education.
• Biographies or information about mathematicians/mathematics teachers/recognized persons.
• Advertisements for mathematics instruction or jobs for mathematics teachers.
• Book advertisements and reviews.
• Other mentions of mathematics or mathematics education.

General: Although mathematics was not a dominant topic, Semanario regularly included mathematics-related materials across its run (1793–1798) fitting the predefined categories. Problems and solutions:

• In early 1794, a sequence of posed problems and published solutions appeared. Example: the classic pursuit problem of a greyhound chasing a hare (Issue 33, 21/01/1794), with three reader-submitted solutions in Issue 35 (28/01/1794) using different methods: algebraic equations (two authors) and proportional reasoning (one author). Solutions were checked numerically (both covering 42 feet; dog 12 jumps, hare 24 jumps since start). This illustrates coexistence of algebraic and arithmetic traditions in Spanish contexts.
• Follow-up problem allocating 1600 pesos among three solvers with specified relations; a published solution (Issue 37, 04/02/1794) provided amounts: 269½, 526, and 804½ pesos, summing to 1600; editors noted 10 other correct submissions.
• Additional reader-submitted problems involved business transactions, equal divisions, and number riddles (e.g., doubling money and giving one peso fuerte, commodity-debt partition in varas of cloth). Some were linked to earlier printed sources such as Corachan (1719). A query on grains in a fanega of wheat and mill-wheel turns (01/02/1794) was also included.
• Editors later reported receiving several solutions but hesitated to print them due to subscriber displeasure (11/02/1794), indicating mixed audience reception. Advanced topic (infinitesimal calculus):
• Issue 204 (09/07/1795) presented a solution approach to a problem posed in Diario de Madrid: for a curve and a luminous point, determine the curve whose tangents are the reflected radii—a problem essentially about the evolute of reflected rays. The approach followed Newton’s geometrical style with Leibnizian differentials; terminology like “evolute” or “osculating circles” was avoided, likely for readability. This aligns with late 18th-century Spanish calculus content (Bails, García, Giannini). A biographical note on Martin Brusein (03/12/1795) was also included. Book advertisements and reviews:
• Announcement of the second edition of Juan Justo García’s Elementos de Aritmética, Álgebra y Geometría (03/05/1794), a key university text later mandated by Royal Decree (1807) for university instruction in elementary mathematics and algebra’s application to geometry.
• Short review (06/02/1796) of Compendiosa explicación de Cuentas por enteros y quebrados, praising clarity, brevity, and utility, especially for fractions.
• Mention of another periodical (Pasatiempo literario, 28/02/1797) that would include mathematics. Job advertisements and instruction offers:
• Formal job advert (19/08/1794) for a mathematics professorship at Estudios Reales of Madrid: salary 13,200 reales de vellón/year; duties included methodical daily teaching, alternating with a colleague, and restarting the course annually; competitive examinations specified (Latin required; 24-hour dissertation, defenses, and public exercises).
• Private instruction ads, e.g., Vicente Calvo offering arithmetic and mathematical problem instruction (1795), and Miguel Vicente Márquez, a water carrier, offering lessons in arithmetic, geometry, plane trigonometry, algebra, and problem solving (12/04/1794), highlighting broader social participation in mathematics teaching. Expository texts linking mathematics:
• Historical/science pieces that touched on mathematics (e.g., Manuél Sevald, 1795a).
• An architecture article (17/01/1797) advocating arithmetic, geometry, and proportional reasoning for architects. Mentions of mathematicians and teachers:
• Classical and modern figures cited: Thales of Miletus, Descartes, Newton, Leibniz.
• Spanish figures: Antonio Eximeno (praised as among the greatest mathematicians of the century in a book review; noted for music theory and strong mathematical culture), Pedro Ciruelo (Salamanca connections), Pedro Enguera (modified Arphe y Villafañe’s Varia Commensuración...).
• A historical woman from Salamanca, Cecilia Morillas (b. 1539), lauded for knowledge in cosmography, mathematics, and astrology; corroborated by external scholarship. Opinions on mathematics:
• A negative opinion piece (Pedro Alonso de la Avecilla, 28/02/1795) critiqued mathematics’ language and utility, questioned precision (e.g., circle ratio), and blamed mathematical progress for maritime deaths—anticipating controversy among readers.
• A pro-mathematics piece by a woman (A. F., 28/04/1798) noted barriers to women’s education yet advocated studying mathematics (along with religion, theology, and physics), expressing personal interest in geometry. Overall pattern: Mathematics appeared in Semanario in varied forms—recreational/educational problems, advanced calculus exposition, book and job notices, and opinion essays—revealing both dissemination and contested reception of mathematics in Enlightenment Spain.

The findings demonstrate that a non-specialist weekly like Semanario de Salamanca served as a vehicle for disseminating mathematical knowledge to a broad public. By identifying and classifying content types, the study shows: (1) mathematics permeated everyday reading through problems, solutions, and practical contexts (commerce, measurement), reflecting prevalent pedagogical traditions (algebraic equations coexisting with proportional/arithmetic methods); (2) cutting-edge topics such as infinitesimal calculus were introduced beyond formal institutions, signaling the reach of Enlightenment science; (3) the press functioned as a marketplace for mathematical labor and education (job adverts, private tutors), evidencing institutional and social demand for mathematical skills; (4) diverse opinions—both skeptical and supportive—highlighted contested cultural attitudes toward mathematics; and (5) frequent references to mathematicians, architecture, and music reveal mathematics’ interconnections across domains. These observations address the research aim by documenting the presence, nature, and reception of mathematics in the 18th-century Spanish press, complementing book-centered histories and aligning with comparable findings in other Spanish periodicals.

The study establishes that Semanario de Salamanca, though not a scientific journal, consistently featured mathematics in multiple formats: problems and solutions (often with varied methods), expository texts, calculus-related content, book notices and reviews, job advertisements, instructional offers, and opinion pieces. Topics were diverse, with commercial problems prominent, and instances of advanced calculus indicating diffusion of recent mathematical advances to lay audiences. Responses ranged from enthusiastic participation to reported subscriber displeasure. The journal referenced renowned mathematicians and local figures, linked mathematics with architecture, music, and other sciences, and reflected societal debates about mathematics. Consequently, periodical publications emerge as valuable sources for understanding the dissemination of mathematics and mathematics education beyond formal settings in 18th-century Spain. Future research should compare multiple periodicals across regions to assess similarities and differences in mathematical content and to map broader patterns of mathematical presence in the press, including outside Spain where contemporaneous journals (e.g., Gazeta de Literatura de México) also published mathematical articles.

• Corpus incompleteness: The analyzed digital collection lacks issues 448–474; approximately 560 issues were available from the 586 published, potentially omitting relevant content.
• Single-case scope: The study focuses on one periodical, limiting generalizability across the Spanish press without comparative analysis.
• Authorship opacity: Frequent use of pseudonyms in Semanario hinders precise attribution and contextualization of contributions.
• Qualitative emphasis: The descriptive, content-analytic approach prioritizes exemplification over quantitative metrics of frequency or distribution of content types.