The longevity of mathematics, where certain knowledge developed hundreds of years ago is still studied today, is not an inherent quality of the ideas themselves. Instead, mathematical ideas owe their enduring nature to the people who study and use them, to scholarly and teaching institutions, and to the material objects in which they are embodied. This crucial mechanism of preservation and conservation is defined as the process of heritage making, which Professor Caroline Ehrhardt examines from the perspective of the social and cultural history of mathematics. As a professor at Université Paris Cité, Ehrhardt presented her recent research on the patrimat project (heritage and heritage making in mathematics). She specifically thanked Gresham College and the British Society for History of Math for the opportunity to discuss how mathematical knowledge is recorded and preserved across generations.
Libraries are fundamental to this heritage making process, acting as places for preserving and transmitting knowledge, but also as sites for creation, where future scholars develop new knowledge from existing collections. The library is commonly referred to as the mathematician’s laboratory, a unique designation reflecting that the material worked with is books and journals made available by these institutions, rather than physical instruments. Certain mathematical texts have acquired such status that they are indispensable for learning; Euclid’s Elements, dating back to around 300 BC, has been continuously translated, transformed, and serves as an essential reference for teaching. The ongoing material connection between ancient texts and modern research is perfectly illustrated by Fermat’s Last Theorem, which was a note in the margin of a 3rd-century AD copy of Diophantus’s Arithmetical and was finally proven using modern number theory at the end of the 20th century.
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The study of 19th-century French libraries, both private collections and secondary school institutions, reveals how the recording and, conversely, the forgetting of mathematical ideas are influenced by their political, intellectual, and publishing contexts. In the early 19th century, scholars actively built specialized private libraries. The large collection of mathematician Louis François Arbogast, consisting of 1,500 to 1,600 volumes, was considered complete enough to write the history of science, containing works ranging from Greek antiquity (like Euclid and Archimedes) to his contemporaries (like Newton and Laplace). These books served as essential working tools. Direct evidence of their use includes handwritten annotations (sometimes expressing displeasure, as noted in Arago’s catalog) and the practical habit of binding separately published papers into single, convenient volumes. The inclusion of extensive mathematical and astronomical tables (logarithmic, trigonometric, divisor tables) in nearly every catalog underscores their effective use in scholarly work.
Yet, building a library was not exclusively about practical utility. Some books were marked "NC" (uncut) or "N" (untrimmed), indicating they had never been opened, having perhaps been received as gifts or purchased for their bibliophilic value.
Figures like Guillaume Libri recognized that mathematical books were a potentially good investment because they had been protected from the general rise in rare book prices. Furthermore, canonical works, even if not directly related to the owner’s research, carried a strong symbolic value. For example, Lagrange owned no fewer than nine editions of Euclid’s Elements. The continuous presence of ancient Greek and Latin authors (Euclid, Archimedes) in these catalogs is largely explained by the ongoing production of new editions, translations, and commentaries that ensured this canonical knowledge remained available and relevant from the 16th to the 19th centuries.
A complementary perspective is offered by the libraries of French secondary schools (Ecoles Centrales and Lycées) following the French Revolution. Here, heritage making was a top-down process, dictated by the Council of Public Instruction, which aimed to preserve books relevant to the future curriculum. Recommended mathematics books were typically recent, analytical, and elementary works chosen for their clarity, comprehensiveness, and applicability to various future jobs, promoting a mathematical heritage that looked toward the future. However, these schools struggled with severe financial and logistical constraints. Many were unable to obtain the books they needed, as the most scientifically interesting material confiscated from the clergy was often sent to major Parisian institutions like the École Polytechnique. While secondary schools did contain classics like Bézout’s textbooks, they also housed renowned advanced works, such as synthesis treaties by Lagrange and Laplace, which far exceeded the required curriculum. These advanced titles were likely distributed as symbolic rewards to top pupils, representing a legacy that celebrated great scientific figures and the analytical advances dominating the academic scene, rather than being preserved for practical teaching purposes. These studies collectively demonstrate that mathematical heritage, though a local resource for research communities, is also fragile, subject to institutional circumstances, political decisions, and constraints beyond the control of mathematicians and librarians.
