Gresham College Lectures How Does Mathematics Last? Heritage and Heritage-making in Mathematics - Caroline Ehrhardt
Discover the fascinating world of mathematical heritage and how knowledge is preserved over generations. Explore the role of 19th-century libraries, from famous mathematicians' collections to school resources. Hear about the significance of annotated texts and how even unread books contribute to a mathematician's legacy. Learn about the challenges schools faced in acquiring crucial textbooks and how library choices reflect deeper academic values. This insightful discussion reveals the intricate connections between mathematics, history, and institutional memory.
46:25
Sale Catalogues Reveal Private Collections
- Sale catalogues of mathematicians' libraries reveal what scholars collected and used in the 19th century.
- Caroline Ehrhardt studied about a dozen sale catalogues to reconstruct intellectual environments and book values.
Usage Markers Show Working Libraries
- Not all books in mathematicians' libraries were used; some remained uncut or served symbolic roles.
- Annotations, compiled papers and numerical tables indicate which volumes supported active research and calculation.
Prizes And Unopened Gifts In Collections
- Some prized books in collections were never opened and came as gifts or for prestige rather than for study.
- Guillaume Libri exemplifies bibliophilic collecting, even involving illicit acquisition of rare volumes.
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Intro
00:00 • 41sec
Defining Heritage-making in Mathematics
00:41 • 2min
Why Libraries Matter for Mathematics
02:18 • 1min
Mathematician Libraries vs. School Libraries
03:45 • 2min
Early 19th-Century Mathematicians' Collections
05:23 • 4min
Using Sale Catalogues as Historical Sources
09:24 • 4min
Evidence of Practical Use in Libraries
12:56 • 4min
Books Kept Unread: Gifts and Bibliophilia
17:02 • 4min
Canonical Texts as Disciplinary Markers
21:08 • 2min
Temporal Span and Editorial Revival
23:05 • 4min
Revolutionary Reforms and School Libraries
27:10 • 2min
Council Recommendations for Teaching Books
28:48 • 2min
Practical Constraints on School Libraries
31:11 • 5min
From École Centrale to Lycées: Library Continuity
35:43 • 52sec
Contents of 19th-Century Lycée Libraries
36:35 • 5min
Top-down Heritage and Symbolic Legacy
41:57 • 31sec
Libraries as Heritage Institutions
42:28 • 51sec
Project Patrimat: Emerging Themes
43:19 • 3min
Outro
45:58 • 15sec
#56485
Diophansi's arithmetics
The Books
Diophantus
Arithmetica is a series of books on mathematics written by Diophantus in Alexandria during the 3rd century AD. It is a collection of 130 problems giving numerical solutions of determinate and indeterminate algebraic equations.
It is an example of Greek mathematics distinct from geometry, and is sometimes described as the beginning of algebra.
It was written in Greek and of the original thirteen books, only six have survived.
#75752
Diophantus Arithmetics
The Books
Diophantus
Arithmetica is a series of books on mathematics written by Diophantus in Alexandria during the 3rd century AD. It is a collection of 130 problems giving numerical solutions of determinate and indeterminate algebraic equations.
It is an example of Greek mathematics distinct from geometry, and is sometimes described as the beginning of algebra.
It was written in Greek and of the original thirteen books, only six have survived.
#35664
Géométrie descriptive
Descriptive Geometry
Gaspard Monge
Géométrie descriptive (Descriptive Geometry) is a mathematical method developed by Gaspard Monge, which allows the representation of three-dimensional objects in two dimensions, using a specific set of procedures.
The resulting techniques are important for engineering and architectural drawings, and are the basis of computer-aided design.
It uses techniques such as orthographic projection to create a representation of a 3D object on a 2D plane.
Descriptive Geometry became an essential tool for engineers, architects, and designers, and is used extensively to solve complex spatial problems.
#35265
Ozanam Treatise
The Treatise
Jacques Ozanam
Jacques Ozanam (1640 – 1718) was a French mathematician best known for his popular mathematics books and recreational problems.
Although he had a strong background in theology, he decided to pursue mathematics instead.
He became a popular mathematics teacher and wrote numerous widely used books, including a treatise on practical geometry, a text on fortifications, and mathematical recreations.
#64345
Lettres à une princesse d'Allemagne
Leonhard Euler
Letters to a German Princess is a collection of popular science letters written by Leonhard Euler to Princess Friederike Charlotte of Brandenburg-Schwedt in the 1760s.
These letters cover a wide range of topics in physics, astronomy, philosophy, and mathematics, explaining complex scientific concepts in an accessible manner.
Euler's goal was to provide the princess with a comprehensive education in the natural sciences, fostering her intellectual curiosity and promoting scientific literacy.
The letters were widely read and translated into multiple languages, contributing to the popularization of science during the Enlightenment.
Euler's clear and engaging writing style made the letters a valuable resource for anyone seeking to understand the fundamental principles of the natural world.
#64384
Mécanique Céleste
Celestial Mechanics
Pierre-Simon Laplace
Mécanique Céleste is a monumental five-volume treatise on celestial mechanics by Pierre-Simon Laplace, published between 1799 and 1825.
This comprehensive work applies mathematical analysis to describe and explain the motions of celestial bodies, including planets, moons, and comets.
Laplace's work built upon the foundations laid by Isaac Newton and others, developing new methods and techniques for solving complex problems in astronomy.
The treatise covers a wide range of topics, including gravitational attraction, orbital dynamics, tidal forces, and the stability of the solar system.
It also includes Laplace's nebular hypothesis, which proposes that the solar system formed from a rotating cloud of gas and dust.
#60532
Ars Conjectandi
The Art of Conjecturing
Jacques Bernoulli
Ars Conjectandi (The Art of Conjecturing) is a foundational work in probability theory written by Jacob Bernoulli and published posthumously in 1713.
This comprehensive treatise explores the principles of probability, combinatorics, and statistics, laying the groundwork for modern statistical inference.
Bernoulli introduces concepts such as the law of large numbers, which states that as the number of trials increases, the sample mean converges to the population mean.
The book also includes discussions of games of chance, mortality rates, and the application of probability to practical problems.
Ars Conjectandi is considered one of the most important works in the history of probability, shaping the development of statistical thinking and providing a foundation for future research.
#50175
Geometry
Cours de mathématiques, à l'usage des gardes du pavillon et de la marine
Maudry
Cours de mathématiques, à l'usage des gardes du pavillon et de la marine, by Antoine-René Mauduit, is a set of mathematics textbooks originally published in 1766 for the training of naval officers.
It included algebra, geometry, trigonometry, conic sections, mechanics and navigation.
#60028
Traité des Fusions
A Treatise of Fluxions
Colin Maclaurin
A Treatise of Fluxions is a comprehensive calculus textbook written by Colin Maclaurin and published in 1742.
It was created in response to the criticisms of calculus made by George Berkeley in The Analyst.
Maclaurin's book set out to provide a rigorous foundation for Newton's methods and became the standard for calculus education in Britain for decades.
#6681
• Mentioned in 6 episodes
Euclid's elements
A. C. McKay
Euclid's Elements is a foundational work of mathematics, comprising 13 books covering geometry, number theory, and other mathematical concepts.
Written around 300 BC, it served as the primary textbook for over two millennia.
The book's rigorous approach to proof, based on postulates and axioms, established a standard for mathematical reasoning that persists to this day.
Its influence on the development of mathematics is immeasurable, shaping the way mathematicians think about and approach problems.
The Elements remains a significant text in the history of mathematics and continues to be studied and appreciated for its clarity and elegance.
#19869
• Mentioned in 2 episodes
L'histoire des mathématiques
Montucla
#73051
Principes mathématiques de la philosophie naturelle
Translation of Newton's Philosophiae Naturalis Principia Mathematica
Émilie du Châtelet
Isaac Newton
Cette traduction, réalisée par Émilie du Châtelet, est la seule version complète en français de la Philosophiae Naturalis Principia Mathematica de Newton.
Elle inclut des commentaires approfondis qui ont contribué à la diffusion des idées newtoniennes en France et en Europe.
Du Châtelet a également apporté des corrections et des précisions importantes à l'œuvre originale, en s'appuyant sur les travaux de scientifiques contemporains comme Clairaut et Bernoulli.
#6681
• Mentioned in 6 episodes
Euclid's elements
A. C. McKay
Euclid's Elements is a foundational work of mathematics, comprising 13 books covering geometry, number theory, and other mathematical concepts.
Written around 300 BC, it served as the primary textbook for over two millennia.
The book's rigorous approach to proof, based on postulates and axioms, established a standard for mathematical reasoning that persists to this day.
Its influence on the development of mathematics is immeasurable, shaping the way mathematicians think about and approach problems.
The Elements remains a significant text in the history of mathematics and continues to be studied and appreciated for its clarity and elegance.
#20341
• Mentioned in 2 episodes
Dialogo
Doue ne i congressi di quatro giornate si discorre sopra i due massimi sistemi del mondo Tolemaico e Copernicano; proponendo indeterminatamente le ragioni filosofiche, e naturali tanto per l'vna, quanto per l'altra parte.
Galileo
'Dialogue Concerning the Two Chief World Systems', published in 1632, is a discourse between three characters: Salviati, representing Galileo's views; Sagredo, an intelligent layman; and Simplicio, a staunch defender of Aristotelian geocentrism.
Galileo skillfully presents arguments for heliocentrism, but Simplicio's stubborn adherence to outdated beliefs leads to his intellectual defeat.
The book's publication ignited controversy, leading to Galileo's trial by the Inquisition and subsequent house arrest.
Galileo's work challenges traditional views and promotes empirical observation and mathematical reasoning.
It remains a cornerstone of the scientific revolution, inspiring generations to question established norms and pursue knowledge through experimentation and critical thinking.
#6681
• Mentioned in 6 episodes
Euclid's elements
A. C. McKay
Euclid's Elements is a foundational work of mathematics, comprising 13 books covering geometry, number theory, and other mathematical concepts.
Written around 300 BC, it served as the primary textbook for over two millennia.
The book's rigorous approach to proof, based on postulates and axioms, established a standard for mathematical reasoning that persists to this day.
Its influence on the development of mathematics is immeasurable, shaping the way mathematicians think about and approach problems.
The Elements remains a significant text in the history of mathematics and continues to be studied and appreciated for its clarity and elegance.
How is mathematical knowledge recorded and preserved across generations? Contrary to the idea that mathematics itself is somehow ‘permanent’, in this talk we will explore heritage-making in mathematics, that is the people, institutions, and material objects that can give mathematical ideas longevity. We will explore the heritage-making found in two very different types of French nineteenth-century libraries: those of famous mathematicians and those of secondary schools. We will especially focus on how the recording – and forgetting – of mathematical ideas is influenced by their publishing, political, and intellectual contexts.
This lecture was recorded by Professor Caroline Ehrhardt on 8th October 2025 at Barnard’s Inn Hall, London.
Caroline Ehrhardt is Professor of History of Science and Deputy Director of IDHE.S at Université Paris 8 professor in history of science at the Université Paris 8 (France). Her research concerns the history of mathematics in France and Europe (1789–1914). She has published on Evariste Galois, on Galois theory and on mathematics education.
Caroline is currently coordinating a collective project funded by the French Agence Nationale de la Recherche, entitled ‘Heritage and patrimonialisation of mathematics, 18th-20th centuries’. She also focuses on the practice of mathematics within French life insurance companies, on interactions between the mathematical and actuarial communities, and the production of mortality tables.
The transcript and downloadable versions of the lecture are available from the Gresham College website: https://www.gresham.ac.uk/watch-now/heritage-maths
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