Sciences, Philosophie, Histoire – UMR 7219, laboratoire SPHERE

– The only existing book on the life and the works of Cholesky and
contemporaries
– Reproduction of an unpublished manuscript on graphical calculation
– English translation of his unpublished paper on the solution of
systems of linear equations and further unpublished documents with
historical and mathematical commentaries

Outside the professional circles of topography and applied mathematics, the life and work of André-Louis Cholesky (1875–1918) are still relatively unknown to the scientific community. This new book appreciably widens the exposure of his remarkable personal achievements in topography and mathematics to a much larger international audience.

Cholesky is also interesting to historians because he is a perfect representative of the "scientists engineers" that, since the early 19th century, had issued from the French scientific high schools. Because they had received a high level of mathematical education, they were able to innovate in their practice of engineering. In the case of Cholesky, this resulted in original contributions in artillery, topography, numerical analysis and graphical
calculation.

In addition, the book places his education and works within the history of several European countries through the 17th to 19th centuries.

The book begins with Cholesky’s biography, followed by his family’s history and an introduction to topography. It continues with a historical analysis of an unpublished paper (translated into English) in which Cholesky explained his method for linear systems. Cholesky’s other works are then described, such as his participation in teaching at a superior "school by correspondence" founded by Léon Eyrolles. His important unpublished book in French on graphical calculation, which is reproduced in its entirety, is analyzed in detail and compared to similar contemporary publications. The biography
of Ernest Benoit, who wrote the first paper on Cholesky’s method, is provided. Various documents, highlighting the life and the personality of Cholesky, round out his story and end the book..

The authors :

Claude Brezinski is emeritus professor of numerical analysis at the University of Sciences and Technologies of Lille (Laboratory Paul Painlevé, UMR CNRS 8524), France. His work mainly concerns extrapolation methods, orthogonal polynomials, Padé and rational approximation and numerical linear algebra. He also published several papers and books on the history of sciences.

Dominique Tournès is professor of mathematics and history of mathematics at the University of La Réunion (Laboratory of Mathematics and Computer Science, EA 2525), France and associate researcher at the SPHERE laboratory (UMR 7219, CNRS and University Paris-Diderot, France). His work focuses on the history of calculation methods and instruments since the seventeenth century, particularly regarding differential equations.

: : Birkhäuser, History of Science
: : XIII, 331 p., 134 illus.
: : ISBN 978-3-319-08135-9
: : 2014

TABLE DES MATIERES

• 1.1 Infancy and Studies, p. 2
• 1.2 The topographer, p. 7
  • 1.2.1 France, p. 9
  • 1.2.2 Crete, p. 12
  • Tunisia and Algeria, p. 17
• 1.3 The teacher, p. 23
• 1.4 The soldier, p. 26
  • 1.4.1 The Groups of firing grids, p. 27
  • 1.4.2 Romania, p. 30
  • 1.4.3 The second battle of Picardy, p. 33

2. Cholesky’s family, p. 45

• 2.1 Cholesky’s ancestors, p. 45
• 2.2 The siblings, p. 53
• 2.1 The next generation, p. 56

3. On topography, p. 63

• 3.1 Triangulation, p. 64
• 3.2 Leveling, p. 71
• 3.3 Cholesky’s double–run leveling, p. 72

4. The method of Cholesky for linear systems, p. 77

• 4.1 The least squares method, p. 77
• 4.2 The adjustment of networks, p. 82
• 4.3 Methods for linear systems, p. 84
• 4.4 Cholesky’s manuscript, p. 91
• 4.5 Analysis of the manuscript, p. 101
• 4.6 After Cholesky, p. 105
• 4.7 Diffusion of Cholesky’s method, p. 107
• 4.8 Early books, p. 114
• 4.9 Nowadays, p. 119

5. Other works of Cholesky, p. 123

• 5.1 Military documents, p. 123
• 5.1.1 Manuscripts, p. 123
• 5.1.2 Typed documents, p. 126
• 5.2 Courses at ESTP, p. 127
  • 5.2.1 Complément de Topographie, p. 127
  • 5.2.2 Cours de Topographie, p. 127
• 5.3 Other manuscripts, p. 128
• 5.4 Books, p. 129
  • 5.4.1 Cours de Topographie, p. 129
  • 5.4.1 Levés d’Etudes à la Planchette, p. 134

6. Léon Eyrolles and his superior school, p. 139

• 6.1 The man and his school, p. 139
• 6.1 The publisher, p. 150

7. An unpublished book by Cholesky, p. 153

• 7.1 Graphical calculation before 1914, p. 154
  • 7.1.1 What is graphical calculation ?, p. 154
  • 7.1.2 A short overview of the history of graphical calculation, p. 155
  • 7.1.3 Theoretical principles of nomography, p. 164
• 7.2 Graphical calculation at the ESTP, p. 169
• 7.3 The unpublished manuscript, p. 172
• 7.4 Genesis of the course on graphical calculation, p. 175
  • 7.4.1 The commission from the ESTP, p. 175
  • 7.4.2 Cholesky’s preliminary research, p. 177
  • 7.4.3 Sources of inspiration for the course, p. 180
• 7.5 Analysis of the course on graphical calculation, p. 182
  • 7.5.1 Subject and organization of the course, p. 182
  • 7.5.2 The graphical representation of numbers, p. 184
  • 7.5.3 Representation of two–variable equations by curves, p. 184
  • 7.5.4 Representation of three–variable equations by surfaces, p. 188
  • 7.5.5 A personal theory of abaques, p. 190
  • 7.5.6 Final comments, p. 193

8. Ernest Benoît, p. 197

• 8.1 Biography of Benoît, p. 197
• 8.2 Benoît’s paper, p. 206
• 8.3 Benoît’s eulogy of Cholesky, p. 207

9. Documents, p. 211

• 9.1 Military documents, p. 211
  • 9.1.1 Mentions in dispatches, p. 211
  • 9.1.2 Individual campaign leaflet, p. 212
  • 9.1.3 Transcription of the marks, p. 216
• 9.2 Notebooks, p. 216
  • 9.2.1 Notebook No,2, p. 216
  • 9.2.2 Notebook No,3, p. 222
  • 9.2.3 Notebook No,5, p. 228
• 9.3 Archives, p. 228

A On trigonometry, p. 233
B Sur la résolution num´erique des systèmes d’´equations linéaires, p. 235
Cours de Calcul Graphique, p. 243
Chronology of the life of André-Louis Cholesky, p. 303
Acknowledgments, p. 306
Bibliography, p. 309
Index, p. 327