# Introduction

1In the year 2000 the *Cahiers d’Economie Politique* (no. 36, pp. 145-151) published a remarkable paper by Emeric Lendjel, entitled “Une contribution méconnue dans l’histoire de la pensée économique : le modèle de l’Abbé M. Potron (1935)”. It definitely drew the attention of historians of economics to Maurice Potron as the most unusual precursor of Leontief and Sraffa. After 2000 Lendjel and many other economists (Abraham-Frois, Fischman, Bidard, Erreygers, Parys, Mori, Fujimoto, Bellino, etc.) produced additional publications on Potron’s work, giving Potron his long overdue place in the history of input-output analysis and mathematical economics.

2Because many of Potron’s writings are hard to find, it is useful to produce a list of Potron’s published and unpublished writings. In the last decade a lot of overlooked material has come to light, and thereby a list of more than eighty Potron items can be constructed. A first version of my Annotated Potron Bibliography appeared as Research Paper 2010-003 in February 2010 (University of Antwerp, Department of Economics, 22 p.). The present text is a revised and more refined version. It adds some writings that I had overlooked in 2010, it gives some additional information on authors that cited Potron’s economics or mathematics, it includes references to the English translations of Potron’s economic papers in the 2010 Bidard-Erreygers edition, and it improves the description of Potron’s hard to find “Solution Booklets” at the end of the paper.

3To avoid misunderstanding, I shortly summarize the scope of the bibliography:

- I try to list all known “scholarly” writings by Potron, in a broad sense, including some letters to scholars of international standing (for example, Hilbert and Frisch). I do not include texts of Potron’s religious sermons, or letters about his teaching, his career or other practical matters. Some correspondence with French colleagues on minor mathematical problems can be found in the Archives Jésuites de la Province de France in Vanves, some private letters are in the family archives.
- It is obvious that many journal articles were also available as offprints, but I mention the offprints only in special cases.
- Economics: before 2000 the citations to Potron’s economics were rare and unaware of Potron’s relevance. Because of Potron’s importance for economics, I try to give some information about all these hardly noticed citations to Potron’s economics in the 20
^{th}century. For the fast growing number of references to Potron in the 21^{st}century economic literature, I refer the reader to*EconLit*and other well-known modern databases. - Noneconomic writings: I mention a selection of interesting citations to Potron’s writings on mathematics and on other noneconomic topics. Although his mathematics was not as innovative as his economics, it was competent and it often appeared in prestigious French mathematical journals. Hence, many of Potron’s mathematical publications were abstracted in the three main review journals of mathematics:
- JFM =
*Jahrbuch über die Fortschritte der Mathematik* - ZBL =
*Zentralblatt für Mathematik und ihre Grenzgebiete* - MR =
*Mathematical Reviews*.

For JFM, ZBL and MR, I usually provide only the name of the reviewers, because the abstracts are easily found in the electronic databases*Zentralblatt MATH*(which covers JFM and ZBL) and*MathSciNet*(which covers MR). I include information on other mathematical sources in cases where it seems useful.

- JFM =
- Solutions to examination questions: in the 1930s Potron produced many articles and some booklets that contained the solutions to the examination sessions for the
*Certificat de Calcul Différentiel et Intégral*(C.D.I.) in all the Faculties of France. I list these items in a special section at the end, separated from the rest of the bibliography, in order not to spoil the reader’s panorama of Potron’s stream of normal publications. Moreover, these short texts are not enjoying the same scholarly status as Potron’s “real” books and articles (his solution booklets were not deposited in the*Bibliothèque Nationale de France*).

4Section 1 contains scholarly writings until 1942 (the year of Potron’s death). Section 2 gives the posthumous publications which appeared since 2000, after Potron’s works had been neglected for many decades. Finally, section 3 contains the “less scholarly” articles and booklets on mathematical examination sessions from the 1930s.

5Note that all **economic** publications in section 1 are concentrated in the periods 1911-1914 and 1935-1942. To make it easier for the (economist) reader to identify quickly the entries that are relevant for economics, I have preceded such entries by the indication **Econ**.

# 1 – Potron’s scholarly writings until 1942

6[1901-1902] “Sur la génération de quelques courbes remarquables par le campylographe du P. Marc Dechevrens, S.J.”, *Annales de la Société Scientifique de Bruxelles*, 26 (Seconde Partie – Mémoires): 41-56.

7Potron’s mathematical study of the campylograph, a sophisticated apparatus to draw geometrical curves, stereoscopic figures and artistic drawings. The first two pages contain an introduction written by the inventor of the campylograph, the Jesuit meteorologist and physicist Marc Dechevrens (1845-1923).

8Volume 26 of the *Annales* covers part of 1901 and 1902. Potron’s paper in the ‘Seconde Partie’ was published in 1902. According to information in the ‘Première Partie’ (p. 76), this work of Father Potron was presented by Father Thirion, in the name of Father Dechevrens, in the Second Section of the meeting held by the “Société Scientifique de Bruxelles” on 21 November 1901 in Ghent.

9An offprint of the article was published by Polleunis & Ceuterick in Brussels in 1902.

10The *Bulletin of the American Mathematical Society*, vol. 9, October 1902, p. 70 (list of new publications) mentions: “Potron. Le campylographe du P. Marc Dechevrens. Etude de quelques courbes remarquables tracées avec cet instrument. Paris: Gauthier-Villars, 1902.”

11[1902] *Letters to David Hilbert.* Conserved in the Nachlass David Hilbert, Cod. Ms. D. Hilbert 315, Niedersächsische Staats- und Universitätsbibliothek in Göttingen.

12In 1902 Potron wrote five letters (in French) to Hilbert. In the first letter (13 July 1902) Potron referred to advice and recommendation by Paul Appell to contact Hilbert. Potron mentioned he had earned an engineering degree from the Ecole Polytechnique, but that he now preferred a career in teaching and research in mathematics. Potron asked for advice on choosing a research topic.

13Although this happened in the middle of the summer holidays, Potron quickly became impatient for an answer. Already on 29 July Potron wrote a new letter to Hilbert, pointing out that «three weeks ago» he had written a letter that probably was lost in the mail and hadn’t reached Göttingen. Therefore Potron repeated his story of 13 July. Hilbert answered in a letter of 31 July, which is not extant. Potron replied on 29 August, and thanked Hilbert for his letter of 31 July. Apparently Hilbert had suggested Potron could spend a few months in Göttingen, because serious guidance was not possible by letters. Potron also thanked Hilbert for his bibliographical advice to read a 1899 work by Hilbert (this must be *Grundlagen der Geometrie*) and to read also a text by Max Dehn. Potron pointed out that he was «not completely free in his actions» because this year and the following years he had to take theology courses in Canterbury, but there were some periods when his stay in England was not necessary, for example starting from April. Potron wondered whether this was a suitable period for studying in Göttingen: maybe yes if he could do private studies, maybe no if Hilbert wanted Potron to attend his lectures on geometry.

14Two days later (31 August) Potron wrote letter number four «to add something he forgot», and he asked Hilbert for a copy of part of his lecture notes.

15And a few days later, 9 September, Potron sent a fifth letter to Hilbert, because in earlier letters Potron had «not given an answer about Hilbert’s advice on research topics». It appeared that Hilbert had suggested to Potron to study elliptic geometry without using continuity notions in the plane, only by means of axioms of congruence. Potron also referred to the historical speech by Hilbert at the International Congress of Mathematicians in Paris in 1900, where Hilbert had presented his famous list of 23 unsolved problems in mathematics. Potron referred especially to Hilbert’s problem number six – mathematical treatment of the axioms of physics – where Hilbert mentioned a book by Boltzmann (this must be *Vorlesungen über die Prinzipien der Mechanik*, 1897) on the principles of mechanics, and Hilbert’s proposal to try to establish the laws of motion of rigid bodies.

16Ultimately Potron chose another topic and promoter, and wrote a dissertation on group theory in 1904, under the supervision of Emile Picard (the dissertation never mentions Hilbert).

17[1904a] *Les Groupes d’Ordre p*^{6}. Paris: Gauthier-Villars, 177 p.

18This book is Potron’s doctoral dissertation in mathematics (Faculté des Sciences de Paris, 28 June 1904). The jury consisted of Emile Picard (supervisor), Paul Appell (chairman) and Henri Poincaré. The reports on the thesis (by Picard) and on the oral defense (by Appell) are conserved in the file AJ16 5538, Archives Nationales, Paris.

19Nearly all the doctoral dissertations in the Faculté des Sciences in Paris obtained the grade of “très honorable”, but Potron received the lower grade of “honorable”. See the dissertation lists in *Revue Internationale de l’Enseignement*, 1905, vol. 50, pp. 141-143, 148, 154. These lists contain 12 dissertations from the Faculté des Sciences in Paris: 10 receive “très honorable”, only 2 receive the low grade of “honorable”.

20At that time Potron was also a student in theology at the Institut Catholique de Paris. Its journal, the *Revue de l’Institut Catholique de Paris* (1904, vol. 9, p. 467-468) doesn’t mention Potron’s low grade, but announces that Potron had defended his doctoral dissertation “with success”.

21Potron’s dissertation is the first attempt to list the groups whose number of elements is the sixth power of a prime number. Therefore it is regularly cited in the mathematical literature. An interesting example is Hall, P. (1940). “The construction of soluble groups”, *Journal für die reine und angewandte Mathematik*, 182: 206-214 (Philip Hall was a member of King’s College, Cambridge; Robert Remak intended to work with Hall in Cambridge in 1940, but Remak could not visit England in 1940, and died on transport to Auschwitz in 1942. Note that Remak, just like Potron, was both a specialist in group theory and a pioneer of linear economics). Some recent remarks on the dissertation of 1904 can be found in Newman, M.F., O’Brien, E.A. & Vaughan-Lee, M.R. (2004). “Groups and nilpotent Lie rings whose order is the sixth power of a prime”, *Journal of Algebra*, 278: 383-401.

22Page 175 of Potron’s dissertation mentions: “Seconde thèse. Propositions données par la Faculté. *Mécanique.* – *Figures d’équilibre d’une masse fluide animée d’un mouvement de rotation uniforme.”* This so-called second thesis needed no printed version. The jury report on the oral defense mentions that Potron had described Poincaré’s research on this topic. To help Potron, a few days before this oral presentation, the Jesuit mathematician Jean-Armand de Séguier wrote two letters (20 and 22 June 1904) to Pierre Duhem, asking for some comments related to Potron’s “seconde thèse” (letters in Fonds Duhem, Archives de l’Académie des Sciences de l’Institut de France, Paris). Note that de Séguier wrote the first monograph that surveyed the new results of abstract group theory: *Théorie des groupes finis. Eléments de la théorie des groupes abstraits*, Paris: Gauthier-Villars, 1904. In the preface de Séguier wrote: “Un ami dévoué, M. Potron, a bien voulu relire le manuscript en entier avec le plus grand soin : je lui en exprime ici toute ma gratitude”. A review (signed M.O.) of de Séguier’s book in *Revue des Questions Scientifiques*, 1905, pp. 258-260 cites Potron’s 1904 dissertation.

23Since a few years a reproduction of Potron’s dissertation can be ordered from many publishers that offer reprints on demand of books that are out of copyright (Nabu Press, Facsimile Publishers, ReInk Books, Book on Demand, Lang, Ulan Press, etc.)

24[1904b] “Sur quelques groupes d’ordre p^{6”}, *Bulletin de la Société Mathématique de France*, 32: 296-300.

25Reviewed in JFM by Alfred Loewy.

26Potron’s note corrects some results of his 1904 dissertation, as is announced by the opening statement: “Cette Note a pour but de rectifier et de compléter les résultats obtenus dans ma Thèse de Doctorat…” This might explain the title used by Potron for the offprint: “Note pour rectifier et compléter les résultats touchant les groupes d’ordre *p*^{6}”, Gauthier-Villars, Paris, 1905. I take the reference for this unseen offprint from the *Moniteur Bibliographique* (see its 1905 list, p. 98, which adds: “Extrait du *Bulletin de la Société Mathématique de France*”). The *Moniteur Bibliographique* contains bibliographical lists of works written by Jesuits, up to 1915; it mentions the titles as signaled by the Jesuit authors themselves, and in many cases it is very incomplete. In total the *Moniteur Bibliographique* lists only eleven entries by Maurice Potron, and it refers to the year 1905 for the offprint, but the original *Bulletin* article is from 1904 (Potron didn’t publish anything in the *Bulletin* in 1905).

27[1904c] “Les (*p* premier) dont tous les sont abéliens”, *Bulletin de la Société Mathématique de France*, 32: 300-314.

28Reviewed in JFM by Alfred Loewy.

29[1904d] “Sur les groupes d’ordre *p ^{m}* (

*p*premier) dont tous les sous-groupes d’ordre

*p*

^{m}^{-2}sont abéliens”,

*Comptes Rendus de l’Académie des Sciences*, 139: 396-399. (Session of 8 August).

30Note presented by Emile Picard.

31[1904e] “Sur les groupes d’ordre *p ^{m}* (

*p*premier,

*m*> 4) dont tous les diviseurs d’ordre

*p*

^{m}^{-2}sont abéliens”,

*Comptes Rendus de l’Académie des Sciences*, 139: 963-964 (Session of 5 December).

32Note presented by Emile Picard.

33[1905] “Note Bibliographique : J.-A. de Séguier, Eléments de la théorie des groupes abstraits”, *Etudes*, 103: 140-141 (5 April).

34Book review by Potron.

35[1905-1906] *Carnets d’Observations.* Paris: Observatoire de Paris (Archives, Reference number A-F. 14)

36The library of the *Observatoire de Paris* conserves five *carnets* bearing Potron’s name, that is, five notebooks of astronomical observations made by Potron. Each notebook contains about 37 double pages, with daily observations and computations. The dates are as follows: 4 April 1905 – 8 November 1905 (no observations between 10 June and 6 October); 9 November 1905 – 23 January 1906; 24 January 1906 – 5 March 1906; 5 March 1906 – 28 March 1906; 3 April 1906 – ends unfinished on 1 May 1906.

37[1906a] “Sur une formule générale d’interpolation”, *Bulletin de la Société Mathématique de France*, 34: 52-60.

38Reviewed in JFM by Carl Weltzien.

39Potron studies some polynomials defined by Emile Borel on p. 82 of his *Leçons* (see [1906c] for Potron’s review of Borel’s book).

40[1906b] “Revue de Livre : B. Baillaud & H. Bourget (Eds.), Correspondance d’Hermite et de Stieltjes”, *Etudes,* 107: 533 (20 May).

41Book review by Potron.

42[1906c] “Revue de Livre : E. Borel, Leçons sur les fonctions de variables réelles et les développements en séries de polynomes / R. Baire, Leçons sur les fonctions discontinues”, *Etudes,* 107: 538-539 (20 May).

43Two book reviews by Potron.

44[1906d] “Note Bibliographique : G. Vivanti, Leçons élémentaires sur la théorie des groupes de transformation”, *Etudes,* 107: 856-857 (20 June).

45Book review by Potron.

46[1906e] “Note Bibliographique : Abel Souchon, La construction des cadrans solaires”, *Etudes*, 109: 427 (5 November).

47Book review by Potron.

48[1907a] “Note Bibliographique : G. Darboux, Etude sur le développement des méthodes géométriques”, *Etudes*, 110: 139-140 (5 January).

49Book review by Potron.

50[1907b] “Note Bibliographique : G. Papelier, Formulaire de mathématiques spéciales”, *Etudes*, 110: 428 (5 February).

51Book review by Potron.

52**Econ** [1911a] “Communication”. Included as a footnote pp. 175-176 in G. Desbuquois, “La justice dans l’échange”, in: *Semaine Sociale de France. Cours de Doctrine et de Pratique Sociales. 8 ^{ème} Session – Saint-Étienne 1911. Compte rendu in-extenso.* Lyon: Chronique Sociale de France, pp. 165-177. Identical footnote pp. 882-883 in G. Desbuquois, “La loi du juste prix”,

*Le Mouvement Social*, 72: 867-884 (October).

53A footnote of about 700 words by Potron, who provides a nonmathematical summary of his forthcoming articles [1912a] and [1913a]. The footnote has no title, but elsewhere Potron [1911b, p. 4] calls it a “communication”. Desbuquois read his paper in Saint-Etienne, in the *Semaine Sociale*, on 1 August 1911 (see the conference programme in *Année Sociale Internationale*, Reims: Action Populaire, 1911, p. 44).

54The imprimatur of the *Semaine Sociale* proceedings was given on 4 November 1911, and so these proceedings were published after the October issue of *Le Mouvement Social.* The two Desbuquois papers choose a different title, but contain an almost identical text, except that the version in the *Semaine Sociale* proceedings is more readable, because it adds titles for the different sections and paragraphs.

55“La loi du juste prix” by Desbuquois also appeared as “brochure 251” from *Action Populaire*, Série Sociale.

56In 1969 Paul Droulers, a Jesuit and historian of social Catholicism, published his book *Politique Sociale et Christianisme. Le Père Desbuquois et l’Action Populaire. Débuts. Syndicalisme et Intégristes (1903-1918)*, Paris: Editions Ouvrières. In this book (see especially pp. 214-216), Droulers explicitly praised Potron’s pioneering mathematical economics and his use of Perron-Frobenius, but other historians of church history didn’t understand Potron’s relevance, and historians of economics didn’t notice Droulers or Potron. Droulers stressed that Potron’s work deserved more attention, and should have been mentioned in Joseph Schumpeter’s classic *History of Economic Analysis.* Droulers referred to [1911a], and also to some other publications by Potron, all from the period 1911-1913 (see below).

57Potron’s text [1911a] is translated into English as “Abstract of a study on just prices and wages”, in [2010: Chapter 1].

58**Econ** [1911b] “A propos d’une contribution mathématique à l’étude des problèmes de la production et des salaires”, *Echos de l’Union Sociale d’Ingénieurs Catholiques et des Unions-Fédérales-Professionnelles de Catholiques*, vol. 2, no. 7: 4-7 / *Echos des Unions-Fédérales-Professionnelles de Catholiques*, vol. 2, no. 7: 4-7 (15 October).

59In 1911 the *Union Sociale d’Ingénieurs Catholiques* (USIC) and the *Unions-Fédérales-Professionnelles de Catholiques* (UFPC) issued two highly overlapping *Echos*, both containing the same Potron article. The two journals used erratically changing titles and numbering systems. The cover of the 15 October 1911 issue of the first journal mentions vol. 3 instead of vol. 2, but that seems to be a numbering error. Copies of the original 1911 *Echos* journals were recently found in the archives of the Mouvement Chrétien des Cadres et Dirigeants (MCC), Paris.

60This is the first text that displays Potron’s pioneering mathematical economics. It announces [1912a] and [1913a], and provides a mathematical summary of these two forthcoming articles.

61There exists an offprint using the title “Contribution mathématique à l’étude des problèmes de la production et des salaires” and mentioning: Extrait des “*Echos de l’Union Sociale d’Ingénieurs Catholiques*”. This offprint is available in the Archives Jésuites de la Province de France in Vanves. It has no date, it omits the editorial opening and closing paragraph, and it includes a few modifications in section 3.

62This offprint is reprinted in [2004: 57-62].

63The original text of the article, plus the modified section 3 from the offprint, are translated into English as “With regard to a mathematical contribution to the study of the problems of production and wages”, in [2010: Chapter 2].

64**Econ** [1911c] “Quelques propriétés des substitutions linéaires à coefficients ≥ 0 et leur application aux problèmes de la production et des salaires”, *Comptes Rendus de l’Académie des Sciences*, 153: 1129-1132 (errata p. 1541) (Session of 4 December).

65Note presented by Paul Appell.

66Reviewed in JFM by Ernst Jacobsthal (who had been a student of Frobenius).

67Mentioned by Paul Droulers (for more details see [1911a]).

68The Dutch Jesuit Theodor Mulder (1914-1992), doctor in economics from Tilburg University, who lectured at the Gregorian University in Rome, wrote a long contribution on Jesuit economic thought in an ambitious Jesuit encyclopedia that was intended to be published in English and Spanish, but after many years of preparation, only the Spanish version of this multivolume encyclopedia finally appeared in 2001. Without giving further bibliographical details, Mulder mentions Potron’s “econometric model that was presented at the Académie des Sciences in 1911” ; Mulder’s remark is on page 1186 of his essay “Economía, Teorías”, in Charles E. O’ Neill & Joaquin Ma. Dominguez, *Diccionario histórico de la Compaňía de Jesús*, Madrid : Universidad Pontificia Comillas, Volume 2, pp. 1177-1187. As Mulder died in 1992, his contribution was surely written long before the 21^{st} century Potron revival.

69Potron’s article [1911c] is reprinted in [2004: 63-66].

70Translated into English as “Some properties of linear substitutions with coefficients ≥ 0 and their application to the problems of production and wages”, in [2010: Chapter 3].

71**Econ** [1911d] “Application aux problèmes de la ‘production suffisante’ et du ‘salaire vital’ de quelques propriétés des substitutions linéaires à coefficients ≥ 0”, *Comptes Rendus de l’Académie des Sciences*, 153: 1458-1459. (Session of 26 December).

72Note presented by Paul Appell.

73Reviewed in JFM by Ernst Jacobsthal.

74Mentioned by Paul Droulers (for more details on Droulers, see [1911a])

75Mentioned by Theodor Mulder (for more details on Mulder, see [1911c]).

76Reprinted in [2004: 67-68].

77Translated into English as “Application to the problems of ‘sufficient production’ and the ‘living wage’ of some properties of linear substitutions with coefficients ≥ 0”, in [2010: Chapter 4].

78**Econ** [1912a] “Possibilité et détermination du juste prix et du juste salaire”, *Le Mouvement Social*, 73: 289-316 (15 April).

79This is the opening article of the April issue, whose cover uses the following slightly permuted title: “Possibilité et détermination du juste salaire et du juste prix”.

80The permuted title (“salaire et prix” instead of “prix et salaire”) is listed in the *American Economic Review*, December 1912, p. 979 in the section “Periodical Abstracts. Theory” by Walter Adriance, but, unlike for most other articles, Adriance provides no abstract for Potron’s text. The same permuted title is also listed in some other journals, for example in *La Réforme Sociale*, 1-16 August 1912, p. 215, in the section “Revue des revues de langue française” by Paul Doin, who is more informative: “L’auteur est un mathématicien; il prétend établir la possibilité de résoudre le problème du juste salaire et du juste prix à l’aide d’équations”.

81In [1914c, Part B, p. 28n] Potron himself cites the permuted title, but in [1913a, §11] he cites the nonpermuted one.

82The nonpermuted title also appeared as “brochure N° 274”, Action Populaire, Série Sociale, published by Maison Bleue, Paris – Action Populaire, Reims –Victor Lecoffre, Paris.

83Mentioned by Paul Droulers (for more details on Droulers, see [1911a]).

84In the social sciences literature of the 1910s I discovered only one reviewer who immediately and explicitly drew attention to Potron’s pioneering use of the matrix theorems of Perron and Frobenius, i.e. an anonymous reviewer in the *Rivista Internazionale di Scienze Sociali e Discipline Ausiliarie,* 31 May 1912, vol. 59, pp. 67-69. This reviewer provided an interesting summary of Potron [1912a], emphasizing the interdependence of just wages and just prices, the problem of their compatibility, and the relevance of the mathematical results of ‘due scrittori, l’uno svedese, il Terron [sic], l’altro tedesco, il Frobenine’. (p. 69). Here the reviewer is repeating Potron’s strange blunder, claiming that Perron was “Swedish”. In point of fact, both Perron and Frobenius were German, and never had a special private or professional connection to Sweden. Probably the anonymous reviewer was either Filippo Ermini (a philologist who usually took care of the section in the *Rivista* that contained summaries of international journal articles) or Giuseppe Toniolo (an economist from the University of Pisa; he was the driving force behind the *Rivista*, and, just like Potron, a supporter of the corporatist system that was proposed in the encyclical *Rerum Novarum* by Pope Leo XIII).

85Reprinted in [2004: 69-93].

86Translated into English as “Possibility and determination of the just price and the just wage”, in [2010: Chapter 5].

87**Econ** [1912b] “Contribution mathématique à l’étude des problèmes de la production et des salaires”, *Journal de la Société de Statistique de Paris*, 53: 247-249 (May).

88According to the editorial introduction, this is part of a letter from Potron to the *Journal*. The text appeared in the section “Variété”, and was published without a title. The above title was given in the table of contents.

89Listed (using the above title) in *American Economic Review*, December 1912, p. 1031 in the section “Periodical Abstracts. Statistics” by Allyn Young, who gives the following vague summary of this nonmathematical text by Potron: “Proposes a method of determining the cost of living in terms of all the products (and labor) used up in the production of consumption goods.”

90Reprinted in [2004: 95-100].

91Translated into English as “Mathematical contribution to the study of the problems of production and wages”, in [2010: Chapter 6].

92**Econ** [1912c] *Relations entre la Question du Chômage et Celles du Juste Prix et du Juste Salaire*. Mimeo conserved in the library of the Université Catholique de l’Ouest (Angers), catalogue number TU908-3-2, date uncertain, 3 p.

93Translated into English as “Relations between the question of unemployment and those of the just price and the just wage”, in [2010: Chapter 7].

94**Econ** [1913a] “Quelques propriétés des substitutions linéaires à coefficients ≥ 0 et leur application aux problèmes de la production et des salaires”, *Annales Scientifiques de l’Ecole Normale Supérieure*, 3^{ème} série, 30: 53-76.

95Reviewed in JFM by Ludwig Bieberbach, who notes that most of Potron’s mathematics will be recognized by German readers of Perron and Frobenius.

96Mentioned by Paul Droulers (for more details on Droulers, see [1911a]).

97Cited by Michel Huber in his *Cours de Statistique Appliquée aux Affaires, Volume V : Statistiques d’Entreprises*, Paris: Hermann, 1948, p. 138. In a (nonmathematical) paragraph on “Part du salaire dans le prix de revient” Huber studies the direct and indirect wages entering the price of a commodity. He refers to the production of bread, which involves not only the wages of the bakery workers, but also the wages in the production of the flour, not only the wages of the mill workers, but also the wages involved in producing the mill equipment, etc. Huber suggests that such complicated questions led Father Potron to the use of matrices, and he refers to Potron’s *Annales* 1913 article, and to Potron’s 1937 lectures (see [1937e]). Huber is the first to point to Potron’s equations for the computation of the direct and indirect labour content (in more traditional parlance “the labour value”) of a commodity. Michel Huber (1875-1947) was an internationally respected statistician (obituary in the *Journal of the Royal Statistical Society*, 1947, pp. 85-86). He knew Potron very well via the Societé de Statistique de Paris.

98Reprinted in [2004: 101-126].

99Translated into English as “Some properties of linear substitutions with coefficients ≥ 0 and their application to the problems of production and wages”, in [2010: Chapter 8].

100[1913b] “Rapports des correcteurs sur les compositions du concours général (10 juin 1913) – Mathématiques”, *Bulletin des Facultés Catholiques de l’Ouest,* September 1913, 20^{ème} année, no. 4, pp. 3-5.

101Pages 3-5 of the report are written and signed by Potron, and contain comments on the mathematical part of the “concours général” of 10 June 1913.

102In the *Moniteur Bibliographique* (1914, XLIII, p.72) Potron signals his contribution to the report and uses the following title: “Compte rendu des compositions de mathématiques du concours général des Facultés Catholiques de l’Ouest pour 1913” (for more information on the *Moniteur Bibliographique,* see entry [1904b]).

103**Econ** [1914a] “Contribution mathématique à l’étude de l’équilibre entre la production et la consommation”, in: L. Varlez & M. Lazard (Eds.), *Assemblée Générale de l’Association Internationale pour la Lutte contre le Chômage. Gand, 5-6 Septembre 1913. Procès-verbaux des Réunions et Documents Annexes*. Paris: Service des Publications de l’Association Internationale pour la Lutte contre le Chômage, Annexe VII, pp. 163-171. Identical text in *Bulletin Trimestriel de l’Association Internationale pour la Lutte contre le Chômage*, 1914, vol. 4, no. 2, pp. 509-517.

104Although Potron’s paper was not presented at the 1913 conference in Ghent (Gand, Gent), it was included as one of the appendices in the conference book in 1914. The articles from the conference book also appeared in various issues of the *Bulletin*. When later citing his own contribution, Potron [1914c, p. 505] referred to the book, not to the *Bulletin.*

105Translated into English as “Mathematical contribution to the study of the equilibrium between production and consumption”, in [2010: Chapter 9].

106[1914b] “Revue de Livre : M. Gandillot, Abrégé sur l’hélice et la résistance de l’air”, *Etudes,* 139: 141-142 (5 April).

107Book review by Potron.

108**Econ** [1914c] “L’organisation scientifique du travail. Le Système Taylor. A. Les Principes”, *Le Mouvement Social*, 77: 497-510 (15 June) – “L’organisation scientifique du travail. Le Système Taylor. B. Les Sanctions de l’Expérience”, *Le Mouvement Social*, 78: 21-33 (15 July).

109Part A is reviewed in the *Rivista Internazionale di Scienze Sociali e Discipline Ausiliarie,* 31 July 1914, vol. 65, pp. 366-367 (for information on the anonymous reviews in this journal, see [1912a] above).

110Part A is cited by Angelo Mariotti in 1918 in a footnote on p. 49 of his article “L’organizzazione razionale del lavoro”, *Rivista Italiana di Sociologia*, 22: 48-73.

111Parts A and B together are translated into English as “The scientific organization of labour. The Taylor System”, in [2010: Chapter 10].

112[1919] “Monde (Le Système du)”, in: Adhémar d’Alès (Ed.), *Dictionnaire Apologétique de la Foi Catholique contenant les Preuves de la Vérité de la Religion et les Réponses aux Objections tirées des Sciences Humaines.* Quatrième édition entièrement refondue. Tome 3, Fascicule 15, Modernisme – Musique religieuse. Paris: Beauchesne. Columns 867-878.

113The *Dictionnaire Apologétique* was a well-known Catholic encyclopedia, whose first three editions had been edited by Jean-Baptiste Jaugey at the end of the 19^{th} century. The present fourth edition was a much larger and completely revised work, edited by Adhémar d’Alès, professor at the Institut Catholique de Paris.

114About eight thousand subscribers received 24 paperback Fascicules, starting with “Agnosticisme – Aumône” in 1909 and ending with “Templiers – Zoroastre” in 1928. The Fascicules were then put together in four hardcover Tomes. A supplement with an index was published in 1931. Potron’s article appeared in Fascicule 15, which was first published in 1919. (See the 1920 review of Fascicules 10 to 15 by Ferdinand Cavalerra in *Nouvelle Revue Théologique*, 47: 59-62).

115Today many libraries own hardcover editions of the encyclopedia, in which Potron’s text is found in Tome 3, which contains Fascicules 13 to 18. In some hardcover editions the title page of Tome 3 mentions the year 1916, but this refers to the publication year of Fascicule 13, the first of this Tome (other hardcovers of Tome 3 mention 1926, but this is the year of a reprint). Each of the four Tomes contains almost a thousand pages printed in two numbered columns.

116Potron’s contribution “Le Système du Monde” describes the history of cosmological doctrines, from ancient Greece via Copernicus, Galileo, Kepler and Newton to his contemporaries Poincaré and Lorentz (Einstein is not mentioned).

117The text is clearly inspired by Pierre Duhem’s multivolume work *Le Système du Monde*. Contrary to many of Potron’s other writings, this 1919 contribution is well written, and provides an extensive bibliography, containing more than fifty items. On 13 November 1910 Potron had asked Duhem to help him with the encyclopedia contribution, because it was “une œuvre entreprise pour la défense de la Foi et de l’Eglise” (letter from Potron to Duhem, conserved in the Fonds Duhem, Archives de l’Académie des Sciences de l’Institut de France, Paris).

118[1921] “Sur une représentation du groupe des 27 droites en groupe de collinéations quaternaires”, *Comptes Rendus de l’Académie des Sciences*, 173: 346-348. (Session of 8 August).

119This note is cited by Jean-Armand de Séguier, “Sur le groupe quaternaire primitif de collinéations d’ordre 25920 et le groupe hessien”, *Comptes Rendus de l’Académie des Sciences*, 173: 433-443. The note by de Séguier was presented by Paul Appell in the session of 1 August, but published later, together with notes from the session of 29 August.

120[1922a] (with François Michel) *La Composition de Mathématiques dans l’Examen d’Admission à l’Ecole Polytechnique de 1901 à 1921: Exercices d’Application du Cours de Mathématiques Spéciales*. Paris: Gauthier-Villars, 452 p.

121Reviewed in JFM by Leon Lichtenstein.

122Other book reviews exist, for example by M.O. in *Revue des Questions Scientifiques*, April 1923, pp. 536-537; by J.W. Young in *Bulletin of the American Mathematical Society*, May 1923, p. 232; by Tomlinson Fort in *American Mathematical Monthly*, May-June 1923, p. 201; anonymous reviews in *The Mathematical Gazette*, vol. 11, no. 164, May 1923, p. 320; and *The Journal of the Franklin Institute*, vol. 196, August 1923, p. 281.

123[1922b] “Sur le groupe quaternaire primitif d’ordre 25920”, *Journal de l’Ecole Polytechnique*, 2^{ème} série, 22: 69-89.

124[1926a] “Sur les théorèmes fondamentaux de la théorie des groupes continus finis de transformations”, *Comptes Rendus de l’Académie des Sciences*, 183: 841-842 (Session of 8 November).

125Note transmitted by Paul Appell.

126Reviewed in JFM by Hans Freudenthal.

127[1926b] “Revue de Livre : Colonel Compaing de la Tour-Girard. Les outils. Leur étude géométrique”, *Etudes,* 189: 511-512 (20 November).

128This book review is signed M.P. (It is not sure that this is Maurice Potron).

129[1926-1927] *Exercices de Calcul Différentiel et Intégral. Volume 1 : Résumé Théorique et Enoncés d’Exercices. Volume 2 : Solutions des Exercices*. Paris: Hermann, 332 + 258 p.

130Volume 1 was reviewed by Helmut Grunsky in JFM; by Jacob David Tamarkin in the *Bulletin of the American Mathematical Society*, 1927, pp. 670-671; by Raoul Bricard in *Nouvelles Annales de Mathématiques*, 1927, p. 180 ; by Gino Loria in *Scientia*, 1930, vol. 47, pp. 197-199.

131Both volumes 1 and 2 received an anonymous review in *Mathesis* (1926, vol. 40, p. 408; 1927, vol. 41, p. 360); by Fernand Simonart in *Revue des Questions Scientifiques* (20 January 1927, pp. 183-184; 20 January 1928, p. 156); by Raymond Alezais in *Etudes* (5 March 1927, pp. 637-638; 20 December 1927, p. 758); and by many others.

132[1927a] “Sur les partages d’un système d’entiers en groupes de sommes données”, *Comptes Rendus de l’Académie des Sciences*, 184: 572 (Session of 7 March).

133Note presented by Maurice d’Ocagne.

134Reviewed in JFM by Arnold Scholz.

135[1927b] “Sur les partages d’un système d’entiers en groupes de sommes données”, *Journal de l’Ecole Polytechnique*, 2^{ème} série, 26: 39-43.

136[1927c] “Quelques remarques sur les équations aux dérivées partielles et les intégrales singulières des équations différentielles”, *Nouvelles Annales de Mathématiques*, 6^{ème} série, 2: 78-82 (March).

137Reviewed in JFM by Oskar Perron, the famous German pioneer of the Perron-Frobenius theory of nonnegative matrices. Note that [1927c] is not related to Perron-Frobenius theory, and that Maurice Potron made a bizarre error in [1912a, p. 291] by characterizing Oskar Perron as a “Swedish mathematician”.

138[1927d] “Sur les théorèmes fondamentaux de la théorie des groupes continus finis de transformations”, *Bulletin des Sciences Mathématiques*, 2^{ème} série, 51: 91-96 (I), 101-114 (II).

139Reviewed in JFM by Hans Freudenthal.

140[1931a] “Sur l’irrationalité du nombre π”, *Revue de Mathématiques Spéciales*, 41: 473-475 (April).

141Reviewed in JFM by Helmut Wielandt.

142[1931b] “Sur un théorème fondamental de la théorie des groupes continus finis de transformations”, *Comptes Rendus de l’Académie des Sciences*, 192: 1302-1304. (Session of 18 May).

143Reviewed in JFM by Hans Freudenthal, and in ZBL by Hans Schwerdtfeger.

144[1932a] “Sur l’irréductibilité des polynomes à plusieurs variables”, *Bulletin de la Société Mathématique de France*, 60: 127-128.

145Reviewed in JFM by Karl Molsen.

146[1932b] “Sur un type de problèmes de cinématique résolus par l’intégrale singulière d’une équation différentielle”, *Revue de Mathématiques Spéciales*, 42: 217-218 (June).

147[1932c] “Sur certaines transformations conformes dans un espace de Riemann”, *Comptes Rendus de l’Académie des Sciences*, 195: 747-749 (Session of 2 November).

148Note presented by Maurice d’Ocagne.

149Reviewed in ZBL by Hans Schwerdtfeger.

150[1932d] “Sur les espaces de Riemann admettant un groupe de transformations isométriques à *n* (*n* + 1)/2 paramètres”, *Comptes Rendus de l’Académie des Sciences*, 195: 850-2 (Session of 14 November).

151Note presented by Maurice d’Ocagne.

152Reviewed in JFM by Willi Rinow, and in ZBL by Hans Schwerdtfeger.

153[1934a] “Sur les espaces de Riemann admettant un groupe isométrique à *n* (*n* + 1)/2 paramètres”, *Journal de Mathématiques Pures et Appliquées*, 9^{ème} série, 13: 197-216.

154Reviewed in JFM by Hans Freudenthal, and in ZBL by Otakar Boruvka.

155[1934b] “Sur l’intégrale de différentielle binome”, *Bulletin de la Société Mathématique de France*, 62, Supplément Spécial (Vie de la société), Comptes Rendus des Séances de l’Année 1934: 36-39 (Session of 11 April).

156[1934c] “Sur la différentielle binôme”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles*, Tome I, 6: 161-169 (June).

157The last two lines of page 167 are corrected by a “Complément” in Tome I, 8: 247 (September-October).

158Reviewed in JFM by Helmut Grunsky, and in ZBL by Lothar Schrutka.

159[1934d] “Sur les normalisants des *s*_{2} dans les groupes gauche et quadratique”, *Annales Scientifiques de l’Ecole Normale Supérieure*, 3^{ème} série, 51: 141-151.

160Reviewed in JFM by Helmut Wielandt, and in ZBL by Bartel van der Waerden.

161[1935a] “Sur l’intégrale de différentielle binome”, *Journal de l’Ecole Polytechnique*, 2^{ème} série, 33: 161-174.

162Reviewed in JFM by Wilhelm Maier, and in ZBL by Lothar Schrutka.

163The offprint, published by Gauthier-Villars in Paris, is reviewed by Adolphe Buhl in *L’Enseignement Mathématique*, 1934, vol. 33, p. 248, and by Robert de Montessus de Ballore in *Revue Générale des Sciences Pures et Appliquées*, 1934, vol. 45, p. 604 (in spite of the date 1934 on the cover, these two journal issues were both printed in 1935).

164[1935b] “Sur une expression de la courbure tangentielle d’une courbe tracée sur une surface”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles*, Tome II, 4: 97-101 (April).

165Reviewed in JFM by Karl-Heinrich Weise.

166[1935c] “Sur l’irréductibilité des polynomes à plusieurs variables”, *Bulletin de la Société Mathématique de France*, 63: 226-230.

167Reviewed in JFM by Werner Schulz, and in ZBL by Nikolai Tschebotarjow.

168**Econ** [1935d] “Sur certaines conditions de l’équilibre économique. Lettre de M. Potron (90) à R. Gibrat (22)”, *Centre Polytechnicien d’Etudes Economiques. X-Crise. Bulletin Mensuel,* nos. 24-25: 62-65 (July-August).

169This is a letter from Maurice Potron to Robert Gibrat. The notation “M. Potron (90)” indicates that Potron entered the Ecole Polytechnique in the year 1890 (Gibrat in 1922).

170Several articles from *X-Crise*, including this one by Potron, are mentioned by the Swiss engineer Charles Jaeger, on p. 51 of the bibliography in his 1937 article “Quelques aspects récents de l’emploi des mathématiques en économie politique”, *Schweizerische Bauzeitung*, 110: 45-51. Jaeger again mentions Potron’s name, and again without further details, in a list of related writers on mathematical economics, on p. 279 in another 1937 article “Le problème de la prévision en économique rationnelle”, *Zeitschrift für Schweizerische Statistik und Volkswirtschaft*, 73: 279-286.

171In the first footnote of his *X-Crise* letter, Potron refers to the following text of his own: “Les équilibres production-consommation et prix-salaires (Editions S.P.E.S., 17, rue Soufflot, Paris 5)”. Most probably, S.P.E.S. ultimately did not publish this Potron text.

172Reprinted in [2000: 153-160] and [2004: 127-136].

173Translated into English as “On some conditions of economic equilibrium. Letter of M. Potron (90) to R. Gibrat (22)”, in [2010: Chapter 11].

174[1936a] *Les Groupes de Lie.* (Mémorial des Sciences Mathématiques, 81). Paris, Gauthier-Villars, 64 p.

175Reviewed in JFM by Friedrich Engel.

176**Econ** [1936b] C*ommunication faite au Congrès d’Oslo.* Typescript of the communication at the International Congress of Mathematicians in Oslo (July 1936). Conserved in the Archives Jésuites de la Province de France in Vanves.

177The title at the top of the typescript and a footnote reference to Frobenius were handwritten by Potron himself.

178Another copy, without these two handwritten additions, was found in the Frisch archives in Oslo, together with a letter from Potron to Frisch (see [1936c]).

179The shorter published abstract of this communication is [1937b].

180Item [1936b] is published in [2004: 137-139].

181Translated into English as “Communication made at the Oslo Congress”, in [2010: Chapter 13].

182**Econ** [1936c] *Letter to Ragnar Frisch*. Dated 20 July 1936. Now conserved in the Archives Jésuites de la Province de France in Vanves.

183Immediately after his communication at the Oslo conference, Potron sent a long letter (handwritten in French) to Frisch, with some additional mathematical explanations and some possible economic applications. This long letter was discovered by Olav Bjerkholt in 2015 among Ragnar Frisch files in Oslo, and the original was then transferred to Vanves.

184Published in [2016].

185[1937a] “Sur l’irréductibilité de certaines intégrales abéliennes aux transcendantes élémentaires”, *Comptes Rendus du Congrès International des Mathématiciens. Oslo 1936*. Oslo: A. W. Brøggers Boktrykkeri A/S, vol. 2: 89-90.

186**Econ** [1937b] “Sur les équilibres économiques”, *Comptes Rendus du Congrès International des Mathématiciens. Oslo 1936*. Oslo: A. W. Brøggers Boktrykkeri A/S, vol. 2: 210-211.

187Short abstract of Potron’s communication in Oslo (for the longer version, see [1936b]). In 1936, various mathematical journals published lists of the Oslo sessions. In these lists, Potron’s economic presentation is entitled “Conditions des équilibres production-consommation et prix-salaires” (See Fehr, Henri (1936). “Le 10e Congrès International des Mathématiciens. Oslo, 13-18 Juillet 1936”, *L’Enseignement Mathématique,* 35: 375-385. See also Morse, Marston (1936). “The International Congress in Oslo”, *Bulletin of the American Mathematical Society,* 42: 777-781).

188Reprinted in [2004: 141-142].

189Translated into English as “On the economic equilibria”, in [2010: Chapter 12].

190**Econ** [1937c] “Sur les matrices non négatives”, *Comptes Rendus de l’Académie des Sciences*, 204: 844-846 (Session of 8 March).

191Note presented by Maurice d’Ocagne.

192Reviewed in JFM by Helmut Wielandt, and in ZBL by Cyrus MacDuffee.

193Cited by Rufus Oldenburger in 1940 in “Infinite powers of matrices and characteristic roots”, *Duke Mathematical Journal*, 6: 357-361.

194Translated into English as “On nonnegative matrices”, in [2010: Chapter 15].

195**Econ** [1937d] “Travaux de Camarades”, *Centre Polytechnicien d’Etudes Economiques. X-Crise*, no. 36: 57 (March).

196Potron announces and summarizes his forthcoming six lectures on “Les rapports existant entre certains problèmes économiques et quelques acquisitions assez récentes d’une théorie mathématique”. The text of these six lectures is found in [1937e].

197**Econ** [1937e] *L’Aspect Mathématique de Certains Problèmes Economiques en Relation avec de Récentes Acquisitions de la Théorie des Matrices Non Négatives*, unpublished text (34 p.) of six lectures presented at the Institut Catholique de Paris in March-April 1937, and an appendix (5 p.) entitled *Le Problème de la Manne des Hébreux*.

198According to the bibliography in [1939a, p. 61] this text was already available in “Paris, 1936, chez l’auteur”.

199Available in the Archives Jésuites de la Province de France in Vanves, and in the library of Université de Bordeaux 1 (Sciences et Techniques – Talence), reference FR 19069.

200Listed in *Journal de la Société de Statistique de Paris*, 1937, vol. 78, p. 259.

201Reviewed by Alfred Barriol in 1942 in the *Journal de la Société de Statistique de Paris*, 83: 205-207; moreover pp. 203-204 of the same issue present an obituary of Potron by Barriol, and pp. 207-208 contain a letter by Potron himself on industrial statistics (see [1942a]). Another important reference to Potron’s 1937 lectures is given by Michel Huber (see [1913a]). Note that Huber (chairman) and Barriol (secretary) had introduced Potron to the *Société de Statistique de Paris* in 1937.

202On 26 March 1953 an internal Jesuit report by Michel Vittrant condemned Potron’s numerical examples in the appendix as ridiculously unrealistic, and then suggested that further study of Potron’s work was useless (report in the Archives Jésuites de la Province de France in Vanves).

203Reprinted in [2004: 143-203].

204Translated into English as “The mathematical aspect of some economic problems in relation to recent results of the theory of nonnegative matrices. Lectures given at the Catholic Institute of Paris”, in [2010: Chapter 14].

205[1938a] (with Jean-Armand de Séguier) *Théorie des Groupes Abstraits* (Mémorial des Sciences Mathématiques, 91). Paris: Gauthier-Villars, 41 p.

206Reviewed in JFM by Helmut Wielandt, and in ZBL by Helmut Ulm.

207This short book by de Séguier & Potron contains twenty-seven bibliographical references on group theory, including four by Robert Remak. Most probably Potron knew only Remak’s mathematics, not his linear economic system. Neither did Remak know Potron’s economics.

208[1938b] *La Décoration des Surfaces Planes.* Mimeo conserved in the Archives Jésuites de la Province de France (Vanves), 12 p.

209Listed in the section “Ouvrages Reçus” of the *Journal de la Société de Statistique de Paris*, June 1938, p. 146, with “Décorations” instead of the correct “La Décoration” in the title.

210**Econ** [1939a] “Sur les matrices non négatives et les solutions positives de certains systèmes linéaires”, *Bulletin de la Société Mathématique de France*, 67: 56-61.

211Reviewed in JFM by Elisabeth Schulenberg, in MR by Isaac Schoenberg, and in ZBL by Nikola Obrechkoff.

212Mentioned, without further explanation, on p. 362 in the bibliography of the following paper: Woodbury, Max A. (1954), “Properties of Leontief-type input-output matrices”, in: Morgenstern, Oskar (ed.), *Economic Activity Analysis*, New York: Wiley, pp. 341-363. This inconspicuous reference to Potron by Woodbury didn’t draw the attention of other input-output specialists, and Woodbury himself concentrated on a wide variety of other topics in the rest of his career.

213Translated into English as “On nonnegative matrices and positive solutions to certain linear systems”, in [2010: Chapter 16].

214[1939b] *Lettres du P. Potron au P. Hoenen à propos de ses articles du Gregorianum en 1938-1939. Copie ddct. par les soins de P. J. Abelé.* File conserved in the Archives Jésuites de la Province de France (Vanves), date uncertain.

215This file in the Archives Jésuites de la Province de France in Vanves was compiled by the French Jesuit Jean Abelé (1886-1961). It contains a one page introduction by Abelé, then one letter from Potron to Hoenen dated 18 December 1939, then five pages of unpublished notes by Potron on the philosophy of mathematics (“Sur la philosophie des sciences mathématiques”), and seven pages by Potron that comment on three articles by Hoenen.

216The Dutch Jesuit Peter Hoenen (1880-1961) was professor of cosmology and philosophy of science at the Gregorian University in Rome. Its journal *Gregorianum* contained the following three Hoenen articles studied by Potron: “De philosophia scholastica cognitionis geometricae” (1938, vol. 19, fasc. 4, pp. 498-514); “De problemate necessitatis geometricae” (1939, vol. 20, fasc. 1, pp. 19-54); “De problemate exactitudinis geometricae” (1939, vol. 20, fasc. 3, pp. 321-350).

217Note that Abelé also mentions the existence of other unpublished (unfound) material by Potron, mainly constituted by his lecture notes at the Institut Catholique de Paris. Abelé singles out Potron’s course on general topology, a subject “that is rarely cultivated in France”.

218[1940a] “Sur la décomposition d’un groupe continu fini”, *Journal de Mathématiques Pures et Appliquées*, 9^{ème} série, 19: 143-161.

219Reviewed in JFM by Friedrich Engel, in MR by Richard Brauer, and in ZBL by Hans Zassenhaus.

220This article is the only one that is signed as J. Potron. As the full name is Maurice Marie-Jean Potron, the initial J. obviously refers to Jean.

221[1940b] “Sur les fondements de l’arithmétique”, *Revue Générale des Sciences Pures et Appliquées*, 51: 141-144.

222**Econ** [1942a] “Lettre sur les statistiques industrielles”, *Journal de la Société de Statistique de Paris*, 83: 207-208.

223This is a letter from Potron, commenting on Alfred Sauvy’s 1941 article “Les statistiques industrielles”, *Journal de la Société de Statistique de Paris*, 82: 131-145.

224Potron’s text appeared in the section “Variété”, and was published without a title. The above title was given in the table of contents.

225Reprinted in [2004: 205-207].

226Translated into English as “Letter on industrial statistics”, in [2010: Chapter 17].

227[1942b] “Orientations nouvelles de l’enseignement des mathématiques”, *Le Xavier* (Collège Saint François-Xavier. Revue trimestrielle), Vannes, Pâques 1942, no. 52: 16-18.

228A copy is available in the Municipal Archives in Vannes.

# 2 – Posthumous publications after 1942

229**Econ** [2000] “Sur certaines conditions de l’équilibre économique. Lettre de M. Potron (90) à R. Gibrat (22)”, *Cahiers d’Economie Politique,* no. 36: 153-160.

230This is a republication of [1935d], introduced by E. Lendjel, “Une contribution méconnue dans l’histoire de la pensée économique : le modèle de l’Abbé M. Potron (1935)”, *Cahiers d’Economie Politique,* no. 36: 145-151.

231**Econ** [2004] *Les Oeuvres Economiques de l’Abbé Potron.* Edited and introduced by G. Abraham-Frois and E. Lendjel. Paris: L’Harmattan, 220 p.

232This French edition republishes many (but not all) economic writings by Potron. For more details, see the book review by Bidard, C., Erreygers, G. & Parys, W. (2006) in the *European Journal of the History of Economic Thought,* 13 (1), 163-167.

233**Econ** [2010] *The Analysis of Linear Economic Systems. Father Maurice Potron’s Pioneering Works.* Edited and introduced by C. Bidard and G. Erreygers. Foreword by Paul A. Samuelson. London and New York: Routledge, 265 p.

234English translations of all the economic publications by Potron, thus comprising some papers not included in [2004].

235In three appendices Bidard and Erreygers also translate three short French texts related to Potron: first the Potron obituary written by Alfred Barriol, second Barriol’s review of Potron [1937e], and third the very negative internal report on the appendix of [1937e] by Michel Vittrant. For more information on Barriol and Vittrant, see entry [1937e].

236See also the book review by Gehrke, C. (2012), in the *History of Economics Review*, no. 56, pp. 123-126.

237**Econ** [2016] “English translation of Potron’s letter to Frisch”, published in an appendix of the following article: Erreygers, G. & Bidard, C. “Maurice Potron, Ragnar Frisch and Potron’s economic model”, *Cahiers d’Economie Politique*, no. 71: 127-149. The original letter was handwritten in French by Potron on 20 July 1936. See also [1936c].

# 3 – Solution Articles and Solution Booklets to examination sessions in the 1930s

238In the 1920s Potron published some widely available books with mathematical exercises and solutions (see [1922a] and [1926-1927]). Even today, these comprehensive books are easily found in many libraries and some antiquarian bookshops. In the 1930s Potron again devoted a lot of time to the solutions to examination questions, this time concentrating on the problems for the *Certificat de Calcul Différentiel et Intégral* (C.D.I.) in all the Faculties of France. The examinations were held every year in June-July (sometimes called the “June session” or the “July session” or the “first session”) and in November (the “November session” or the “second session”). Potron solved the questions of both sessions for 1933, 1934, 1935 and 1937.

239These solutions were presented in various issues of the *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* a journal concentrating on the teaching of mathematics. This journal ran only five volumes: vol. I appeared in 1934, II in 1935, III in 1937 (but is officially called “year 1936”), IV in 1938, V in 1939. The references [SA1] to [SA9] below contain Potron’s “Solution Articles” in this journal. All these articles present examination problems and short solutions, usually first for Paris, and then in alphabetical order for the other French faculties. In a footnote p. 49 in the first article [SA1-1934], Potron announces that he would present more detailed solutions later: “On trouvera des solutions plus développéés dans la brochure du même auteur (Librairie Hermann, Paris).” Initially Potron seemed to have the ambition to use the same detailed approach as in his comprehensive 1926-1927 books, but ultimately he restricted himself to the articles in the *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles*, and to a few small booklets, also called “cahiers” or “brochures”. It is not easy to trace these booklets, because none of these were deposited in the *Bibliothèque Nationale de France. S*ome copies could be traced in other libraries or antiquarian bookshops. The most plausible conclusion is that in the 1930s three different booklets with exercises were published by Potron. I denote these three “Solution Booklets” by [SB1] to [SB3].

# Solution Articles

240[SA1-1934] “Calcul différentiel et intégral. Session de juin 1933 avec indications sur les solutions par M. l’abbé Potron”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* February 1934, 49-64; March 1934, 82-84.

241[SA2-1934] “Calcul différentiel et intégral. Session de novembre 1933”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* March 1934, 85-96; April 1934, 109-129.

242[SA3-1934-1935] “Calcul différentiel et intégral. Juin-juillet 1934. Avec indication des solutions par M. l’Abbé Potron”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* September-October 1934, 254-256; November 1934, 271-288; December 1934, 305-318; January 1935, 19-23.

243[SA4-1935] “Calcul différentiel et intégral. Session de novembre 1934 avec indication des solutions par M. l’Abbé Potron”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* January 1935, 24-32; February 1935, 46-64; March 1935, 79-86.

244[SA5-1936] “Calcul différentiel et intégral. Enoncés et indications sur les solutions par M. l’abbé Potron. Session de juin 1935”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* February 1936, 47-64; March 1936, 77-92.

245[SA6-1936] “Calcul différentiel et intégral. Session de novembre 1935”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* March 1936, 93-96; April 1936, 110-128; May 1936, 141-155.

246[SA7-1938] “Agrégation des Sciences mathématiques. Concours de 1937. Problème de calcul différentiel et intégral. Solution par l’abbé Potron”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* April 1938, 97-110.

247Here Potron solves the problem that was announced on pp. 26-28 of the January 1938 issue.

248[SA8-1938-1939] “Calcul différentiel et intégral. Première session de 1937. Enoncés et indications sur les solutions par M. l’abbé Potron”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* July-August 1938, 211-224; September-October 1938, 235-256; November 1938, 281-288; December 1938, 314-318; January 1939, 18-23.

249[SA9-1939] “Calcul différentiel et intégral. Deuxième session de 1937”, *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles,* January 1939, 24-32; February 1939, 45-64; March 1939, 77-84.

# Solution Booklets

250[SB1-1933] *Exercices de Calcul Différentiel et Intégral. Solutions des Problèmes Posés au C.D.I. dans les Facultés de France en Juin-Juillet 1933*. Paris: Impr. Varityper. Probably 1933, 43 p., 28 x 21 cm.

251A copy of this booklet was obtained from the bookseller *L’Encrivore* in Metz. Exactly the same Varityper reference is listed in the catalogue of the Bibliothèque Municipale de Lyon (Collection jésuite des Fontaines, SJ T 380/14), with the publication date “circa 1933”.

252In the first part (pp. 1-12) Potron presents the examination problems for June-July 1933 and indicates their solutions; in the second part (pp. 13-43) he provides a systematic overview of the topics that are implicit in the examination questions, and he groups the different parts of the examination questions under these topics.

253The back of page 43 mentions: “Imprimé par Varityper (France) Ltd – 20/22 Rue Richer, Paris 9^{ème}”. Varityper is not only the name of the company that printed the text, but also the name of the ingenious typewriter used for producing the text. It is possible that later a more definitive version was published by Hermann (as a publishing company), but more probably Hermann (as a bookshop) acted as the distributor or seller of the text.

254See the appendix below for a list of alternative titles mentioned in book reviews or advertisements, where ultimately the conclusion is that most probably all the alternatives in the appendix are nothing else but sloppy descriptions of [SB1-1933].

255[SB2-1935] *Certificat de Calcul Différentiel et Intégral. Solutions des Problèmes Posés à la Session de Novembre 1933*. Paris : Croville-Morant. Probably end 1935.

256This unseen reference is mentioned in an advertisement on the frontispiece of [SB3-1936], as being available “à la Librarie Croville-Morant”. The publication “en brochure” of Potron’s solutions for the November sessions of 1933 is also announced in the *Bulletin de l’Institut Catholique de Paris*, 1935, p. 382.

257Probably the brochure was published only at the end of 1935, because in the summer of 1935 Potron complained about the long delays in publishing the booklet with the solutions for November 1933. See Potron’s letter to Raymond Alezais, dated 17 July 1935 (conserved in the Archives Jésuites de la Province de France in Vanves); here Potron mentions: “J’avais eu l’idée de faire une brochure dactylographiée de nov. 33 pareille à celle de juillet 33. J’avais proposé la chose à Croville-Morant, qui avait paru favorable à l’idée.” But then Potron saw no fast progress, and asked Alezais to contact Croville-Morant for an enquiry about the date of publication.

258[SB3-1936] *Calcul Différentiel et Intégral. Certificat d’Etudes Supérieures. Sessions de 1934. Enoncés et Indications sur les Solutions.* Paris: Hermann, 1936, 74 p.

259A copy was used from the library of the *Universität des Saarlandes*, catalogue number 52-11156.

260Also listed in the catalogue of the *Universidade de Santiago de Compostela*, Biblioteca de Matemática, ref. 26 317 ; and in the catalogue of the HEI Bibliothèque of the *Ecole des Hautes Etudes d’Ingénieur,* in Lille, ref. ABB-HE2504205900.

261Advertised in many issues of the *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles.*

262This booklet contains the questions for all the sessions of 1934 (which means both June-July and November). It uses the subtitle *Extrait du Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles.* Contrary to [SB1-1933], Potron now just “extracts” the questions and his short solutions from his *Bulletin* articles, without performing the additional painstaking task of constructing and classifying more detailed “solutions développées”. In this sense [SB3-1936] was less ambitious than [SB1-1933] and maybe therefore was not sent out for review to journals.

# Appendix : Some alternative Solution Booklets ?

263It is possible, but not very likely, that some alternative Solution Booklets exist. I list some references from French or foreign journals to Potron Solution Booklets below, where I use exactly the same titles as in the reviews or advertisements (capitals used if and only if used in the original reference). It is doubtful that we find a “new item” in the list below.

264Abbé POTRON. – Exercices de Calcul différentiel et intégral. Solutions des Problèmes posés au C.D.I. dans les Facultés de France en juin-juillet 1933. Un cahier in 4° de IV-44 pages. Prix: 10 francs. Hermann & Cie. Paris.

265This is an exact copy (including the same capitals) of the title of a book review by Adolphe Buhl (Toulouse) in *L’Enseignement Mathématique*, 1933, vol. 32, pp. 286-287. Buhl signals: “ce premier cahier a un aspect provisoire : il semble que ce soit de la dactylographie reproduite par la lithographie” (p. 287). Buhl’s description of the contents fits with the Varityper text [SB1-1933] above, which had a preface of one empty and three printed pages, and a text of 43 pages plus the Varityper company reference at the back of page 43. Moreover, Buhl points out the advantages of a quick printing method; so this is a rush production, most probably the Varityper version [SB1-1933] itself. Buhl’s reference to Hermann & Cie might be explained by the advertisement at the back cover of the Varityper version, which advertises the well known Potron [1926-1927] books published by Hermann.

266This is probably nothing else but [SB1-1933].

267Potron. – SOLUTIONS DES PROBLEMES donnés au *Certificat de Calcul Différentiel et Intégral,* à la session de juin-juillet 1933, dans toutes les Facultés de France.- Une broch. de 50 pages (28 x 11) – Paris. Hermann. 1933. – 10 fr.

268This is an exact copy (including the same capitals) of an anonymous description in a list of “Ouvrages Récemment Parus” in the *Revue des Questions Scientifiques*, 1934, pp. 160-161. The description of the contents of part one and two suggests this text is similar to [SB1-1933]. It is most probable that the description by the editorial office is not authoritative: for example “28 x 11” is an extremely unusual format, and probably must be “28 x 21”, the format of [SB1-1933]. The “50 pages” can also be explained as the sum of the preface, plus 43 pages of exercises, plus printer’s address, plus advertisement.

269This is probably nothing else but [SB1-1933].

270*Certificat de Calcul différentiel et intégral: Solutions des problèmes posés à la session de Juin 1933.*

271This is the title as advertised in 1936 on the frontispiece of [SB3-1936]. This advertisement probably shortens the exact title of the Varityper version [SB1-1933]. From Potron’s texts and correspondence, it is obvious that alternative expressions are used to indicate the first examination session: “Juin 1933” or “Juillet 1933” or “Juin-Juillet 1933” all refer to the same “Première Session de 1933”. Note that the advertisement in [SB3-1936] suggests that the text is available from Hermann.

272This is probably nothing else but [SB1-1933].

273Potron (Abbé). – Exercices de calcul différentiel et intégral. – *1 vol. in-4° de 43 pages. Librairie Hermann, Paris, 1934. (Prix: 10 fr).).*

274This is the title of a book review by Robert de Montessus de Ballore in *Revue Générale des Sciences Pures et Appliquées*, 1934, vol. 45, pp. 603-604.

275The description of part one and part two by Montessus de Ballore and the mention “43 pages” suggest that this is again [SB1-1933]. There is one strange point: Montessus de Ballore writes: “M. l’Abbé Potron rend un service éminent aux étudiants en publiant les solutions des problèmes posés au certificat de Calcul différentiel et intégral dans les facultés de France, en juin-juillet 1934.” This reference to “1934” is probably a lapse. It is hard to believe that Potron published a booklet with the June-July sessions of 1934 already in 1934 itself, because in his correspondence with Azelais, in the summer of 1935, Potron was still complaining about the slow production process of his solutions, being unhappy that books with the November 1933 sessions and the 1934 sessions were still unpublished (see [SB2-1935] and [SB3-1936]). It is reasonable to assume that Montessus de Ballore confuses 1934 with 1933.

276This is probably nothing else but [SB1-1933].

277Potron (-.). Exercices de calcul différentiel et intégral. Paris, Hermann, 1934. 43 pp.

278This title is included in the list of new publications in the *Bulletin of the American Mathematical Society*, March 1935, vol. 41, p. 206.

279This is probably nothing else but [SB1-1933].

280I suppose Potron sent copies of [SB1-1933] to different journals, because it was the result of a time consuming process of solving and classifying the examination exercises. It was more sophisticated than the simple solutions in his articles in the *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles*. From Potron’s correspondence with Azelais in 1935, it is obvious that Potron wanted to speed up his output. It is not clear whether the unseen [SB2-1935] was just an extract from the *Bulletin Mathématique des Facultés des Sciences et des Grandes Ecoles* like [SB3-1936], or contained additional explanations and classifications in the style of [SB1-1933]. Even though different reviewers give slightly different bibliographical references, we may assume that all journal reviews of Potron 1930s Solution Booklets actually refer to [SB1-1933].

281I conclude that Potron produced only three different Solution Booklets in the 1930s, namely [SB1-1933], [SB2-1935] and [SB3-1936], unless someone in the future discovers a 1930s Solution Booklet that is really physically different from these three items.

# Acknowledgements

In the past twelve years this Potron bibliography benefited from useful information from Gilbert Abraham-Frois, Robert Bonfils, Guido De Baere, Christian de Borchgrave, Chantal Dufour, Jocelyne Dufour, Guido Erreygers, Thomas Hawkins, Emeric Lendjel, Kris Van de Casteele, the staff of the National Archives in Paris, the Institut Catholique de Paris, the Archives Jésuites de la Province de France in Vanves, the Université Catholique de Lille, the Université Catholique de l’Ouest in Angers, the Municipal Archives in Vannes, the Niedersächsische Staats- und Universitätsbibliothek in Göttingen, and the interlibrary loan service of the University of Antwerp. Special thanks to Anne-Catherine Putz (Mouvement Chrétien des Cadres et Dirigeants, Paris), who surprised me in June 2006 by providing me with a copy of Potron’s “unfindable” first economic article (the 1911*Echos*paper). I am indebted to Jean-François Stoffel for useful additions and for very interesting information on Potron-Duhem and de Séguier-Duhem letters, and to Olav Bjerkholt for discovering Potron-Frisch material in Oslo. My greatest debt is to Christian Bidard for reading numerous drafts and suggesting many additional references. All corrections and additions are welcome.