İnşaat Mühendisi ve Amatör Matematikçi Aram Margosyan’ın İstatistik Üzerine Görüşleri

Aram Margosyan (1853-1931), Paris’teki École des Ponts et Chaussées’den (Köprüler ve Yollar Okulundan) mezun olduktan sonra Nafia Vekâleti’ne bağlı olarak Demiryolları’nda çalışmaya başlamış ve burada müdürlüğe kadar yükselmiştir. Nafia Vekâleti’nde çalışırken Hendese-i Mülkiye’de matematik ve mühendislik dersleri vermiş ve kitaplar yayınlamıştır. Osmanlı Türkiye’sindeki değişik görevlerinin yanı sıra Fransa’daki amatör matematikçiler grubu içinde kendine yer edinmiştir. Sihirli kareler konusundaki Fransızca kitabı, meşhur bir İngilizce eğlence matematiği kitabının Fransızca uyarlanması içinde alt bir bölüm olarak tekrar yayınlanmıştır. Margosyan, yurtdışındaki tanınmışlığını, “Margossian Method”u da içeren, bu esere borçludur. Fransız amatör matematikçi André Gérardin’in yönettiği Sphinx-Œdipe dergisinde yayınladığı ilk yazısında, Margosyan açık bir problemi çözdüğünü iddia etmiştir. Margosyan da Sphinx-Œdipe dergisinin kurucuları arasındadır. Osmanlı Mühendisler ve Mimarlar Cemiyeti Mecmuası’na, artık Osmanlı Demiryolları müdürü olmadığını vurguladığı iki mektup göndermiştir. Özellikle çıkarımsal istatistiğin önemini örneklerle anlatan mektubu, Margosyan’ın geniş bir matematik kültürünün göstergesidir. Bu makalemizde, Margosyan’ın hayatı hakkındaki bazı bilgileri sunduktan sonra istatistik yazısındaki görüşlerinin matematiksel içeriklerini değerlendirip bu yazıyı kaleme alma nedenini de anlamaya çalıştık.

Anahtar Kelimeler:

Aram Margosyan, Margossian, çıkarımsal istatistik, Matematik tarihi, Sihirli kareler, Euler subay problemi, Osmanlı İmparatorluğu, Türkiye

A Civil Engineer and an Amateur Mathematician: Aram Margossian’s Views on Statistics

After graduating from the École des Ponts et Chaussées in Paris, Aram Margossian (1853-1931) started working as an engineer in the Ottoman Ministry of Public Affairs, where he was later promoted to director of the railway administration. While working in this ministry, he lectured on mathematics and engineering at the Hendese-i Mülkiye, the school of civil engineering in Istanbul, and published books on these topics. In addition to his positions as a civil engineer, bureaucrat, and university teacher, he was also a distinguished amateur mathematician. Margosyan wrote a book on magic squares in French, which became the key to his fame. Part of Margosyan’s book was included in the French version of a book on recreational mathematics. Both books comprise what is known today as the Margossian Method. In his first paper published in the journal Sphinx-Œdipe, Margossian (1912) claimed to have solved an open problem. He also was one of the founders of Sphinx-Œdipe, a French journal of mathematics, at which point he sent two letters to the Journal of Ottoman Society of Engineers and Architects, in which he underlined the fact that he no longer was the director of the Ottoman Railways. The present article analyzes the content of these letters which he’d written after establishing his expertise in mathematics. The letters’ stress on the importance of statistical inference presents a good example of Margosyan’s deep understanding of mathematics. The current article also analyzes his views on the mathematical underpinnings of statistical inference and attempts to understand his rationale for writing these letters.

Keywords:

Aram Margosyan, Margossian, Statistical inference, History of mathematics, Magic squares, Euler’s officer problem, Ottoman Empire, Turkey,

PDF

___

Arşiv Kaynakları / Archival Sources
Archives de l’École nationale des Ponts et Chaussées
Ecole des Ponts et Chaussées, Session 1876-1877, Photographies des élèves, Service documentaire, Archives, Inventaire albums photo, Photo no. 17, 26.
Basılı Kaynaklar / Printed Sources
Arnoux, Gabriel. Les Espaces Aritmetiques Hypermagiques. Paris: Gauthier-Villars, 1894.
Bachmann, Paul ve Edmond Maillet. “Propositions Élémentaires de la Théorie des Nombres.” Encyclopédie des Sciences Mathématiques Pures et Appliquées, c.1. Editör Jules Molk içinde 1–75. Paris, Leipzig: Gauthier-Villars, B. G. Teubner, 1906. https://gallica.bnf.fr/ark:/12148/bpt6k290952/f9.image. r=Propositions Elementaires de la Theorie des Nombres.
Ball, Walter William Rouse. Mathematical Recreations and Essays. 4th edition. New York: The Macmillan Company, 1905.
———. Mathematical Recreations and Essays. 6th edition. London: The Macmillan Company, 1914.
———. Mathematical Recreations and Essays. 10th edition. London: The Macmillan Company, 1922.
———. Mathematical Recreations and Essays. Editör Harold Scott MacDonald Coxeter. 11th edition. New York: The Macmillan Company, 1947.
———. Mathematical Recreations and Problems of Past and Present Times. 2th edition. New York: The Macmillan Company, 1892.
Ball, Walter William Rouse, ve Harold Scott MacDonald Coxeter. Mathematical Recreations and Essays. 13th edition. New York: Dover Publications, 1987.
Ball, Walter William Rouse, ve Harold Scott MacDonald Coxeter. Mathematical Recreations and Essays. 12th edition. Toronto and Buffalo: University of Toronto Press, 1974.
Bozkuş, Yıldız Deveci. XIX. Yüzyılda Osmanlı İmparatorluğu’nda Ermeni Entelektüeller. Ankara: Nobel Akademik Yayıncılık, 2020.
Callet, François. Tables Portatives de Logarithmes. Paris: Firmin Didot, 1795.
Cipolla, Michele. “Matematica Ricreativa.” Enciclopedia delle Matematiche Elementari 3, 2 (1987): 481–538.
Denes, Jozsef, ve A. Donald Keedwell. Latin Squares and their Applications. New York and London: Academic Press, 1974.
Eden, Alp. “Toplumun Eylem Matematiği: Ahmet Hamit Dilgan.” Matematik Dünyası 28, 110 (2021): 79–90.
Eden, Alp, ve Semiha Betül Takıcak. “Aram Margosyan’ın Sihirli Kareler Kitabı.” Matematik Dünyası 29,112 (2022): 20–26.
Ergin, Osman. Türk Maarif Tarihi. C. 3–4. İstanbul: Eser Matbaası, 1977.
Fienberg, Stephen E. “What is statistics?” Annual Review of Statistics and Its Application 1 (2014): 1–9. https://doi.org/10.1146/ANNUREV-STATISTICS-022513-115703.
Feller, William. “The Strong Law of Large Numbers.” An Introduction to Probability. C.1, 3th edition içinde 243-245. New York: John Wiley & Sons, 1968.
[Fenmen], Mehmed Refik. “Rumuzât-ı Fenniyemizin Islahı Mes’elesi.” Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası 1, 3 (1909): 69.
Frame, James Sutherland. “Review: W. W. Rouse Ball, Mathematical Recreations and Essays.” Bulletin of the American Mathematical Society 46, 3 (1940): 211–13. https://www.ams.org/journals/bull/1940-46-03/ S0002-9904-1940-07170-8/S0002-9904-1940-07170-8.pdf.
Frisinger, H. Howard. “The Solution of a Famous Two-centuries-old Problem the Leonhard Euler-Latin Square Conjecture.” Historia Mathematica 8, 1 (Şubat 1981): 56–60. https://doi.org/10.1016/0315- 0860(81)90005-7.
Furinghetti, Fulvia. “Mathematical Instruction in an International Perspective: The Contributıon of the Journal l’Enseignement Mathématique.” One Hundred Years of L’Enseignement Mathematique, Moments of Mathematics Education in the Twentieth Century, Proceedings of the EM–ICMI Symposium. Editör Coray Daniel, Fulvia Furinghetti, Helene Gispert, Bernard R. Hodgson, ve Gert Schubring içinde 19–47. Geneva: L’Enseignement Mathématique, 2003.
Gérardin, André (Ed.) Sphinx-Œdipe. C. 16. Nancy (France), 1921.
———. “Supplément au Sphinx-Œdipe de Semptembre 1921: Amis des Nombres.” Sphinx-Œdipe 16 (1921): 145.
Gispert, Hélène. “Les Débuts de l’Histoire des Mathématiques sur les Scènes Internationales et le Cas de l’Entreprise Encyclopédique de Felix Klein et Jules Molk.” Historia Mathematica 26, 4 (Kasım 1999): 344–60. https://doi.org/10.1006/hmat.1999.2260.
Günergun, Feza. “Osmanlı Mühendis ve Mimarları Arasında İlk Cemiyetleşme Teşebbüsleri.” Osmanlı İlmî ve Meslekî Cemiyetleri: 1. Millî Türk Bilim Tarihi Sempozyumu 3-5 Nisan 1987. Yayına Hazırlayan Ekmeleddin İhsanoğlu içinde 155-196. İstanbul: Edebiyat Fakültesi Basımevi, 1987.
Hacking, Ian. Logic of Statistical Inference. Cambridge: Cambridge University Press, 1965.
Hâmit Dilgan, Ahmet. Matematiğin Tarih ve Tekâmülüne Bir Bakış. İstanbul: İstanbul Teknik Üniversitesi Matbaası, 1955.
İhsanoğlu, Ekmeleddin, Ramazan Şeşen, M. Serdar Bekar, Gülcan Gündüz ve Veysel Bulut. Osmanlı Bilim Literatürü Tarihi Zeylleri. C. 2. Editör Ekmeleddin İhsanoğlu. İstanbul: IRCICA, 2011.
İhsanoğlu, Ekmeleddin, Ramazan Şeşen, ve Cevat Izgi. Osmanlı Matematik Literatürü Tarihi. C. 2. Editör Ekmeleddin İhsanoğlu. İstanbul: IRCICA, 1999.
İnönü, Erdal. Mehmet Nadir: Bir Eğitim ve Bilim Öncüsü. Ankara: TÜBİTAK, 1997.
Kaçar, Mustafa, Tuncay Zorlu, Burak Barutçu, Atilla Bir, C. Ceyhan, ve Aras Neftçi. İstanbul Teknik Üniversitesi ve Mühendislik Tarihimiz. Editör Mehmet Karaca. İstanbul: İTÜ Vakfı, 2012.
Kraitchik, Maurice. La Mathématique des Jeux ou Récréations Mathématiques. Bruxelles: Imprimerie Stevens Frères, 1930.
———. Mathematical Recreations. 2nd ed. New York: Dover, 1953.
Küçük, Serhat. “Osmanlı Basınının Mühendislik Mirası.” International Academic Social Resources Journal
7, 37 (2022): 568–81. https://doi.org/10.29228/ASRJOURNAL.61805.
Luciano, Erika. “The Enciclopedia delle Matematiche Elementari and the Contributions of Bolognese.” Mathematicians in Bologna 1861–1960. Editör Salvatore Coen içinde 343–72. Basel: Springer Basel, 2012. https://doi.org/10.1007/978-3-0348-0227-7.
Margossian, Aram. “Association Française pour l’Avancement des Sciences. Congrès (048 ; 1924 ; Liège). Auteur du texte.” Simple Observation sur la définition du calcul des probabilités içinde 135. Paris: Association Française pour l’Avancement des Sciences, 1925. https://gallica.bnf.fr/ark:/12148/ bpt6k5774828p/f159.item.r=Association française pour l’avancement des sciences.
———. “Carrés Latins et Carrés d’Euler (Modules Impairs).” L’Enseignement Mathématique 30 (1931): 41–49. https://doi.org/10.5169/seals-23882.
———. “Carrés Latins Semi-diagonaux”. L’Enseignement Mathématique 34 (1935): 365–77. https://doi. org/10.5169/seals-26618.
———. “De l’Ordonnance des Nombres dans les Carrés Magiques.” Récréations Mathématiques et Problèmes des Temps Anciens et Modernes. C. 3. Editör W. W. Rouse Ball içinde 1–64. Paris: A. Hermann et Fils, 1909. http://nek.istanbul.edu.tr:4444/ekos/NEKAV/nekav14081.pdf.
———. Contribution à l’Étude des Carrés Magiques: De l’Ordonnance des Nombres dans les Carrés Magiques Impairs. Paris: Librairie Scientifique A. Hermann, 1908.
———. “Les Carrés d’Euler (Problèmes des Officiers).” Editör André Gérardin. Sphinx-Œdipe 7, özel sayı (1912): 1–16.
———. “Tribune Publique, 460.” Encyclopédie des Ences Mathématiques Pures et Appliquées. C. 4. Editör Jules Molk, içinde 76. Pairs, Leipzig: Gauthier-Villars, B. G. Teubner, 1912. https://iris.univ-lille.fr/ bitstream/handle/1908/3624/44124-4-2-1.pdf?sequence=1.
Margosyan, Aram. Fenn-i Mihanik-i Riyâzî, Fenn-i Hareket ve Fenn-i Kuvva. İstanbul: Mühendishâne-i Berrî-i Hümâyûn Matbaası, 1302.
———. “Hendese-i Mülkiye Muallimlerinden Mehmed Refik Beye.” Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası 1, 3 (1909): 69–70.
———. Hesâb-ı Tahlîli, Kitâb-ı Evvel: Hesâb-ı Tefâzülî. C. 1. İstanbul: Matbaa-i Daire-i Askeriyye, 1304.
———. “İstatistik Hakkında Bazı Mülâhazât.” Osmanlı Mühendis ve Mimar Cemiyeti Mecmuası 1, 6 (1910): 137–41.
Mosteller, Frederick, Robert E. K. Rourke, ve George B. Thomas. Probability with Statistical Applications.
Massachusetts: Addison-Wesley Publishing Company, 1961.
“Nécrologie(s).” Nouvelles Annales de Mathématiques 4e série 15 (1915): 115–16. http://www.numdam.org/ article/NAM_1915_4_15 115_0.pdf.
“News and Notices.” The American Mathematical Monthly 68, 3 (12 Mart 1961): 313–18. https://doi.org/10.1080/00029890.1961.11989661.
“Notes.” Bulletin of the American Mathematical Society 28, 3 (01 Mart 1922): 134–39. https://doi.org/10.1090/ S0002-9904-1922-03520-3.
Okay, Cüneyd. Eski Harfli Mühendislik Dergileri. İstanbul: Kurtiş Matbaası, 2004.
———. “Eski Harfli Mühendislik Dergileri.” Türkiye Araştırmaları Literatür Dergisi 2, 4 (2004): 629–40.
———. Osmanlı Mühendis ve Mimar Cemiyeti Belgeleriyle. Ankara: TMMOB Mimarlar Odası Ankara Şubesi, 2008.
Pakalın, Mehmed Zeki. Sicill-i Osmanî Zeyli: Son Devir Osmanlı Meşhurları Ansiklopedisi. Çeviren Mustafa Keskin. C. 11. Ankara: Türk Tarih Kurumu, 2008.
Pamukciyan, Kevork. Ermeni Kaynaklarından Tarihe Katkılar: Zamanlar, Mekânlar, İnsanlar. C. 3. İstanbul: Aras Yayıncılık, 2003.
Pearson, Karl. “X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 50, 302 (21 Temmuz 1900): 157–75. https://doi.org/10.1080/14786440009463897.
Plackett, R. L. “Karl Pearson and the Chi-squared Test.” International Statistical Review 51 (1983): 59–72.
Ponts Alliance (France). “Association Amicale des Ingénieurs Anciens Élèves de l’École des Ponts et Chaussées de France / Bulletin.” 1908. https://gallica.bnf.fr/ark:/12148/bpt6k992874z/f43.item.r=Aram Margossian Association des ingénieurs civils anciens élèves de l’École des ponts et chaussées de France Margossian.
———. “Association Amicale des Ingénieurs Anciens Élèves de l’École des Ponts et Chaussées de France / Bulletin.” 1912. https://gallica.bnf.fr/ark:/12148/bpt6k1423826m/f38.item.
Roberts, Siobhan, ve Asia Ivić Weiss. “Harold Scott MacDonald Coxeter.” Biographical Memoirs of Fellows of the Royal Society 52 (Ocak 2006): 45–66. https://doi.org/10.1098/rsbm.2006.0004.
Roscoe, Henry Enfield, ve Carl Schorlemmer. A Treatise on Chemistry, The Non-Metallic Elements. C. 1.London: Macmillan And Co., 1881.
Santur, Mehmet Fikri. “Yüksek Mühendis Mektebi Tarihçesi.” Mühendis Mektebi Mecmuası (Mezunlar Broşürü) 4, 47 (1931): 1-3 (185-187).
Schumpeter, Joseph A. “Vilfredo Pareto (1848-1923).” The Quarterly Journal of Economics 63, 2 (1949): 147–73. https://about.jstor.org/terms.
Seneta, Eugene. “A Tricentenary History of the Law of Large Numbers.” Bernoulli 19, 4 (01 Eylül 2013): 1088–1121. https://doi.org/10.3150/12-BEJSP12.
Société Scientifique de Bruxelles. “Bibliographie.” Revue des Questions Scientifiques XVII, 3 (1910): 627–28. https://archive.org/details/revuedesquestion00soci_65/page/626/mode/2up?q=Margossian.
Société Scientifique e Bruxelles. “Bibliographie.” Revue des Questions Scientifiques XXII, 3 (1912): 245–47. https://archive.org/details/revuedesquestion00soci_70/page/n255/mode/2up?q=Margossian.
Stigler, Stephen M. “Karl Pearson’s Theoretical Errors and the Advances They Inspired.” Statistical Science 23, 2 (01 Mayıs 2008): 261–271. https://doi.org/10.1214/08-STS256.
Toprak, Zafer. “Osmanlı Devleti’nde Sayısallaşma ya da Çağdaş İstatistiğin Doğuşu.” Osmanlı Devleti’nde Bilgi ve İstatistik. Editör Halil İnalcık ve Şevket Pamuk içinde 95–112. Ankara: Başbakanlık Devlet İstatistik Enstitüsü, 2000.
Uluçay, Çağatay, ve Enver Kartekin. Yüksek Mühendis Okulu (Yüksek Mühendis ve Yüksek Mimar Yetiştiren Müesseselerin Tarihi). İstanbul: Berksoy Matbaası, 1958.
Ünalın, Çetin. “Mimar ve Mühendisler Tarafından II. Meşrutiyet Döneminde İstanbul’da Yayımlanmış İki Dergi: Génie Civil Ottoman (1910) ve Zeitschrift Für Technik und Industrie in der Turkei (1916).” Osmanlı Bilimi Araştırmaları 10, 2 (2009): 59–96.
Whittaker, Edmund Taylor “W. W. Rouse Ball.” The Mathematical Gazette 12, 178 (15 Ekim 1925): 449–54. https://doi.org/10.1017/S0025557200247207.
Tezler / Dissertations
Fleisher, Edward. “On Euler Squares.” New York University, Doktora Tezi, 1935.
Elektronik Kaynaklar / Electronic Sources
Boyer, Christian. “Diophante”. Bibliothèque de l’Institut Henri Poincaré, 2005. Erişim 13 Nisan 2022. https:// www.library.illinois.edu/mtx/DiophanteNumberTheoryJournal/DiophanteEnglPreface.pdf.
Bullynck, Maarten. “From Exploration to Theory-driven tables (and Back Again). A History of Tables in Number Theory.” HAL Open Science, 2014. Erişim 12 Mayıs 2022. https://hal.archives-ouvertes.fr/hal- 01383821/document.
Danielsson, Holger. Magische Quadrate. Version 05.03.2022. Erişim 1 Nisan 2022. https://www.magic- squares.info/docs/magische-quadrate.pdf.
Nabonnand, Philippe. “Jules Molk (1857-1914).” Facultés et Université de Nancy aux 19e-20e siècles, 2016.
Erişim 12 Nisan 2022. https://histoire-universite-nancy.fr/s/una2gm/item/1144.
“Nouvelles Diverses - Nominations et Distinctions.” L’Enseignement Mathématique 22 (1922). Erişim 13 Nisan 2022. https://archive.org/details/lenseignementmat22inte/page/n83/mode/2up?q=%22Les+amis+des%22.
“zbMATH Open, André Gérardin”. Erişim 16 Haziran 2022. https://zbmath.org/?q=ia%3Agerardin.andre. “zbMATH Open, Maurice Kraitchik”. Erişim 16 Haziran 2022. https://zbmath.org/authors/?q=kraitchik.