A Civil Engineer and an Amateur Mathematician: Aram Margossian’s Views on StatisticsSemiha Betül Takıcak, Alp Eden
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.
İnşaat Mühendisi ve Amatör Matematikçi Aram Margosyan’ın İstatistik Üzerine GörüşleriSemiha Betül Takıcak, Alp Eden
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.
Aram Margossian was born in Istanbul in 1853. He completed his university education at the École des Ponts et Chaussées in Paris in 1878. Upon completing his degree, he returned to Ottoman Turkey and worked in the Ministry of Public Affairs as an engineer, where he was later promoted to the director of the railway administration. Concurrently with his post in the ministry, he lectured at the Hendese-i Mülkiye, the school of civil engineering, and published his lecture notes. Not only had Margossian been a civil engineer, a bureaucrat, and a university professor, he would also become a distinguished amateur mathematician later in his life. His book on magic squares, Contribution à l’Étude des Carrés Magiques: De l’Ordonnance des Nombres dans les Carrés Magiques Impairs (1908) was published in France and became the key to his fame. In this authentic book, Margossian extended various known methods for generating magic squares.
In addition to his book, the current study has identified three articles he wrote on Euler and Latin squares. In the first article from 1912, Margossian tried to solve an open problem known as Euler’s officer problem. The first part of the current paper will discuss the significance and repercussions of this work and attempt to show why his solution to the problem was incomplete. Margossian published this article in the review journal Sphinx-Œdipe in a separate supplementary issue. This journal was edited and hand-written by André Gérardin. Also, Margossian’s name appeared on the cover of the 1921 issue of Sphinx-Œdipe as one of the founders of the magazine. In 1921, Gérardin and Kraitchik formed an international mathematical circle called Les Amis des Nombres. As a Belgium engineer and mathematician, Kraitchik was instrumental in making Margossian’s methods a household item by referring to them extensively in his book (Kraitchik, 1930). Margossian also became a member of Les Amis des Nombres in 1921. Through his active participation in various mathematical circles and his continuing involvement with his alma mater, Margossian was able to integrate with the French intellectual milieu.
In 1909, he became a member of the Ottoman Society for Architects and Engineers, one of the most important scientific and professional societies of the period. Between 1908- 1910, the majority of its members were engineers from the Ministry of Public Affairs and/or university professors from Hendese-i Mülkiye Mektebi. Margossian (1909, 1910) published two opinion articles in the Journal of the Ottoman Society for the Architects and Engineers. In the first opinion piece, Margossian defended the use of Western symbols and Western scientific terminology over the Ottoman/Arabic symbols and terminology that were currently in use. His second article bore the title “Some Remarks on Statistics” and differed from other articles in the same journal in terms of its technical sophistication. The second part of this paper will analyze that article in detail and attempt to establish what Margossian had been trying to do by filling in some details.
In his article on statistics, Margossian showed the importance of statistical inference in all fields of knowledge where data analysis is of utmost importance. Margossian started by showing how a collection of numbers obtained from tables of logarithm values can be analyzed using Pearson’s chi-square test as well as how their probability distribution can be inferred. His first scientific example involved chemistry and the well-known historical controversy on calculating the oxygen content of water. By implicitly invoking the Law of Large Numbers, he pointed out that the number of observations that had been made were insufficient to infer an accurate conclusion about the mean value of the data. His second example, from social sciences, involved the Parretto Law for the distribution of wealth. To deduce this law for a specific society, one needs a sophisticated version of the least square line fit. By showing the mathematical skills that are required to deal with these problems Margossian supported his claim that engineers, especially those educated in the West, were the best candidates to learn and apply statistical inferences in all fields of daily life. Margossian further claimed that positions should exist in each ministry for such people.
Margossian was an Ottoman Armenian who probably became unemployed after 1909. His interest in trying to define new employment opportunities for the engineers of his period is perfectly understandable. 1909 is believed to have been a turning point in his life, one where he had been transformed from a civil servant in the Ottoman Empire to an amateur mathematician in France. The article published in 1912 is believed to have played a key role in this transformation. Margossian died in Strobl near Austria in 1931 and had probably left the country during World War I.