Vidinli Huseyin Tawfik: A Modern Turkish Specialist of Linear Algebra

This article is a biography essay on the life and works of Vidinli Tawfiq Pasha, a 19th-century Ottoman scholar, statesman and general of 19th-century Istanbul, and a noteworthy mathematician who published in 1882 an important book in Linear algebra, a new branch of mathematics at that time. After a short biographical sketch, we present a complete compilation of his writings in Linear Algebra and in other fields.

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Salim Ayduz*

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Figure 1: Vidinli Tawfik Pasha. Source: IMAGE The Bulletin of the International Linear Algebra Society, 15 (Summer 1995), p. 24.


Vidinli Huseyin Tawfik Pasha (Born in Bulgaria, Vidin 1832- died in Istanbul 16 June 1901) is an Ottoman General, Mathematician and Statesman. At the 19th century, scientific studies during the westernization process in the Ottoman world did not go beyond translation of European scholar's books into Turkish. In this atmosphere, Tawfiq Pasha of Vidin (mostly knows as Vidinli Huseyn, Tawfik Pasha in Turkish literature) made research on the very new area in mathematics, the quaternions, and he published a research book on this subject entitled Linear Algebra in English. The book was first published in 1882 (169 pages) and a second revised and enlarged edition was published by A. H. Boyajian in 1892 (188 pages) in Istanbul. He was the first mathematician to make innovative research on Linear Algebra. Moreover, his book was one of the first original publications ever published by an Ottoman scientist in modern times after that the originality of the tradition of Islamic science in the Ottoman period knew a lasting decline. In the following article, we introduce Tawfik Pasha's life and works.

1. His Life

Our mathematician was named Tawfik, but to indicate his birthplace and also to distinguish him from his classmate, another Tawfik Pasha, who was a mathematician too, he was known with the nickname Vidinli Tawfik Pasha. His father Hasan Tahsin Efendi pertained to Imamzadeler family. His first education started at Rüştiye Mektebi (Primary School) in his birthplace at Vidin, in Bulgaria. After completing his education there, he moved to Istanbul at the age of 14-15 years old and stayed at one of his relative's houses. Due to his desire to paint, he preferred to enrol into the newly established illustration branch of Mûhendishâne-i Berrî-i Humâyûn (Imperial School of Military Engineering) in Hasköy. When he faced problems in understanding the perspective, he was sent to Mekteb-i İdadi-i Askeriye (Preparatory School for Military) in Macka Barracks in 1834, particularly to study Euclidian geometry. When he graduated from this school, he enrolled into Mekteb-i Harbiye (War Academy). He took private lessons from Tahir Pahsa who was his teacher and who had graduated from Cambridge University. In 1859 Vidinli Tawfik graduated from the War Academy and attended Erkân-i Harbiye (High Officials Academy) with the rank of staff officer of captain (Mulazim). When he finished this school in 1860, he was first appointed to Harbiye as a teacher and then to Erkân-i Harbiye as deputy teacher. Upon the death of Tahir Pasha, he was enroled to teach algebra, advanced algebra, analytic geometry, analysis and differential calculus, mechanics, astronomy and integral calculation. He added new chapters, regarding derivative and series, to his teacher's book which he wrote at the same level as contemporary European mathematicians did. In chorological order he became first staff captain (kurmay yüzbaşi) (1860), senior captain (kidemli yüzbaşi) (1863), major (binbaşi) (1867), lieutenant colonel (yarbay) (1869), colonel (albay) (1872), brigadier (mirliva) (1874), pullet (ferik) (1878) and marshal (1893).

During his enrolment as first deputy teacher and later teacher at the War Academy, he had, in addition to this task, the duty of teaching accounting in Kasimpasa Mekteb-i Rüşdiyesi (Junior High School), and mathematics and astronomy in Dar Al-Funun (University). When he was promoted as district governor rank, on condition to keep his lessons in Harbiye, he was appointed to the newly established Experience and Examination Station in Tophane-i Amire (The Royal Cannon Foundry).

Afterwards, Vidinli Tawfik was sent to Paris by Chief Commander Hüseyin Avni Pasha to inspect ballistics and rifle production and he stayed there two years as Military Attaché. He also became the deputy principle of the Mekteb-i Osmanî (School of Ottomans) in Paris. Meanwhile, alongside studying at the factory, he attended Paris University and Collège de France to improve his mathematical knowledge. He got in touch with the famous Turkish author Namik Kemal and other Turkish intellectuals and was welcomed by them.

In 1872 Tawfik Pasha came back to Istanbul and returned to his position in Tophane-i Amire. Later, he became mathematics teacher at Mekteb-i İdadi-i Askeri (Preparatory School for the Military) and the assistant class and physics teacher at Mekteb-i Fünun-i Harbiye (War Science Academy).

In 1872, Tawfik Pasha dismissed from all his duties and ranks, was appointed as a member of the committee which was established to inspect Henry and Martini rifles production which was ordered from United States by the Ottoman State. He went to the United States to learn English and also to inspect rifles production. After two years he came back to Istanbul (1874). After a couple of months he went to the United States again. After four years he came back to Istanbul and was appointed as a Minister of Imperial School of Military Engineering (Mühendishane-i Berri-i Hümayun Nazirliǧi) (1878). Besides this, he was also appointed as the head of the Tophane-i Amire Parliament (Tophane-i Amire Meclisi Başkanliǧi) (1880), after that he became the member of the Commission of the Public Works (Umur-i Nafia Komisyonu) and later became the Minister of Finance (Maliye Naziri) in 23 December 1880. In 27 July 1881 he was dismissed from this task and in 15 August 1882 he became the inspector of the Royal Cannon Foundries (Tophane-i Amire Fabrikalari müfettişliǧi).

In 1883 Hüseyin Tawfiq was appointed to Washington as Minister Plenipotentiary. After finishing this task he came back to Istanbul to occuy the office of member of the commission for military inspection and then he went to Germany as head of the commission which established to inspect the Mauser rifles which he would buy for the military service. Upon someone's denounciation, he was called back and appointed to Roma as an envoy; but he did not go.

In 1889 Hüseyin Tawfiq became the Minister of Commerce and Public Works (Ticaret ve Nafia Naziri) for five years and then he became the Member of the High Commission for the Military inspections. Later he became the Head of the Council for Accounting (Divân-i Muhasebât Reisi) and then a second time appointed as Minister of Finance (2 October 1897). After one year, again, he became the member of the High Commission for the Military inspections (1898). Meanwhile he carried out the aide-de-camp (Yaver) for the Sultan. Vidinli Tawfiq Pasha passed away in 16th June 1901.

Our mathematician knew English and French. He was honoured by receiving the first rank of Egel Ruj medallion from Germany, second rank Légion d'honneur medallion from France and second rank Leopold Medallion from the Belgium.

His speeches entitled Memalik-i Osmaniye and İslamiyet (Ottoman Lands and Islam) became famous when he made them upon the appointment to membership for the New Island History Society.

Hüseyin Tawfik Pasha, was a great scholar and as an eminent Ottoman intellectual in modern mathematics, he wrote important books in mathematics, astronomy and physics. While he was in the United States he dealt with ballistics and mathematics and published his famous book named Linear Algebra which comments on linear algebra. The book was known in the Ottoman literature as hisab-i muthanna (two ways calculation). It was the first book ever written in modern mathematics in Ottoman lands.

In 30 March 1864, with his friends Yusuf Ziya Pasha, Gazi Ahmed Muhtar Pasha, Sakizli Ahmed Esad Pasha and Ali Naki Efendi, Hüseyin Tawfik established a charity named Jamiyat Tadrisiyah al-Islamiye to help poor Muslim children to complete their education and instruction. He also wrote articles in the monthly journal of the society titled Mebahis al-Ilmiyya which was first published in 1867.

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Figure 2: Vidinli Tawfiq Pasha's tomb stone (photo by Simo Pimtanen). Source: IMAGE The Bulletin of the International Linear Algebra Society, 19 (Summer/Fall 1997), p. 15.

His contribution and career are described as follows by a present-day commentator:

"In the unpublished Memoirs of the noted Ottoman mathematician Salih Zeki, Hüseyin Tawfiq Pasa appears as a man of exceptional ability and honest character who everywhere encouraged scientific research. He reached as high a point in his scientific endeavours as permitted by his sterile environment. This remarkable man in the history of science in Turkey was later almost entirely forgotten and all his works written in Turkish were regrettably lost! Of his venerable memory, only a street hearing his name in Vezneciler (a quarter of Istanbul south of the Golden Horn and west of the Sultan Ahmet Square or Hippodrome) and a mute tombstone in the Eyüp cemetery- remain" [1].

2. His Publicatons

2.1. Linear Algebra (in English). Dealing with Linear Algebra, the book is a very original work in which de dealt with quaternions, a new mathematical subject at that time. Quaternions were first invented by the Irish mathematician-astronomer W. R. Hamilton (d. 1843) and became very important when they were applied to physics. At the end of the book, Hüseyin Tawfik established three-dimension algebra which contains complex numbers' algebras and also that formed with the three dimensions space vectors league. He also showed the application of this method to various problems which belong to elementary geometry. His book was first published in 1882 and secondly in 1892 in revised version. A paperback reprint of both the original versions, bound together in one volume, was published by the Istanbul Technical University [Bilim ve Teknoloji Tarihi Arastirma Merkezi Yayin, no. 5] in 1988. This reprint was edited by Kazim Çeçen and includes a preface by Ilhan Kayan, an introduction by Kazim Çeçen and a "contemporary assessment" by Cahit Arf (in Turkish and in English). In addition, A. M. C Şengör wrote a biography (in Turkish) of Hüseyin Tawfik. According to Salih Zeki, this book offers a new calculation method in the system of three dimensions method of Argand's Algebra. This commentator adds that Tawfiq Pasha studied to solve Argand's problems a long time and while he was travelling towards to United States he solved the problem in his cabinet using a tobacco paper. He assures that he saw this piece of paper when Tawfiq Pasha was alive but he could not find it after his death.

Figure 3: Irish stamp on the Quaternions, issued by Ireland on May 4, 1983. (Source).

Benjamin Pierce's (1809-1880) book Linear Associative Algebra was first published in 1870 in Washington and reprinted in 1882. Hüseyin Tawfiq's book was one of the earliest printed books on this subject in the world and it preserved originality on this area until the 1920's.

A copy of the original book is in Harvard University Library and bound within the frontal matter is an original letter dated February 5th 1885 from, and signed by, Huseyin Tawfiq to Justin Winsor, Esq., Librarian of Harvard College Library, bequeathing the book at "the request of the distinguished professor J. M. Peirce of the Department of Mathematics in Harvard College".

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Figure 4: The original edition of Linear Algebra published in 1882.

2.2. Hasâb al-Muthannâ (two ways calculations): Published in the journal Mebâhis-i İlmiye Mecmuasi in 1866, it was another article about algebra written by Hüseyin Tawfiq.

2.3. Zayl Usûl al-Jabr (Appendix on the method of Algebra) (in Turkish): An appendix about derivatives upon Tahir Pasha's book Usûl al-Jabr and also about Mc. Lauren Taylors's series (İstanbul 1278/1861).

2. 4. Yeni Ölçülerin Menâfi ve İstimâline Dâir Risâle-i Muhtasara (An Abridged treatise on the advantages and usage of the new measurements) (in Turkish): Explains how to solve problems in the newly applied system of weights and measurements (Istanbul 1882).

2.5. Heyet Kitabi (Book on Astronomy) (in Turkish): Hüseyin Tawfiq wrote this book while he was instructor at the Muhendishane (Imperial School of Military Engineering); we have not got any copy of it.

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Figure 5: Front cover of Linear Algebra published by the Istanbul Technical University in 1988.

2.6. "Mahsûsât ve Gayr-i Mahsûsât" (in Turkish): An article published in the journal Mebâhis-i İlmiye in response to Resul Mestî Efendi's previous article where it is claimed that the Earth does not move (1867).

2.7. Rubu Tahtasina Dâir Bir Risâle (A Treatise on the Quadrant) (in Turkish): He wrote this book while he was staff captain and received a fifth degree Majidî Medallion.

2.8. Fann Makina (Science of Machine) (in Turkish): This book comments on machines, parts of the machines, gears, spinning wheels, winding wheels etc. The appendix which mentions steam and machines was written by Mehmed Sadettin (d. 1892).

According to the sources that mention the life of Huseyin Tawfik we know he wrote some more books which we cannot place so far. Those books are Mamâlik-i Osmâniya wa Islâmiyat (Ottoman Lands and Islam), Jabr-i Hattî (Plane Algebra), Usûl-i İlm-i hisâb (Principles of the science of calculation) and Jabr-i a'lâ (T) (High Algebra).


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End Notes

[1] Kazim Çeçen, Hüseyin Tevfik Paşa ve "Linear Algebra", Istanbul Teknik Universitesi Bilim ve Teknoloji Tarihi Araştirma Merkezi Yayin no. 5. 1988, p. 15.

*Senior Researcher at the Foundation for Science, Technology and Civilisation, UK and Research Visitor at the School of, Languages, Linguistics and Cultures, The University of Manchester, UK.

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