Scholar of mathematics and astronomy, founder of trigonometry. (B. 10 June 940, Khorasan / Iran – D. 998, Baghdad) His full name is Ebu el-Vefa Muhammed b. Muhammed b. Yahya b. İsmail b. el-Abbas el-Büzcanî and he was also known as “Engineer” and “Calculator”. There is no further information about his life. He was born in Buzcan town located between Herat and Nişabur (nowadays Türbet-i Câm). He received his basic knowledge in the field of mathematics from his uncles Ebu Amr el-Mugâzilî and Ebû Abdullah Muhammed b. Anbese. Later he went to Baghdad and completed his education with recognized scholars of the period. He started to give lectures and make researches in the fields of mathematics and astronomy in Baghdad. He realized most of his observations here in the period of Büveyhî ruler İzzüddevle Bahtiyar b. Muizzüddevle. He corresponded with Birûnî to benefit from his opinions on this issue. Meanwhile they compared the observation results of “birküs” incident observed by Birûnî in Harizm and by Ebü’l-Vefâ in Baghdad. Birûnî mentioned his observations in some of his works. It is known that Ebü’l-Vefâ corresponded with his contemporary Ebu Ali el-Hubûbî and Hububî asked him some formula to discover the space of triangles.
Starting from 959 until his death, Ebu’l Vefa was busy with science in Baghdad. He received a basic education in the fields of mathematics and astronomy and did studies on trigonometry primarily. He wrote books in this field and analyzed Ptolemy’s and Diophantus’ works, explaining them. In the field of astronomy he worked on the movements of the moon.
Ebu’l Vefa who has a distinct place in the history of science thanks to his services in the fields of mathematics and astronomy developed a wall octant to calculate the declinations of stars in an accurate and correct way. Other than this, he developed advanced methods to make calculations in trigonometric tables and invented new methods to solve some problems in spherical trigonometry. He calculated value tables of sinus b and tangent b with angle intervals of fifteen minutes for astronomic observations.
These proportions determined by Ebu’l Vefa who presented the trigonometric relations between the six ground proportions of trigonometry for the first time are still used nowadays. Besides he explained the sinus theorem in spherical trigonometry.
Ebu’l Vefa followed important mathematicians such as Habeş el-Hasib and el-Mervezi, defining functions of tangent and secant. Although Copernicus is known as the discoverer of secant, the famous historian of science Monte Candon’s and Carra de Vaux’ researches proved that this discovery belongs to Ebu’l Vefa.
Aside from trigonometry Ebu’l Vefa also researched on the science of algebra at depth. He managed to solve 4th degree equations which were unknown until that time. He could solve numerous problems which could not be solved by ancient Greeks and Indians using geometric methods.
A crater on the moon was named Abul Wafa after him. The famous historian of science Plorian Cajori said the following things about him in his book titled “History of Mathematics”:
“Ebu’l Vefa without doubt developed Harezmi's inventions in mathematics and geometry. He especially focused on the relations of geometry and algebra. Thus he managed to solve some algebraic equations using geometry. He established the fundaments of differential calculations and analytic geometry. As it is known, differential calculation is an important and a very useful topic invented by the human intelligence and it is the basic source of modern scientific and technologic developments. Besides he analyzed Battani’s works on trigonometry and explained the complicated and ambiguous parts.”
Kitab ül Kâmil, which is accepted as his most important work, is about trigonometry and astronomy. In the first chapter of the work problems required to be known before the movement of stars are explained, in the second chapter analysis of movements of stars and in the third chapter things which make stars move.
Kitab'ül-Kamil (On trigonometry), Ez-Ziyc'üs Şamil (On astronomy), Kitabü fi Amel-il-Mistarati vel-Pergar vel-Gunye, Kitab ma Yahtacu İleyh-il-Küttab vel Ummal min İlm-il-Hisab, Kitabun Fahirün bil Hisab, Kitabun fi ilmi Hisab-il-musellesat-il-Küreviyye, Kitabun fil-Felek, Kitabun fil-Hendese, Kitab'ül-Medhal ila Aritmetik, Tefsir-i-Harezmi fil Cebri vel-Mukabele.
REFERENCE: Hilmi Ziya Ülken / Türk Tefekkür Tarihi (1933), S. N. Nasr / Kozmoloji Öğretilerine Giriş (1985, s. 84), Adnan Adıvar / Bilim ve Din (1980, s. 80),Yeni Rehber Ansiklopedisi (2. bas. c. 6, s. 148-149, 1993), “Ebü’l-Vefâ’ Muhammed” (TDV İslâm Ansiklopedisi (1994, c.10, s. 97), M. Şemsettin Günaltay / Ebü'l-Vefa Bozcani'nin Türklüğü ve Hayatı Hakkında (tebliğ, Kayseri Zabıtları, s. 299), İslam Ansiklopedisi - İslâm Âlemi Tarih, Coğrafya, Etnografya ve Biyografya Lügati (c. 4, Eskişehir 2001), İhsan Işık / Ünlü Bilim Adamları (Türkiye Ünlüleri Ansiklopedisi, C. 2, 2013) - Encyclopedia of Turkey’s Famous People (2013).