Mathematician and astronomer (B. 1380, Maveraünnehir / Kâş – D. 1437, Semerkand). His full name was Cemşid bin Mes’ud bin Mahmud et-Tabib el Kâşî and his pseudonym is Gıyaseddin. He started his education life in Kâş. His father was the leading religious scholar and scientist of the time. Firstly, he learnt sarf (philology), nahiv (syntax) and fıkıh (Islamic law) and had comprehensive knowledge on Islamic law. He studied on logic, rhetoric, mathematic and astronomy. Due to his passion for science; he went on long journeys and worked fearlessly. He served under the Karakoyunlu İskender Sultan in 1416. He was invited to the Semerkand by the ruler of the city, Ulugh Beg, himself a great scientist.
Firstly, he investigated the works of Nasirüddin Tusi and Kutbuddin Şirazi. He started to work in an observatory in Meragâ and reorganized the astronomical tables. In this way, he leaded to expand the horizons of astronomy. He explained the star charts (zic), the distances of planets, determination of solar and lunar eclipse, the production and usage of the vehicle named “Tabak-ül-Menatık”, an instrument to determinate astronomical patterns.
European science historians suggest that Kepler was the one who discovered that the shape of an orbit was not circular, but elliptical. In fact, Gıyaseddin Cemşid had explained this fact in his work named “Nüzhet-ül Hedaik” one hundred year before Kepler. He provided the development of research, observation and experimental method through his scientific works and his wisdom. He determined closely the patterns of lunar eclipse on 1406, 1407 and 1408. He explained and proved that the orbits of the moon and the mercury lied on an ecliptic plane. Thus, Kepler’s effort to claim that Cemsid’s thesis was his, proved invalid and groundless.
If the small things that we use in daily life haven’t been discovered; we wouldn’t reach the state-of-the-art today. The idiom in Turkish language which means “mere fleabite” to indicate a valueless case comes from the zero at the left of the comma in decimal fractions. At the time when the decimal fractions hadn’t been discovered yet; controversial circumstances happened in all scientific fields, from fractional numbers to space technology.
“Comma” is an important punctuation for the texts, but it isn’t a must to use it. However, it is an absolute must for mathematics. Besides his researches on astronomy, Gıyaseddin Kâşi much more focused on mathematics. He was the first person who used the comma in arithmetic operations. When one looks at his work “Risalet’ül Muhitiyye” it can be clearly observed. He was also the first person to discover the decimal fraction system and had a book on this subject. He made the decimal fraction rule for the first time and used decimal fractions for addition, subtraction, multiplication and division. However, the discovery of the decimal fractions was attributed to Simon Stefan. German science historian Pouluckey proved that Cemsid was the inventor of the decimal system at the end of his researches on 1948 and the science world accepted his claim. Cemsid had invented this system 160 years before Simon Stefan did. He applied four basic operations on decimal numbers. This system was started to be used after XVI. Century in Europe. In his work on the decimal fractions system, “Risalet-ül-Muhitiyye”, he clearly showed the proportion of the circumference to the radius of circumference. In this book, he differentiated the integer from the decimal number without using comma punctuation, by placing the word “integer” (sihah) for the first time. His thesis is much more correct than his predecessors. In his thesis on the business accounts, he used comma punctuation in decimal fractions instead of using the term “integer”.
Moreover, Gıyaseddin Cemşid is famous for his original inventions to solve high-degree numerical equations approximately. He had also inventions in algebra. He explained taking roots of any degrees especially in “Miftah-ül Hisab” that was devoted to Ulugh Beg. The Western World invented this 300 years later through Isaac Newton. He accounted the ways of taking roots in “Miftah-ül Hesab”. Although, it was claimed that taking roots by using the “Broom Expansion” which is a formula in mathematics invented by Newton; Derek Stewart proved in his book named “Sources of Mathematics” that Cemsid invented this method three years before Newton and he was the first person to solve the “Binomial” equations.
Cemşid computed the correct value of “Pi” number for its nine first decimal digits (3,1415926535898732) and computed the sine value of 1 degree arc for the 18 digits of decimal numbers accurately. The basic formula in trigonometry, which is known as the “El Kashi Equity”, was developed by him and some basic formula in trigonometry was also named after him. His inventions on arithmetic and trigonometry might be found in “Risalet-ül Muhitiyye” and “Risalet-ül Veter ve’l Ceyb”.
He invented the hand calculator and the decimal fraction, found the approximate solutions for the problems with inaccurate results, found the perfect logarithm and algorithm and computed the value of “Pi” number to a high degree of accuracy, as well as invented the hand calculator. At the same time, he is the person who solved the binomial equation which is named after Newton. The solution of the equation took place in the book named “Miftah el-hisab” (The Key to Arithmetic). Cemsid, he is also the writer of a masterpiece on the arithmetic based on the sexadecimal number system, “Risale el-muhitiyye” (Overall Booklet on the Circle).
He has great contributions to the building of the Semerkand Observatory (1421). He was also the first director of the observatory. He contributed efforts in preparation of the “Zic” (star charts) of Ulugh Beg (1394-1449). Citing him, Ulugh Beg said: “His works are the perfective of their predecessors”, “A person who is able to solve all kind of confusing issues” and added that he was known as “Allâme Cemşid” (T.N. Learned Man).
Through his works, he influenced his colleagues until XVII. Century and drew great attention until XX. century. He made a distinguished name for himself especially in mathematics on the Western science world. When we look at the science history between the VIII. and XVI. Centuries, we realize that he was the most important mathematician and astronomer of the time. During his time, the astronomy and mathematics developed so much that European world reached this level around the end of XVII. Century. Gıyaseddin Cemşid had many works on mathematics and astronomy. His works have been used as the basic reference guide for long years, especially between XVI. and XVII. Centuries, by the well-known scientists of the time.
Risalet-ül Muhitiyye (Rules for decimal numbers and the value of Pi number), Kitab-u Miftah-il-Hisab (The Key to Calculation: Five volumes on calculations with integers, calculations for fractional numbers, calculations for astronomy, calculations for topographical field, calculation with unknown equations), Risalet-ül-Kemaliye veya Süllen-üs-Sem’a (“Layers of the Sky”: the Determination of Distances and Sizes of the heavenly bodies, Kitab-u-Ziye-il-Hakani fi Tekmili Ziye-il-İlhani (The coordinates of the stars that are observed on the book of Nasirüddin Tusi’nin Ziyei’l-İlhani), Nüzhet-ül-Hadâik (On his own discovery Takabül-Menatık which is a telescopic vehicle.)
REFERENCE: Salih Zeki / Âsâr-ı Bakiye (1329), Aydın Sayılı / Uluğ Bey ve Semerkand’daki İlim Faaliyeti Hakkında Gıyâsüddîn-i Kâşî'nin Mektubu (1985), Sadettin Ökten / “Kâşî - Uluğ Bey'in ilmî çevresine mensup matematikçi ve astronom” (Türkiye Diyanet Vakfı İslam Ansiklopedisi, c. 25, s.15,16, 2002), İhsan Işık / Ünlü Bilim Adamları (Türkiye Ünlüleri Ansiklopedisi, C. 2, 2013) - Encyclopedia of Turkey’s Famous People (2013).