The twelfth century is branded by some historians as a “renaissance” – that is, it was a period of intellectual growth and inquiry, harkening back to classical knowledge. Cathedral schools thrived and universities were established. A thirst for knowledge gripped European scholars, but they were not content with the limited resources the West had to offer, particularly in the field of mathematics. This spurred a great search for knowledge, known as the Latin translation movement. The greatest centre of translation was the Toledo School of Translators in Spain. The most eminent translators of the twelfth century include Adelard of Bath, Gerard of Cremona and Plato of Tivoli.
Although cathedral schools thrived and universities were being established, mathematical knowledge in the twelfth century had stagnated. In Europe, the extent of advanced mathematics available in Latin was Boethius’ short treatise on arithmetic, which was found to be impractical, and his missing book on geometry. A lack of knowledge of Greek prevented the Western world from utilising other classical learning. The Arabs, however, were able to use it as they had conquered a large number of Greek-speaking lands. Interestingly, mathematics became important to Muslims because as their empire spread it became increasingly difficult to determine the direction of the holy city of Mecca, which they are required to pray to five times a day. As a result, scholars began to study the position of the stars and this would inspire developments in astronomy and trigonometry. The Arabs would establish a notable place of learning known as the ‘House of Wisdom’ in Baghdad where Greek science and philosophy were translated into Arabic. This Greek-Arabic translation movement was the forerunner to the Latin movement and “secured the scientiﬁc heritage of Greek science in ﬁelds like mathematics, astronomy, astrology, alchemy, physics, medicine, logic, and ﬁnally also philosophy, and it decisively contributed to establishing an autonomous scientiﬁc culture in the Arabic world, which continued and developed the Greek tradition.”  Among the ﬁrst works involving sophisticated mathematics that were translated were the Almagest and Euclid’s Elements. These works translated in the Greek-Arabic translation movement would filter across the Islamic Empire, and when they reached Spain, would come into contact with Western Christians.
Spain became one of the greatest epicentres of knowledge in the twelfth century. With its amalgamation of cultures, it provided a “fertile soil” for intercultural exchange. Toledo was the most important centre of learning in Spain as before the reconquista of 1085, the Islamic Caliphate had established a firm atmosphere of scientific learning. Although the Islamic elite would disappear, the books remained and in Toledo a school of translators was founded. One of the most prominent Latin translators, Gerard of Cremona, would travel to Toledo in the search of Ptolemy’s Almagest and translated it into Latin in 1167. The Almagest is a significant work (indeed it translates into “the Great”) from the second century that explores the motion of the stars and planets through mathematics and astrology. As it has been noted, Western Europe was without any such treatises but it would now become available through Gerard’s translation, who would later been known as the dictus magister. The work of Abu Kamil, the first Islamic mathematician to work with algebraic numbers higher than X2, would also be preserved by the Toledo School, however the translator is unknown.
Plato of Tivoli was an Italian mathematician who lived in Barcelona from 1116 to 1138. He is known for translating the Greek mathematician Theodosius’ Sphaerics which is a three volume work on spherical geometry that would be instrumental in furthering Euclidean geometry in the West. Plato’s other significant translation was the Jewish mathematician Abraham bar Hiyya’s work Treatise on Measurement and Calculation, which Plato translated as Liber Embadorum in 1145. It includes the first complete solution of the quadratic equation x2 – ax + b = 0 known in Europe. It greatly influenced the work of Fibonacci.
All though he had no connection with the Toledo School of Translators, Adelard of Bath was another prominent Latin translator. Adelard was a nobleman and scholar whose desire for further knowledge in mathematics and natural philosophy led him to Syria in 1114. Here he acquired Arabic and decided to translate Euclid’s the Elements into Latin in order to make it available to the West. Euclid of Alexandria’s (325-265 BC) Elements is a treatise on mathematics and geometry that can be considered the most important textbook ever written. Adelard’s translation of the Elements would greatly influence Western mathematics and remain the standard text until the sixteenth century. He also translated a treatise on Indian arithmetic by the important Islamic mathematician Al-Khwarizmi. This would bring to the West not only Classical Greek mathematics, but Ancient Indian mathematics as well.
The Latin translation movement, like the Greek-Arabic movement, would prevent much learning from being lost. For example, the decimal value system (which originated in India) could be found in the arithmetical work of Al-Khwarizmi, yet this Arabic original was lost and only preserved through a twelfth century Latin translation. Euclid’s Elements would be the most essential mathematical tool in the centuries to come and his axioms would inspire Newton and Russell, amongst others.
The twelfth century was an epoch of mathematical fruition and its legacy would allow Europe to eventually dominate mathematical inquiry in the following centuries.
 Charles H. Haskins, The Renaissance of the Twelfth Century (Cambridge: Harvard University Press, 1955), 6.
 James Hannam, God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science (London: Icon Books Ltd., 2010), 66.
 Ibid, 21.
 Mohammed Abattouy, “Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective,” Science in Context 14 (2001): 2.
 Mohammed Abattouy, “Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective,” 12.
 Charles Burnett, “The Coherence of the ArabicLatin Translation Program in Toledo in the Twelfth Century,” Science in Context 14 (2001): 250.
 Ibid. 252.
 Victor J. Katz, A History of Mathematics: An Introduction (London: Addison Wesley, 1998), 291.
 David E. Smith, History of Mathematics (New York: Dover Publishing Inc., 1951), 201.
 James Hannam, God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science, 66.
 Michael Mahoney, “Mathematics,” in David C. Lindberg (ed), Science in the Middle Ages (Chicago: University of Chicago Press, 1978), 153.
 Charles H. Haskins, “Adelard of Bath,” The English Historical Review 26, no. 103 (1911): 495.
 Mohammed Abattouy, “Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective,” 10.
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Hannam, James. God’s Philosophers: How the Medieval World Laid the Foundations of Modern Science. London: Icon Books Ltd., 2010.
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Haskins, Charles H. The Renaissance of the Twelfth Century. Cambridge: Harvard University Press, 1955.
Haskins, Charles H. and Putnam Lockwood, Dean. “The Sicilian Translators of the Twelfth Century and the First Latin Version of Ptolemy’s Almagest.” Harvard Studies in Classical Philology 21 (1910): 75-102.
Holmes, Urban T. “The Idea of a Twelfth Century Renaissance.” Speculum 26, no.4 (1951): 643-651.
Katz, Victor J., A History of Mathematics: An Introduction. London: Addison Wesley, 1998.
Lindberg, David C. Science in the Middle Ages. Chicago: University of Chicago Press, 1978.
Smith, David E. History of Mathematics. New York: Dover Publishing Inc., 1951.
Reference this post (Chicago): Veronica Fitzpatrick, “The 12th Century Translation Movement and Mathematics,” Veronica Fitzpatrick (blog), March 27, 2016, http://veronicafitzpatrick.com/the-12th-century-translation-movement-and-mathematics/
Image: An illustration from the medieval translation of Euclid’s “Elements” c. 1310 © British Library Digital Collection. Wikimedia Commons.