Scientific and cultural development in human societies has been a continuous process. Progress has not been a stand-alone phenomenon for any geographical area; it has been enhanced in one part of the world by furthering the knowledge attained earlier by other communities in some other part of the world. This article traces the signature work of two European scientists, one of the pre-Renaissance era and the other of the early Renaissance – so as to demonstrate the overlap between the Islamic Golden Age and the European Renaissance. Chronologically, as the former was coming to a close in the late 13th century with the destruction of its centers of learning by the Mongols, the latter was taking root in the shape of universities in Italy, England, France and Spain.

The fact that the early Renaissance borrowed from Muslim intellectuals and scientists has mostly been ignored by Western thinkers. In fact, until the middle of the previous century, it was assumed by Western thinkers that they owed nothing in scholarship to any other civilization except the ancient Graeco-Roman world, terming the 1,100-year-long interval between the end of the Roman empire in the mid-4th century till the rise of the Renaissance in the mid-15th century as ‘Dark Ages.’ This attitude was the result of two factors. First, the contact between Western Christendom and Islamic World was often marked by conflict, e.g. in Spain, Constantinople and the Crusades. Second, Western hubris created by their successful exploration of the world since the Age of Discovery from the 1490s that left no part of the globe beyond the reach of European naval power. General education and sciences proliferated rapidly in Europe with the invention of the printing press in the mid-15th century, and their techno-political superiority dominated every nation in Asia and Africa for about two centuries. This hegemonic mindset created such a sense of superiority in Western peoples that they felt it below themselves to acknowledge that they were once less accomplished than the races they had come to colonise so completely.

This haughtiness can be illustrated by many examples, some of which are quoted here. Macaulay viciously regarded one shelf of a good European library as worth more than the whole literature of India and Arabia. Voltaire famously, but certainly erroneously, stated that during the dark ages, “*barbarism, superstition and ignorance covered the face of the world.”* Europeans credited ancient China with very few achievements despite the superiority and continuity of high cultural and technical achievements of that land. Encumbered by his ‘White Man’s Burden,’ Kipling regarded the brutal colonization and plunder of Afro-Asian nations by the Western nations as the ‘*civilizing burden of western nations*’. As a result, while European scholars were well aware of Islamic achievements in medicine, astronomy, mathematics, history and philosophy, they downplayed their influence, thus betraying poorly-justified arrogance and a jaundiced view of history.

Coming back to the subject of this article, the impact of the scholarship of Golden Islamic Age on the European Renaissance, this article examines the seminal work of Copernicus.

The Tusi Couple is such an exact copy of the original that Copernicus has labeled the same geometric points as A,H,D,B and G – where Tusi has used the phonetic equivalents of these letters in Arabic

Copernicus (1473-1543) is probably the first modern scientist in Western civilization. His principal thesis that the solar system is heliocentric and not, as had been believed till then, geocentric, was as inspirational a theory as the discovery of gravitation by Newton or of relativity by Einstein. Western scholars would regard it blasphemous even to hint that Copernicus plagiarized. However, there is no denying that some of the basic mathematical concepts and astronomical observations in his thesis were borrowed from Muslim scientists but not acknowledged. In his paper titled *De Revolutionibus Orbium Coelestium* (‘On the Revolutions of Heavenly Spheres’, published AD 1543), Copernicus has cited Al-Battani (Albategnius, d. 929), a Muslim scientist of the Islamic Golden Age, some 23 times. However, there some glaring omissions in his acknowledgments that continue to haunt Western scholars.

In his paper, Copernicus used a concept that is now called the Tusi Couple and that was devised by Nasiruddin Tusi (d. 1274). He also used a mathematical argument now known as the Urdi Lemma developed by Mohiyuddin Urdi (d. 1266). His motion of the moon model is strikingly similar to the one developed by Ibn Shattir (d. 1375). None of these three discoveries/achievements, critical to his work, have been referenced to by Copernicus. Another factor requiring consideration is that there are no documents showing how Copernicus developed these ideas to prove that it was his original work.

The Tusi Couple is such an exact copy of the original that Copernicus has labeled the same geometric points as A,H,D,B and G – where Tusi has used the phonetic equivalents of these letters in Arabic. Swerdlow and Neugebauer wrote in their joint work *Mathematical Astronomy *that such Arabic theorems were indeed circulating in Italy around the year 1500; thus implying that Copernicus could have learned about them from his contacts in Italy. Copernicus apologists, e.g. Pedersen, Veselovsky and Blasjo among others, are of the opinion that he was not influenced by Islamic scientists and that any similarity in their work, including figures, concepts and notations, is mere coincidence. Others, e.g. Swerdlow, O’Leary and Saliba have undertaken extensive investigation to discover possible routes of transmission of Arab texts in Latin translations to Italy. Copernicus spent the years 1496 to 1503 in Italy, including studying medicine at the University of Padua, where the work of Tusi and others was well known and available in Latin and Greek – both languages being known to him. All these factors hint that Copernicus would have been aware of the work of Muslim scientists.

Second case is of Fibonacci (c. 1175-1250), the pre-Renaissance mathematician who formulated the Fibonacci series, and who introduced Arabic/Indian numerals to Europe, without which no mathematical progress was possible in that society. Before him, Europeans were using the Roman numerals with all their limitations – and in mathematical terms perhaps it makes sense for them to refer that era as the Dark Ages! It is these Arabic/Indian numerals that brought them to some semblance of mathematical light.

Fibonacci (c. 1175-1250) was born in Pisa but spent his childhood in North Africa where his father was a customs officer. He was educated in Muslim/Arab schools and traveled through Egypt, Algeria, Syria and Greece. The Arab/Indian numerals, therefore, came naturally to him. He returned to Pisa in 1200 and published his ‘Book of Calculations’ in 1202. The first chapter of Part 1 begins: *“These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.”*

Fibonacci then goes on to describe the methods for performing arithmetical operations using these numerals. He devotes one chapter to algebra and another to business calculations. However, strangely, not once does he mention, except once in an indirect way, the names of al-Khwarizmi (780-850) or Abu Kamil 850-930) though the works of these mathematicians were being taught in the schools that Fibonacci had attended.

This absence of reference is striking because, as Roshdi Rashed points out in his “Fibonacci et les mathématiques Arabes,”

“[…]*in his chapter on algebra Fibonacci deals with more than 90 problems, 22 of which come from al-Khwarizmi’s Algebra* *(in Gerard of Cremona’s translation), 53 come from the Algebra of Abu Kamil (the remaining 25 or so can all be explained as Fibonacci’s own variants of problems in both these Arabic authors).”* That leaves nothing much that is original in his work.

It was well known in those times that al-Khwarizmi introduced Indian numerals to the Arab world and that he was the inventor of Algebra as the word itself comes from his book *Al-gebr wal Miqabla*. The word Algorithm, too, is derived from his last name. His books had been translated into Latin and were widely circulated after his death. Abu Kamil al-Masri, a follower of al-Khwarizmi, was born in Cairo and lived there, with his books being widely read in that great city. It would be strange, indeed, if Fibonacci, who had been educated in this part of the world, was not aware of their work. Dr. Charles Burnett, a professor in Cambridge, in his *Leonard of Pisa (Fibonacci) and Arab Mathematics* writes that the manner of writing by Fibonacci was very similar to that of Abu Kamil’s book. It is no coincidence that within two years of his move to Pisa, Fibonacci was able to write his book.

The unreferenced influence of Abu-Kamil on Fibonacci can also be gauged from the fact that whereas the later stated in his book that he would write a method of describing geometry in algebra, one part of the former’s ‘Book of Algebra’ is titled ‘*On applications of algebra to the regular pentagon and decagon.*’ Also one chapter of Fibonacci’s book is ‘Recreational mathematics’, which also includes the Fibonacci Series, whereas one of the three parts of Abu Kamil’s above mentioned book is ‘problems of recreational mathematics.’

Another early Muslim work whose influence is evident in Fibonacci’s work is the book on ‘Ratio and Proportion’ by Ahmad ibn Yusuf al-Masri (835-912), who lived in Baghdad and Cairo. His work was well known at the time and translated into Latin.

Burnett concludes that, “*I suspect that his (Fibonacci’s) reason is that he thinks that, or wants to give the impression that, his own work is truly innovatory.*” The professor goes on to prove that it was impossible that Fibonacci had never come across the books by Muslim mathematicians. In today’s world by Western academic norms, this blatant case of plagiarism would be hard to defend!

The incidents presented above relate to unacknowledged Muslim contributions to the European Renaissance in its very incipient stages. Apart from philosophy, astronomy and medicine, Muslim contributions in mathematics have also gone unnoticed. In addition to propagating Arabic/Indian numerals and the invention of Algebra, they created tables for all six trigonometric relationships and established trigonometry as a separate mathematical discipline. The laws of sines and tangents were discovered by Tusi and the law of cosines by al-Kashi. These developments are at the heart of modern mathematics.

With the change in political conditions in the aftermath of the First World War, European recognition of Muslim sciences has taken a positive turn. Now 24 of the Moon’s craters and several minor planets are named after Muslim scientists from the Islamic Golden Age.

From the 8th to 14th centuries, Islamic and Western Christian civilizations shared common borders from Spain in the west through the Mediterranean Sea across Africa to Anatolia in the east. There was extensive interaction between two regions in shape of trade, diplomacy and warfare. Translation of literature from Latin, the language of learning in Europe, to Arabic, the language of learning in the Muslim world, and vice versa ensured that scholarly works were circulated in Spain, Italy, Syria, Baghdad and various centers of learning in Persia. It was but natural that that both regions were influenced by each other. However, while the Muslims openly acknowledged the Greek influences on their work, the Westerners have generally denied Muslim scholarship.

*Parvez Mahmood retired as a Group Captain from PAF and is now a software engineer. He lives in Islamabad and writes on social and historical issues. He can be reached at parvezmahmood53@gmail.com*