Last weeks program was a continuation of the effect of progress in Islamic sciences in the Middle Ages and its effect on the Renaissance in Europe. We tried to look into some of the basic routes through which Muslim learning and sciences penetrated into Europe including Europeans studying at Muslim universities as well as the Crusades. We started with specific examples of historical manifestation and of the attitude the Quran teaches towards science and learning. We discussed more particularly the area of Astronomy and chemistry. We gave various examples of Chemicals that still hold their names which come from Arabic words. For example alcohol.

**Host: How did the numerals that we use come to be called Arabic numerals?**

Jamal Badawi:

The Arabic Numerals that we use at the present time were originally used in India. However to Muslims goes the credit of popularizing the use of these numerals and brining them to Europe and introducing them to the world at large. Along with spreading their use but the development of Muslims in the field of mathematics also helped to make them be known as Arabic numerals. In addition to numerals one of the great mathematicians by the name of Muhammad Bin Ahmad during the 10th century actually invented the concept of zero. The Arabic word for zero is sifr which means void. This is related, in the opinion of some scholars to the term that came to be known as cipher and decipher. The discovery of the zero was not a simple thing and according to many science historians it revolutionized the discipline of mathematics. It made it possible to express all numbers using ten characters, giving them absolute value and a value by position. In fact without this the whole later development of mathematics would have been stifled. The zero as a concept came to be known in Europe only about 300 years after Muslims used it in the 13th century.

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**Host: It is claimed that the term Algebra comes from Arabic and is connected to the Islamic civilization, is this correct?**

Jamal Badawi:

Algebra is a means of universal arithmetic. It is the use of numbers, letter and symbols used to analyze and express relationships between concept of quantity in terms of formulas and equations. In a simpler way Algebra is calculation using symbols. The term is of Arabic origin. The arabic term is Algebr which means to unite or to put pieces together. Algebr was initiated by a Muslim mathematician Muḥammad ibn Mūsā al-Khwārizmī who lived in the 9th century and was connected with the House of Wisdom (that was established in Bagdad). His book on the subject called “Hisab Aljebr Walmukabala” which means calculation by symbols. This became a classic that for hundred of years was used as the basic in mathematics. The interesting thing is that the name al-Khwarismi is similar to algorithm and actually the algorithm was named after Al-Khwarismi. This is the study of the decimal system of counting which was introduced by him. In fact one of the major historians in the history and development of science, George Sarton, says that Al-Khwarismi “is one of the founders of analysis or Algebra as distinct from Geometry.” This made Algebra a distinct discipline. In addition to this we find so many other mathematicians who contributed to the field of Algebra like Abu Al Wafa who lived in the first part of the tenth century. He contributed a great deal of study which perfected the work of Al-Khwarismi and he also worked on quadratic equations. In fact many according to Sarton many of the works of the Muslim passed on to Europe through translation from Arabic to Latin by such people as Robert of Chester, Adler of Bathe and John of Civil.

**Host: Did Muslim mathematicians contribute to Geometry as well?**

Jamal Badawi:

Yes, in fact without the contribution of Muslim mathematicians in Geometry many of the golden treasures of the past could have been totally lost. Take for example the work of Euclid; without Muslims being keen about learning and preserving that heritage it would have been totally lost to history. In fact the first translation of Euclid’s work to Arabic was done in the first half of the 9th century. From this Arabic translation that heritage was passed on to Europe. It was later translated from Arabic to Latin. It is not really a matter of preserving the teachings of the past but there were lots of additions and commentaries added to it from as early as the 9th century. One of the most important commentaries on Euclid’s work came in the 13th century by Naṣīr al-Dīn al-Ṭūsī. His commentary and critique of Euclid provided the impetuous for the study of non Euclidian Geometry. This influenced people in the 18th century who were the forerunners of the so-called non-Euclidian Geometry which emerged in the 19th century. In addition to this we find that according to George Sarton makes tremendous reference to that as it is one of the most tremendous works in science. He indicates that in the 13th century the leading books in Geometry were in Arabic and Latin (which were translated from Arabic). In fact attention was not only given to the theoretical aspects but Muslims were practically oriented too which lead to the sub area of Trigonometry.

**Host: Could you shed some light on the field of Trigonometry?**

Jamal Badawi:

Trigonometry is a very important field in mathematics as it has a variety of application in surveying, navigation and engineering. According to John Draper Muslims were the first to develop Trigonometry in it’s modern form. The Greeks of course had some knowledge of Trigonometry but Muslims developed it into its modern form and in fact they were the first to use the sine and cosine. Al-Battani is credited for sine and cosine functions. This would probably be related to the deep interest in astronomy. Trigonometry has lots of application in astronomy. It is interesting that some of the work done by Muslim Trigonometry specialists on Tangents was not known in Europe until 500 years later. Some areas passed on to Europe faster but this is one area that took much longer. They also have works on Spheric Trigonometry which might be related to Astronomy. George Sarton in his Introduction to History of Science to say in Volume 2.1 page 12 he says the development of Trigonometry was entirely due to Muslim efforts during a the Middle Ages. He also says: “This outline of Trigonometry in the twelfth and thirteenth century can not but give the reader a very high idea of Muslim science. All the progressive work to the very end of this period was published in Arabic. Latin Trigonometry was but a pail reflection of the Arabic and it was already a little behind the times when it was new for the Arabic efforts did not stop but continued with increased efficiency.” This is really a fascinating area where a great deal of contributions were made by Muslim mathematicians and really provided the impetuous and inspiration for later mathematicians to continue.

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**Host: Are there additional examples of contributions to field of mathematics that you may be able to share?**

Jamal Badawi:

If we go back to the 10th century (particularly the second half) we find a Muslim mathematician Abu Al-Wafa who was regarded by historians to be the first one to show the generality of the sine theorem relative to spherical triangles. He also gave a new method for constructing the sign tables. In the 11th century very famous mathematicians, Alberoni and Ibn Sina (known in the West as Avicenna) contributed work at a very high level and full of originality. In Egypt a great astronomer and mathematician lived in the the 11th century who contributed a great deal was Ibn Yunus. One of the fascinating contributions came in the second part of the 11th century by a man who is known for being a poet than a scientist, Omar Al-Khayyam (Omar Khayyam in English). Al-Khayyam was so bright in mathematics that according to Sarton he conceived a very remarkable classification of equations. It is said that he recognized 13 different forms of cubic equations which is rather complex for that time. He tried to solve all of them and even gave partial geometric solutions to some of them the equations. In addition to this we find other people who contributed to the different branches of mathematics. For example in the first half of the 11th century we find a Muslim Mathematician, Ibn Al-Samh who contributed to the field of Calculus. Others also contributed to Commercial Arithmetic which is called Almuamalat in Arabic.

**Host: What was the simple most important Muslim contribution to the field of physics?**

Jamal Badawi:

It is agreed that the most important single contribution of Muslim physicists was the science of optics. In fact we can speak of optics without mentioning the name of Abu-Al Hassan Ibn-Al Haytham, the adulterated Latinized name is Alhazen. He lived in the first half of the 11th century and he was described by George Sarton as “the greatest Muslim physicist and one of the greatest students of optics of all times.” Alhazen according to Sarton exerted a great deal of influence on Western science. Furthermore, he showed great progress in the experimental method and which was the forerunner of Bacon and Kepler. As a result of his work we find that the development and use of the microscopes and telescopes developed at a later time. One of the main reasons for this contribution is basically a classic that he wrote called Kitab Almanathir or Optics. Indeed this work is regarded by historians as the beginning of the modern science of optics. I will give examples on some of his bright discoveries which were made in the first part of the 11th century. First of all, there was a common misconception in Greek science about how the person sees. In Greek science they used to believe that a ray of light proceeds from the eye to the object. He corrected this and he indicated that the ray of light actually illuminates from the object to the eye. For that time this created a major shift in the science of optics. In addition to this he showed a great deal of understanding of light refraction and light reflection which are both very important phenomena in physics. In fact he made a very important discover of the curvilinear path of the ray of light threw the atmosphere. This discovery led him to explain the concept of twilight: which is the reason why we can see the sun and the moon before they rise and after they set. At the early age of scientific development during the 11th century he was able to determine that the retina is the seat of vision and that the impressions that are made by light upon the retina is conveyed along the optic nerve to the brain. He was also able to explain why we are able to see one vision even though we use two eyes. His explanation was that this was due to the formation of the visual images on the symmetrical portions of both retinas. No wonder that we find that many of his works and particularly the ones focused on optics were translated and used over and over again for several centuries in Europe. Alhazen was definitely the most outstanding physicist in the area of optics but in fact he was not the only one. There are some other Muslim physicists who introduced additional notable improvements such as Nasir Al Din Al Tusi, Qutb Al Din Al Shirazi and Kamal Al Din Al Farisi.

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**Host: What other contributions to physics did Muslims contribute to?**

Jamal Badawi:

For example one of the most important things that revolutionized trade and resulted in the improvement of navigation is the compass. It is true that the Greek knew something about the properties of the magnet. It is also true that the Chinese understood some of the basic directive properties of the magnet. According to historians like George Sarton these nations were not able to put their knowledge and information into practical application. It is believed that it was the Muslims who adopted these ideas and put them into use. They were the first to use the magnetic needle for the purpose of navigation.

Another interesting aspect was their investigation into the field of hydrostatics which started as early as the 9th century. One of the interesting books Mezan Alhikmah (means theThe Book of Balance of Wisdom) on the subject of hydrostatics was written by Abu al-Rahman al-Khāzini. George Sarton sais“standard work on this subject was written by al-Khāzini and it is one of the main physical treatises of the Middle Ages.” He also says that he worked on tables of specific gravities of certain liquids and solids and he talked about a variety of physical facts and theories. Another aspect that may be of interest to physicists and engineers is the area of hydraulics. The idea of a water wheel was known in past history and there are some archeological evidence to this effect. According to Sarton the Muslim physicist introduced a great deal of improvement on the use of water wheels. He said “they made very remarkable use of them.” This in fact might explain the great deal of prosperity in agriculture. It contributed a great deal to various methods of agriculture and improvement in the production of this particular area. In fact historians narrate that evidence shows that (particularly in Syria) waterwheels were used quite frequently and efficiently. In the city of Hama in the 13th century there were as many as 32 efficient water wheels that were in use (this is the same city that was attacked by the Army of Hafez al-Assad in Syria in which 20-30 thousand people were slaughtered). It is so overwhelming to see the strides that were made in this particular field and all others which we discussed before. We are not saying that all the contributions were made in science. We will see later that there were contributions to geography, history, law and other fields that were just as remarkable. We started with the contribution to science because that stands clearly in the face of some of the erroneous arguments hat might be predominant in the West that Islam stands against progress and is only befitting for nomadic people who ride camels and live a simple life in the desert. Forgotten are the great contributions to the development of sciences which manifested over several hundreds of years which paved the way for what we know today as modern scientific progress.

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