Al-Khwarizmi The Father of Algebra By Ibrahim B. Syed, Ph.D., D.Sc., F.A.C.R. • Clinical Professor of Medicine • University of Louisville School of Medicine • And • President • ISLAMIC RESEARCH FOUNDATION INTERNATIONAL, INC. • Louisville, KY 40242 Al-Khwarizmi •A Portrait of AlKhwarizmi Portrait of Al-Khwarizmi • This is taken from a stamp from the former USSR MUHAMMAD BIN MUSA ALKHWARIZMI (Algorizm) (770 - 840 C.E.) • Abu Abdullah Muhammad Ibn Musa al-Khwarizmi was born at Khwarizm (Kheva), a town south of the river Oxus in present day Uzbekistan. LEARNING ALGEBRA • RESEARCH ON BRAIN shows Algebra concepts can be taught -as early as in Kindergarten • Second graders at The School at Columbia Univ. are learning algebra • Other countries: To 6th or 7th graders • US: 25% of middle graders get algebra • In California, Algebra is taughtbeginning of the 8th grade WHAT IS ALGEBRA? • Algebra is a branch of Maths. • Describes relationships between things that vary over time • Variables denoted by letters and symbols. • Algebra is a study in logic. WHY LEARN ALGEBRA? • Careers today demand skills like problem solving, reasoning, decisionmaking, and applying solid strategies etc. • Algebra provides one with a wonderful grounding in those skills. • Colleges require it and some employers demand it. WHY LEARN ALGEBRA? • Algebra is a very unique discipline. It is very abstract. • The abstract-ness of algebra causes the brain to think in totally new patterns. • Algebra builds a better brain. WHY STUDY ALGEBRA? • When the brain is stimulated to think, the hair-like dendrites of the brain grow more extensive and more complex enabling more connections with other brain cells. We often hear that we use only a small percentage of our brain's capacity. The study of algebra is a way to increase our use of this marvelous muscle. By studying algebra, more "highways" are "built" upon which future "cargo" is transported -- cargo other than algebra. Abu Jafar Muhammad Ibn Musa al-Khwarizmi • 21st Century is the age of Information Technology (IT) • Modern Computers are indispensable in everyday life. • Al-Khwarizmi is the grandfather of Computer Science. • He is the Father of Algebra. TEXTBOOK OF ALGEBRA • A Page from alKhwarizmi's Kitab al-Jabr walMuqabala, the oldest Arabic work on algebra produced in the 9th century BAYT AL-HIKMA-Center for Jafar Muhammad Study and Research Abu ibn Musa al-Khwarizmi lived in Baghdad(Gift of God) in the early ninth century. Baghdad at that time was at cultural crossroads, and, under the patronage of the Abbasid caliphs, the socalled House of Wisdom at Baghdad, produced a Golden Age of Arabic science and mathematics. In Baghdad, scholars encountered and built upon the ideas of ancient Greek and Indian mathematicians BAYT AL-HIKMA • There, al-Khwarizmi encountered the Indian numeral system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and he wrote a treatise on what we call Arabic numerals. It was translated into Latin in the twelfth century as Algoritmi de numero Indorum (that is, AlKhwarizmi on the Hindu Art of Reckoning) and was crucial in the introduction of Arabic numerals to medieval Europe. It may well represent the first use of zero as a positional place holder. From that title, we have the word "algorithm." ALGEBRA- A Practical System for solving problems in • • • • • • • • Cases of Inheritance Contracts Surveying Tax collection Legacies Partition Lawsuits and Trade Algebra-A Practical System for solving real life Problems in the Islamic empire at that time • In all their dealings with one another. • Where the measuring of lands. • The digging of canals. • Geometrical computations. • Other objects of various sorts and kinds are concerned. LAWS OF ALGEBRA • Distributive: x(y+z) = xy+xz, (x+y)z = xz+yz • Associative: (x+y)+z = x+(y+z) (xy)z = x(yz) • Commutative: x+y = y+x xy = yx • Identity: x+0 = 0+x = x x 1 = 1x = x • Inverse: x+(-x) = (-x)+x = 0 • x(x-1) = (x-1)x = 1 Al-Khwarizmi's most important work: al-Kitab al-mukhtasar fi hisab al-jabr w'al-muqabala or The Compendious Book on Calculation by Completion [or Restoring] and Balancing. This book is an explanation of the solution to quadratic and linear equations of six varieties. Al-jabr refers to the process of moving a subtracted quantity to the other side of an equation; al-muqabala involves subtracting equal quantities from both sides of an equation. Textbook of Algebra • Hisab al-jabr w'al-muqabala was translated into Latin(Robert Chestetr) in 1145 as Liber algebrae et almucabala, from which we have the word "algebra" for the whole process. • But don't expect al-Khwarizmi's al-jabr to look anything like our algebra. • Al-Kwharizmi's book is written entirely in prose, with none of the symbols we use today. Some Problems-Formal • "If from a square, I subtract four of its roots and then take one-third of the remainder, finding this equal to four of the roots, the square will be 256. " • He explained it in the following manner: • "Since one-third of the remainder is equal to four roots, one knows that the remainder itself will equal 12 roots. Therefore, add this to the four, giving 16 roots. This (16) is the root of the square. The above can also be stated in terms of modern notation as • 1/3 (x2 - 4x ) = 4x." Therefore x = 16. "A man is hired to work in a vineyard 30 days for 10 Dollars. He works six days. How much of the agreed price should he receive?" • It is evident that since days are one-fifth of the whole time; and it is also evident that the man should receive pay having the same relation to the agreed price that the time he works bears to the whole time, 30 days. The month, i.e., 30 days, represents the measure, and ten represents the price. Six days represents the quantity, and in asking what part of the agreed price is due to the worker you ask the cost. Therefore multiply the price 10 by the quantity 6, which is inversely proportional to it. Divide the product 60 by the measure 30, giving 2 Dollars. SOLUTIONS OF EQUATIONS He first reduces an equation (linear or quadratic) to one of six standard forms: 1. Squares equal to roots. Example: ax2 = bx 2. Squares equal to numbers. Example: ax2 = b 3. Roots equal to numbers. Example: ax = b 4. Squares and roots equal to numbers. Example: ax2 + bx = c e.g. x2 + 10 x = 39. 5. Squares and numbers equal to roots. Example: ax2 + c = bx e.g. x2 + 21 = 10 x. 6. Roots and numbers equal to squares. Example: ax2 = bx + c, e.g. 3x + 4 = x2. Solve the equation: x2 + 10 x = 39 He (Al-Khwarizmi) writes :... a square and 10 roots are equal to 39 units. what is the square which combined with ten of its roots will give a sum total of 39? The manner of solving this type of equation is to take one-half of the roots just mentioned. Now the roots in the problem before us are 10. Therefore take 5, which multiplied by itself gives 25, an amount which you add to 39 giving 64. Having taken then the square root of this which is 8, subtract from it half the roots, 5 leaving 3. The number three therefore represents one root of this square, which itself, of course is 9. Nine therefore gives the square. The Geometric Proof • Al-Khwarizmi starts with a square of side x, which therefore represents x2 (Figure 1). • To the square we must add 10x and this is done by adding four rectangles each of breadth 10/4 and length x to the square (Figure 2). • Figure 2 has area x2 + 10 x which is equal to 39. Geometric Proof • We now complete • the square by adding the four little squares • each of area. 5/2x5/2 = 25/4. • Hence the outside square in Fig 3 has area 4 x 25/4 + 39 = 25 + 39 = 64. • The side of the square is therefore 8. • But the side is of length 5/2 + x + 5/2 • so x + 5 = 8, giving x = 3. Al-Khwarizmi's concept of algebra can now be grasped with greater precision: it concerns the theory of linear and quadratic equations with a single unknown and the elementary arithmetic of relative binomials and trinomials. ... The solution had to be general and calculable at the same time and in a mathematical fashion, that is, geometrically founded. ... The restriction of degree, as well as that of the number of unsophisticated terms, is instantly explained. From its true emergence, algebra can be seen as a theory of equations solved by means of radicals, and of algebraic calculations on related expressions... GEORGE SARTON(18841956) Author of Introduction to History of Science (3 Volumes) Former Prof. At Harvard Univ. Wrote on Al-Khwarizmi as • ... the greatest mathematician of the time, and if one takes all the circumstances into account, • one of the greatest of all time.... Al-Khwarizmi wrote on • Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu Art of Reckoning) gave ALGORITHM deriving from his name in the title of the book. • He explained the use of ZERO • He developed the decimal system • Developed several arithmetical procedures including operations on fractions. • He developed in detail Trigonometric tables containing Sine functions and tangent functions • Developed calculus of two errors, which led him to the concept of differentiation Al-Kwarizmi's Books • Kitab al-Jama wal-Tafreeq bil Hisab al-Hindi and • Kitab al-Jabr wa al-Muqabala Were translated into Latin and were used for several hundred years in Europe Al-Khwarizmi's works influenced Leonardo of Pisa • Fibonacci was the "greatest European Mathematician of the middle ages", his full name was Leonardo of Pisa. • Discovered the enormous practical advantages of Zero and the Decimal System compared to the Roman numerals, which were still current in Western Europe. ASTRONOMY • Al-Khwarizmi wrote on • Calendars • True positions of the sun, moon, and planets • Spherical astronomy • Parallax and eclipse calculations • Visibility of the moon (21ST CENTURY Muslims are confused on the sighting of the moon) • Wrote a book on Astronomical Tables-A SIGNIFICANT CONTRIBUTION TO THE SCIENCE OF ASTRONOMY GEOGRAPHY • Kitab surat al-ard (book of the form of the earth) • Gave latitudes and longitudes for 2,402 cities and landmarks, forming the basis for a world map. • Corrected in detail Ptolemy's views on Geography GEOGRAPHY • Supervised 70 geographers to create a map of the then known world which shows the pacific coast of South America –about 700 years before Columbus discovered America. • Measured volume and circumference of the earth. • Wrote Kitab al-Tarikh and Kitab al-Rukhmat (on sundials) Al-Khwarizmi's World Map • Al-Khwarizmi's Map actually includes the whole coast of Peru and part of the coast of Chile. We find rivers and capes, in particular two especially characteristic capes lying on the PeruEcuador coast; the Satyrorum Promontorium or the Cape of Satyrs, which is Punta Aguja, and the Notium Promontorium or Southern Cape which is Punta Pariña, Turkish Admiral Piri Reis's World Map-1513 CE is on the left side(Antarctica discovered in 1820). On the Right Side is Muhammad Al-Idris's map of 1154 CE Satellite Photo Vs Piri Map IMPACT ON EUROPE • Adelard of Bath (England) was born in 1075. He studied and taught in France and visited Syria, Sicily and Spain He died in 1160. He translated several works on Mathematics and Astronomy. Among the most important works he translated was the Astronomical tables AlMajriti (1126). He translated Al-Khwarizmi's tables and other works on the abacus and astrolabe. His 'Quaestiones naturales' consists of 76 scientific discussions derived from Muslim sciences. IMPACT ON EUROPE • Gerard born in 1114 in Cremona (Italy). In Toledo, Spain he learnt Arabic so he could translate available Arabic works into Latin. He died in 1187 in Toledo, Spain (Andalusia). Among his translations were the surgical part of Al-Tasrif of Al-Zahravi (Albucasis), the Kitab al-Mansuri of AL-Razi (Rhazes) and the Qanun of Ibn Sina (Avicenna), Banu Musa's works, Al-Biruni's commentry on Al-Khawarizmi (after whom concept "Algorithm" is named), the tables of Jabir b. Aflah and Zarqali. Al-Khwarizmi's books translated into Latin • Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hindi (on Arithmetic) • Al-Maqala fi Hisab al-Jabr wa-alMuqabilah ( on Algebra) by Englishman, Robert of Chester (1145 CE) • Arabic numerals and number system assisted progress in science, accounting and bookkeeping. MUSLIM IMPACT ON EUROPE • Baghdad, Damascus, Cairo and Cordoba were the centers of civilization. Here Muslim scientists made tremendous progress in applied & theoretical science and technology. • While Europe festered in the Dark Ages. Muslim Impact on Europe • Scholars and students from various parts of the world and Europe came to Cordoba to study. • In the 9th century the library of the monastery of St. Gall was the largest in Europe with 36 volumes. At that time, that of Cordoba contained over 500,000 volumes. Arabic Maths Worldwide • Muslim mathematicians invented geometrical algebra, solved third and fourth degree equations. • The world witnessed a new stage in the development of mathematical science, driven by the numerous translated works from Arabic into European languages. Advancement of Sciences in Europe • The sciences, with Arab mathematics as their essence, flourished and developed in the disciplines we know today. • Without the number zero and Arabic numerals in Europe, the world as we know today would have been different. NUMBER ZERO • Muslim mathematical study concentrated in three areas: ongoing progress in algebra, the development of arithmetic algorithms, and the increasing complexity in geometry. • The number zero and decimal system in Europe was the basis for the Scientific revolution. • Problems that took days (using Roman Numerals) to solve could now be solved in minutes (using Arabic numerals). FAMOUS WORKS • Al-Jabr wa-al-Muqabilah from whose title came the name "Algebra" • Kitab al-Jam'a wal-Tafreeq bil Hisab al-Hindi (on Arithmetic, which survived in a Latin translation but was lost in the original Arabic) • Kitab Surat-al-Ard (on geography) • Istikhraj Tarikh al-Yahud (about the Jewish calendar) • Kitab al-Tarikh • Kitab al-Rukhmat (about sun-dials) From EAST TO EUROPE • Europe would have been a lot poorer-economically, culturally and scientificallyhad it resisted the globalization of mathematics, science and technology at that time. • Today Western science and technology are flowing to many parts of the world. (Our Ulama are resisting them) Breaking the Boundaries • The Renaissance, the Enlightenment and the Industrial Revolution were great achievements. These developments drew on the experience of the Muslim world, India and China. • Today a mathematician in Boston invokes algorithm to solve a difficult computational problem, then he/she is commemorating Al-Khwarizmi The square root of math itself • Al-Khwarizmi is one of many whose works influenced the European Renaissance, the Enlightenment and the Industrial Revolution. • Modern prosperity is due to science and technology, which have delivered better lives for people, longer lives, and for larger populations. 13th Century Muslim World • Led the whole world with its development of the culture of philosophy, science, mathematics, astronomy, physics, chemistry and medicine. • If the Muslim world had been able to continue on the Qur'anic commands on scientific research, the cause of human progress would have advanced by about 500 years. CONCLUSION • Algebra and algorithms are enabling the building of computers, and the creation of encryption. • The modern technology industry would not exist without the contributions of Muslim mathematicians like Al-Khwarizmi. Ms. Carly Fiorina, Hewlett-Packard's former Chairman and CEO • In Minneapolis, MN on Sept. 26, 2001 said, "There was once a civilization that was the greatest in the world. • This civilization was driven by invention. • Its architects designed buildings that defied gravity. • Its doctors examined the human body, and found new cures for disease. • Its astronomers looked into the heavens named the stars, and paved the way for space travel and exploration. Ms. Carly Fiorina • When other nations were afraid of ideas, this civilization thrived on them, and kept them alive. • When censors threatened to wipe out knowledge from past civilizations, this civilization kept the knowledge alive, and passed it on to others. • While modern Western civilization shares many of these traits, the civilization I'am talking about was the Islamic World, 800-1600 CE, which included the Ottoman Empire, the Courts of Baghdad, Damascus and Cairo. (She forgot Cordoba) Ms. Carly Fiorina • We are unaware of our indebtedness to this other (Islamic) Civilization, its gifts are very much part of our heritage. . Sufi poet-philosophers like Rumi challenged our notions of self and truth. • Leaders like Suleiman the Magnificent contributed to our notions of tolerance and civic leadership based on MERITOCRACY, NOT INHERITANCE. • It was leadership that harnessed the full capabilities of a very diverse populationthat included Christian, Islamic and Jewish traditions." •THE END •THANK YOU FOR YOUR ATTENTION! THE END •THANK YOU FOR YOUR ATTENTION!