700

In the 8th century , Abu Ja'far Al Mansour the Abbasid Caliph (714-775) founded Khizanat AL Hikma(House of Wisdom) for the purpose of translating foreign books. Many foreign works were translated into Arabic from Greek, Chinese, Sanskrit, Persian and Syriac.Scholars produced important original research.New discoveries motivated revised translations that commented,corrected or added to the work of ancient authors.Ptolemy's Almagest,is an Arabic modification of the original name of the work: Megale Syntaxis.

800

1 Youhana Yousef Al Harrani,christian (died 815), wrote the book:"Summary of Two Geometrical Tables".

2 Sinan ibn Al Fateh Al Harrani Al Hasib(died 825),wrote the books: Addition and Seperation , The Cubes , Fundamentals of Arithmetic.

3 Al-Ḥajjaj ibn Yusuf ibn Matar (died 833). He was the first author who translated Euclid's Elements from Greek into Arabic.He translated Ptolemy's Almagest, which at that time had also been translated by Hunayn ibn Ishaq and Sahl al-Ṭabari. At the beginning of the 12th century, Adelard of Bath translated al-Ḥajjaj's version of Euclid's Elements into Latin.

4 Sahl ibn Bishr al-Israili(died 845), often known as Zahel or Zael.Sahl is believed to be the first who translated the Almagest of Ptolemy into Arabic.

5 Muhammad in Musa Al Khwarizmi.persian (died 850?), wrote the book:"AL Gabr wa AL Muqabala"(The Book of Calculation by Completion and Balancing).Gave the world three famous words: Algorithm, Algebra and the Indian Zero as it was transferred to the west through his book.Came up with a general rule to solve Quadratic equations.

6 Al-Abbas ibn Saed al-Jawhari was a geometer. His most important work was his Commentary on Euclid's Elements which contained nearly 50 additional propositions and an attempted proof of the parallel postulate.

7 Sanad bin Ali , Abu Al Tayyeb, jewish (died 864), wrote four texts on algebra, Indian arithmetic, mental calculation, and Euclidean irrational quantities, the latter being one of the earliest commentaries on Book X of Euclid's Elements.Sanad had found the size of the Earth by measuring the dip of the horizon from the summit of a high mountain.

8 Abu Yousuf Yaqub bin Ishaq AlKindi(Latin:Alkindus), (died 873?), He also wrote four volumes. On the Use of the Indian Numerals (Ketab fi Isti'mal al-'Adad al-Hindi) which contributed greatly to diffusion of the Indian system of numeration in the Middle-East and the West. In geometry, among other works, he wrote on the theory of parallels.

9 Abu Kamil Shuja ibn Aslam(died 880), wrote a Book of Algebra,In Europe, similar material to this book is found in the writings of Fibonacci, and some sections were incorporated and improved upon in the Latin work of John of Seville.Abu Kamil uses the equation x⁴ + 3125 = 125x² to calculate a numerical approximation for the side of a regular pentagon in a circle of radius 10.

10 Abu Abdallah Mohammed ibn Isa Al-Mahani (died 884?).Al Mahani showed by using terms of Algebra that the division of the line segment that Archimedes uses, depends on a cubic equation of the form:
x³ + c² b = cx² (a>0 ,c>0) which he failed to solve after giving it lengthy meditation.

11 Abu Haneefa Al Daynouri (died 895), wrote the book:"Research in Indian Arithmetic".

12 Abu Al Abbas Al Sarkhasi (died 895), wrote the book:"Arithmetic of Numbers and Algebra ".

13 Thabit ibn Qurra (died 901), Thabit stated and proved his theory on Amicable Numbers.He also gave the pair (220 , 284) of amicable numbers.

14 Banu Musa (Sons of Moses),Muhammad.Ahmed and AL Hassan (9th century),mathematicians and engineers,in their(Book of the Measurement of Plane and Spherical Figures, Banu Musa gave volume and area number values.They were actually building on concepts and coming up with their own original works.

900

15 Abu Barza Abd Al Hamid ibn Turk Al Hasib Al Jili (died 911), wrote the books:"The book of Areas" and "The book of commercial transactions"

16 Qusta bin Luqa Al-Ba'albakki, i. e. from Baalbek or Heliopolis, Lebanon,(died 912), Qusta translated Greek works on astronomy, mathematics, mechanics and natural science into Arabic. He also produced works of his own.

17 Ahmad Ibn Abdallah Habash Hasib Marwazi(died 922?),seems to have been the first to determine the time by an altitude, and introduced the notion of shadow (umbra versa) corresponding to our tangent. He compiled a table of tangents, probably the earliest of its kind.

18 Abu al-Abbas al-Faḍl ibn Ḥatim al-Nayrizi (died 932), Nayrizi wrote commentaries on Ptolemy and Euclid.He gave a proof of the Pythagorean theorem using the Pythagorean tiling.

19 Ahmed bin Muhammad Al Hasib (died 927), wrote the book "Addition and Seperation".

20 Ahmed bin Omar Al Karabisi (died 927), wrote the books:"Areas of Houses", "Area of the Rings"and "Explaining Euclid".

21 Al Hakeem Al Adli (died 927), wrote the books:"Areas", "Book of Algebra"

22 Abu Abd Allah Muḥammad ibn Jabir al-Battani (died 929), al-Battānī produced a number of trigonometrical relationships:
sec²a = 1 + tan²a
b sinA = a sin(90 - A).Solved the equation sinx = a cosx

23 Abu Ishaq , Ibrahim ibn Sinan ibn Thabit bin Qurra (died 946),Thabit was his granfather, wrote the books:"Problems in Geometry","Three conics drawing".

24 Ali bin Ahmed bin Omran Al Mousili (died 955), wrote the book:"Explaining Abu Kamil's book of Algebra".

25 Abu Yousuf , Yaqub Al Razi, wrote the books:"The collective in Arithmetic", "Two errors calculation".

26 Abu Yousuf Al Massisi (died 961), wrote a book on areas.

27 Abu Sahl Wayjan ibn Rustam Al Kuhi (died 961), was able to solve the problem of inscribing a regular pentagon into a square, resulting in an equation of fourth degree. He alse wrote a treatise on the "perfect compass", a compass with one leg of variable length that allows to draw any conic section: straight lines, circles, ellipses, parabolas and hyperbolas.

28 Kushiar Al Jili , Abu Al Hasan (died 961), wrote the book:"The Fundamentals of Indian Arithmetic",.

29 Abu Jafar Muhammad ibn Hasan Khazini (died 991), wrote a commentary on Ptolemy's Almagest in which he gives nineteen propositions relating to statements by Ptolemy. He also proposed a different solar model from that of Ptolemy.

30 Abu al Hasan Ahmad ibn Ibrahim Al-Uqlidisi (died 980), adapted the indian numerals to pen and paper instead of the traditional dust board, a move that helped to popularize this system.Wrote Kitab al-Fusul fi al-Hisab al-Hindi (The Arithemetics of Al-Uqlidisi) around 952.It is especially notable for its treatment of decimal fractions, and that it showed how to carry out calculations without deletions.

31 Abu Al Nasr AL Kulwazi (died 982), wrote the book:"Indian Arithmetic".

1000

32 Abu Al Wafa Al Buzajani, Muhammad ibn Muhammad ibn Yahya (died 1000?),He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers. He also introduced the sec and cosec functions, as well studied the interrelations between the six trigonometric lines associated with an arc.

33 Abu Mahmud Hamid ibn Khidr Khujandi (died 1000?), he stated a special case of Fermat's last theorem for n = 3, but his attempted proof of the theorem was incorrect. The spherical law of sines may have also been discovered by Khujandi.

34 Maslamah bin Ahmed AL Majriti (died 1007), wrote the book:"The Science of Numbers"

35 Abu Saed Ahmed ibn Mohammed ibn Abd Jalil Sijzi (died 1020), made a special study of the intersections of conic sections and circles. He replaced the old kinematical trisection of an angle by a purely geometric solution (intersection of a circle and an equilateral hyperbola).

36 Abdullah bin Hasan Al Saydanani(died 1029?), wrote the books:"Problems in multiplication and division" , "Explaining the book of AL Khwarizmi".

37 Muhammad bin Yahya bin Aktham Al Qadi (died 1029?), wrote the book:"Number Problems".

38 Ja'far bin Ali Al Mohandis(engineer) Al Makki (died 1029?), wrote the book:"Geometry Book".

39 Al Istakhri AL Hasib (died 1029?), wrote the book:"The Collective in Arithmetic".

40 Muhammad ibn Al Hasan AL Kharaji(died 1029 ?), his work on the binomial theorem, the binomial coefficients and the Pascal triangle. In his book Al-Fakhri(the prestigeous) al-Karaji computed (a+b)³ and in (The marvelous, “Al Badee’), he computed (a-b)³ and (a+b)⁴ .

41 Al Qadi Al Nasawi(died 1029?), wrote the book:"Un veiling Euclid".

42 Ibn AL Samah AL Mahri(died 1035), wrote the books:"Intro to geometry, explaining Euclid", "Nature of Numbers".

43 Abu Ali Al Hasan ibn AL Haytham (Latin:AL Hazen) (died 1039).His theorems on quadrilaterals, including the Lambert's, were the first theorems on elliptical geometry and hyperbolic geometry.His contributions to number theory include perfect numbers.He may have been the first to state that every even perfect number is of the form 2^n-1(2ⁿ-1) where 2ⁿ − 1 is prime

44 Abu Al Saqr Al Kubaysi AL Hashimi (died 1039), wrote the book:"Types of Numbers".

45 Abu Al Rayhan Muhammad bin Ahmed AL Biruni(Latin:Alberonius) (died 1048), Ninety-five of 146 books written by Biruni, were devoted to astronomy, mathematics.These include theoretical and practical arithmetic, summation of series, combinatorial analysis,irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems.

46 Muhammad bin Surra Al Asfahani (died 1058), wrote the book:"The collective in Arithmetic".

47 Abū ʿAbd Allāh Muḥammad ibn Muadh al-Jayyani(died 1079), wrote The book of unknown arcs of a sphere, which is considered "the first treatise on spherical trigonometry" in its modern form

48 Al Muthafar ibn Ismael Al Isfazari (died 1087), wrote the book:"Intro to Areas".

1100

49 Omar Al Khayyam, (died 1121),He wrote the influential Treatise on Demonstration of Problems of Algebra (1070), which laid down the principles of algebra, part of the body of Persian Mathematics that was eventually transmitted to Europe. In particular, he derived general methods for solving cubic equations and even some higher orders.

50 Abu Baker ibn Abi Bishr Al Kharqi(died 1138),wrote the book:"The complete treatise in Arithmetic ".

51 Ahmed bin Muhammad AL Surri ibn Al Salah (died 1148), wrote the book:"The seven articles".

52 Abu Muḥammad Jabir ibn Aflaḥ (died 1150), wrote Iṣlaḥ al-Majisṭi (Correction of the Almagest)

53 AL Samaw'al ibn Yahya ibn Abbas(Samuel ben Azariah) (died 1175), AL Samaw’al has a major contribution in the development of Algebra through his book, “AL Bahir Fi AL Gabr” (The Fascinator in Algebra) which he wrote when he was only 19 years old.He presents a system of 210 equations in 10 unknowns!Introduced the method for approximating the nth root of an integer (known as Ruffini-Horner’s method).

54 Abu Bakr Muhammad ibn Abdallah al-Hassar (died 11??), developed the modern symbolic mathematical notation for fractions, where the numerator and denominator are separated by a horizontal bar.

1200

55 Abu Abdullah Muhammad ibn Umar ibn al-Husayn at-Taymi Fakhruddine AL Razi (died 1209),wrote the book:"confiscations of Euclid "

56 Sharaf Al-Din AL Tusi(died 1209).He wrote a treatise on the two lines that approach each other ,but never intersect.

57 Abu Al hasan Al Murrakishi(died 1261), wrote the book:"Principles of Calendar"

58 Njmuddine ibn Al Labboudi(died 1271), wrote the book:"Summary of Euclid's Book".

59 Nasir Al-Din AL Tusi(died 1274).In Treatise on the quadrilateral al-Tusi gave the first extant exposition of the whole system of plane and spherical trigonometry.AL Tusi deals with the solution of equations, he proceeds with a geometrical construction of the roots and the determination of the discriminant.

60 Mohyiddine AL Mughrabi(died 1280), wrote the book:"Euclidean Geometry".

61 Ibn Abi al‐Shukr (died 1283), His works deal with geometry and trigonometry. His writings on trigonometry "contain certain original elements".

62 Shamsuddine AL Samarqandi (died 1291), wrote the book:"Figures of Geometry".

1300

63 Qutb al-Din al-Shirazi (died 1311).Student of Nasir al-Din Al Tusi and teacher of AL Farisi,he wrote the book"Translation of editing Euclid" a work on geometry in Persian in fifteen chapters containing mainly the translation of the work Nasir al-Din Tusi.

64 Kamal al-Din Hasan Ibn Ali Al-Farisi(died 1319).He noted the impossibility of giving an integer solution to the equation x⁴ + y⁴ = z⁴.It has been noted that the amicable couple (17296, 18416) was known to him.

65 ibn Al Banna'a Al Murrakishi, (died 1321), wrote between 51 to 74 treatises, encompassing such varied topics as Algebra, Astronomy, Linguistics, Rhetoric, and Logic. One of his works, called Talkhīṣ ʿamal al-ḥisāb(Summary of arithmetical operations), includes topics such as fractions, sums of squares and cubes etc.

66 ibn AL Khawam Al Baghdadi (died 1324),wrote the book:"Arithmetic Rules".

67 Sharfuddine Hussain Al Taybi (died 1342), wrote the book:"Introductions to the science of Arithmetic".

68 Emaduddine Yahya bin Ahmed (died 1344), wrote the book:"The book of Arithmetic"

1400

69 Abu Al Abbas Shihabuddine ibn Al Hae'm, (died 1412), wrote the book:"Gems of Arithmetic"

70 Ghiyath al-Din Jamshid Al-Kashi(died 1424),He is the author of “Key to Arithmetic“. He tried to reach high levels of accuracy by studying quadrilaterals of 3×2²⁸ sides while Archimedes studied only those of 3×2⁵ sides.In French, the law of cosines is named Théorème d'Al-Kashi (Theorem of Al-Kashi), as al-Kashi was the first to provide an explicit statement of the law of cosines.

71 Qadi Zadeh Al Roumi (died 1432), wrote the book:"Treatise on Sines".

72 Shihab al‐Din ibn al‐Majdī (died 1447), wrote "Book of Substance", a voluminous commentary on Ibn al-Banna''s Summary of the Operations of Calculations.

73 Ulugh Beg (died 1449), wrote accurate trigonometric tables of sine and tangent values correct to at least eight decimal places.

74 Ala al-Dīn Ali ibn Muhammed (died 1474), wrote the book:"Treatise on Arithmetic".

75 Abu Al hasan Al Qulsadi Al Qurashi(died 1486), wrote the book:"Revealing the secrets of Arithmetic". He made the first attempt at creating an algebraic notation,he took the first steps toward the introduction of algebraic symbolism by using letters in place of numbers

1500

76 Sibt Al Mardini(died 1501), wrote the book:"Guiding students to the science of Arithmetic".

77 ibn Ghazi Al Muknasi (died 1513), wrote the book:"Wish of the calculator in the science of Arithmetic"

78 ibn Hamza Al Mughrabi (died 1543), wrote the book:"Arithmetic of Numbers".

79 Muhammad Baqir Yazdi (died 15??), He gave the pair of amicable numbers 9,363,584 and 9,437,056 many years before Euler's contribution to amicable numbers,

1600

80 ibn Al Qadi AL Muknasi (died 1616), wrote the book:"Intro to Goemetry".

81 Bahauddine Al Aamili (died 1622), wrote the books:"Summary of Arithmetic", "Summary of Algebra".