Trabajo realizado sobre los matemáticos y pensadores andalusíes para un proyecto eTwinning.

1. Spanish mathematicians in Al-
Andalus
Performed by students of 2nd ESO IES Odra-Pisuerga for
proyecto eTwinning "Sharing Geometry"

2. In Europe, mathematics has no origin as old as in many countries in the Far and
Middle East, reaching only notable successes in the medieval era and especially
developed in the Renaissance.
In the Middle Ages can be seen certain cultural obscurantism, no doubt because of
war and social events of the time. Only some religious monasteries some manuscripts,
evidence of a cultural awakening first were written.
Mathematics comes to Europe from contact with the
Arabs. Until that time, the geometry of the Greeks to
which he had not been added almost nothing was
known. It was the Arabs who introduced the decimal
system, and zero positional Hindus and generalized by
the Arabs, Algebra and Trigonometry in the countries
they conquered numbering. The numbers were
natural, rational, irrational, all positive. The negatives
were false solutions.
After reading the book "The Lord Zero" have made this
little research on the role of the Arabs in Spain in the
development of mathematics during the Middle Ages.

3. - Expansion in the time of Muhammad years 622 – 632
- Expansion during the Orthodox Caliphate years 632-661
- Expansion during the Umayyad Caliphate years 661-750
Fuente: Wikipedia
Map of the Arab expansion from Muhammad to reach the Al-Andalus

4. The birth of Arab figures
In the ninth century to the unity of the Arab-Muslim empire have disintegrated and
North Africa and Muslim Spain no longer belonged to the Caliphate of Baghdad, but
due to pilgrimages to Mecca, were frequent commercial exchanges.
When East Arab met Hindu arithmetic, quickly spread throughout the Maghreb and
Spain. Until then, Western calculators used archaic methods, but from the mid-ninth
century Hindu figures also used as their eastern brethren, and, like them, the writing
in the sand.
At first, the script was very similar, but has evolved over time, and it is these Western
Arabic numerals, also called "ghobar figures" which, from Spain, becoming the
Christian peoples of medieval Europe.

5. Around the year 967, a French monk named
Gerbert d'Aurillac, traveled to the court of the
Count of Barcelona, ​​Borrell II, where he remained
three years in the monastery of Santa Maria de
Ripoll, Gerona, where possibly traveled to
Cordoba and Sevilla, which allowed him to make
contact with Arabic numerals and started the
study of mathematics and astronomy.
Then he taught at Reims where he taught and
spread the Arabic numerals. He later became
Pope with the name of Sylvester II.
By Celia Ruiz García
In addition to spreading the Arabic numerals, popularized the use of the astrolabe is an
astronomical unit. He also produced a new version of the monochord, a consistent
musical instrument in a soundboard on which a variable-length string with which the
sound vibrations were measured and tense musical intervals
Gerberto d’Aurillac, the mathematician Pope

6. The Toledo School of Translators
In the cultural environment of the mid-twelfth century born a phenomenon known as the
School of Translators of Toledo, which was not a school but a group of Christian, Jewish
and Arab scholars who worked together in research and translation of all Arab culture
works of antiquity. It was a way to make them known to the rest of Europe.
By Diego Merino Martínez
This was during the first period with Archbishop
Raimundo.
During a second period with Alfonso X the Wise,
specially treated for Astronomy, Physics and
Mathematics translated.
Thanks to this great boost Monarch Azarquiel
treaties, Ptolemy and Abu Ali al-Haitam, but also
works as recreational chess books, craps tables
and collections of short stories as fruitful for
Western literatures as Kalila and Dimna resulted
and Sendebar. In this second phase translations
are no longer done in Latin but in Castilian.
Original works as the astronomical tables of
Alfonso was also composed.

7. Abu-l-Qasim Maslama called al Mayrity
Abu Al-Qasim Maslama born in Madrid in the mid-
tenth century and died in Córdoba in 1007. Was very
young I traveled to Córdoba where he was a pupil of
important mathematicians as' Muhammad ibn Abd al
Gafir and astronomer Abu Bakr ibn Abi Isa.
He was an important scientific school in Cordoba
where they studied and important mathematical
astronomers as Ibn al Samh, Ibn al-Jayyât, Ibn al-
Saffar, al-Zahrawi , Ibn-Khaldun and Kirmani.
He wrote several works of commercial arithmetic, but
more important is a Commentary on Ptolemy's
Planisphere.
He also wrote a short treatise on the astrolabe where
its technical construction and instructions on their use
is described.
Both his works as his disciples enjoyed great fame and popularity throughout the Arab
world and Latin of his day, and also had a decisive importance as a basis for the
construction of the spherical astrolabe conducted later astronomers court of King Alfonso
X the Wise.
By J. Manuel Martín García

8. Summary table of the main disciples of Abu al-Qasim Maslama
Abulhasar Ali Abensuleiman
al-Zaharwi
Born in Medina al-Zahra, near Cordoba city. He was wise
in arithmetic and geometry. He practiced medicine with
a big fame. He wrote about commercial contracts. He
lived in Seville where he prospered as a wise illustrious.
Abulcasim Asbag
Abenmohámed el Garnati ibn
al-Samh
Born in Granada about 980 and died in the same city in
1035. Mathematical genius, knew of Arithmetic,
Geometry and Astronomy. He also delved into grammar
and Medicine. Alfonso X studied astronomy books and is
believed to have written the manuscript could
Arithmetic deposited in El Escorial, short treatise on
arithmetic and computer to teach the simplest figures
and calculations.
Abuabdallah Muhammed Ibn
Saffar al Cortobi
Born in Córdoba of a noble family with scientific
tradition. He became a scholar in Literature and
Calculus. Became blind and paralyzed but this did not
prevent him from devoting himself to teaching. He made
a brief treatise on the astrolabe. After traveling in
Morocco, Fez, Tunis and Baghdad, he returned to Spain
where he died

9. Abubequer Ibn al Jayyat.
Born in 980 got great command of mathematics and
astronomy, especially in Geometry and Arithmetic. He
was court astrologer of Cordoba, Toledo and Zaragoza.
Abumoslem Omar Banahmed
Ibn Jaldun al Jadram
Born into a distinguished family in Seville, was educated
in Córdoba. He died in Seville in 1057 after having
achieved fame as a philosopher, mathematician,
astronomer and physician.
The remarkable influence of Maslama also evident through the huge number of his works
which were translated into other languages ​​such as that performed in the twelfth
century Johannes Hispalensis of the work to that entitled al-Muamalat o “Liber
Mahameleth”.
This book has a theoretical part where is the theory of proportions and arithmetic
operations and procedures which give good approximations for square roots inaccurate.
References on solving equations of first and second degree are also given.
They end up leaving Córdoba and leave to other cities where each was creating school so
that several generations of mathematicians succeeded fairly competent around Al-
Andalus.

10. Abu l-Hakam Amr ibn Abd al-Rahman ibn Ahmad ibn Ali
al-Kirmani
Born in Córdoba, where he was a pupil of
Maslama, and died in Zaragoza in 1066.
He was a mathematician, philosopher and physician
who transmitted important knowledge of Eastern
culture in Al-Andalus after traveling to major cities
in the Arab East to study mathematics, medicine
and astronomy.
Throughout these trips not only acquired these
traditional scientific knowledge, but also
philosophical and literary, being the introducer of
The Encyclopedia of the Brothers of
Purity, Neoplatonic movement.
A little later he moved to Zaragoza serving three
kings of Taifa of Zaragoza in the second half of the
eleventh century, Al-Muqtadir, Al-Mutaman and Al-
Musta'in II, which was the grand vizier. Thus arose
several scientific foci, in which mathematics was
just a science practiced by scholars versed in
multiple disciplines.
By Jorge Pérez Nogales

11. Ibn Mu'adh al-Jayyani
By Andrea Ortega
We know he was born in Jaén, although the exact date
is unknown. Member of a prominent family jienense
Muslim jurists . Some of his ancestors were Kadis of
Jaén, Córdoba and Seville . He himself was qadi of Jaén
and Sevilla vizier . He traveled to Egypt during his trip
to Mecca , where he came into contact with
mathematicians of the time in the East.
His fundamental contributions to mathematical knowledge were making mathematics
understandable ratio of incommensurable magnitudes contained in the fifth book of
Euclid's Elements as a rational reason ; make the first work or treatise known spherical
trigonometry, largely thanks to the contributions of Egyptian mathematicians , which
resolved several theorems and all problems arising in the spherical triangles when four of
its elements are known and also , collected in a systematic way the mathematical
knowledge of the time .
Abd'Allah Muhammad Ibrahim al-Yayyani was a
mathematician Al-Andalus, which particularly noted
for his research and contributions in trigonometry,
which was first dissociated studies astronomyi.

12. Al-Mutamán, the geometer King
Yusuf Al- Mutamán was king of the Taifa of Zaragoza between 1081
and 1085 . He was a scholar king, protector of science and
mathematics scholar
The masterpiece in the intellectual field of Al- Mu'tamán was his
Book of perfection and optical appearances Kitab al- Istikmal
besides being a compendium of Greek mathematics of Euclid and
Archimedes among others, and transmit Thabit ibn Qurraa
teachings, the Banu Musa and Ibn al- Haytha enter original
theorems. His work was transmitted through Maimonides to
Egypt, and from there spread throughout central
Asia, documenting even in Baghdad in the fourteenth century, but
its influence did not reach the West.
It studies the irrational numbers , conic sections , squaring the parabolic segment , areas
and volumes of various geometric shapes or drawing of the tangent of a circle , among
other mathematical problems.
A Al-Mutamán se debe la primera formulación conocida del Teorema de Giovanni
Ceva, que no sería conocido en Europa hasta 1678
By Óscar Porro
Teorema de Ceva

13. Aben Essamej
Mathematical hispano-arabic, S. XI, also a disciple of Abu
Al-Qasim Maslama. Among his works are the 'Comments
treaties Euclidean Geometry', as an introduction to
mathematics. 'From the nature of numbers', 'From the
calculations used in commerce' as well as a Master of
Mathematics treaty, very remarkable work in those days.
'Treaty on the construction and use of the astrolabe', in
collaboration with his disciple Aben Essofar.
Astrolabe
Essamej also wrote astronomical Tables and a Treaty of
Mathematics.
The astrolabe is possibly the oldest computer pocket
officially known. This mechanism was used to determine
the position of the heavenly bodies, or had a way to
capture in his wit, all sky map of the time were, with only
placed by a technique of angular position astrolabe itself.
By Luis Miguel González

14. Abu Muhammad Jabir ibn Aflah
Arab mathematician and astronomer whose Islah al-majisti
(Correction of the Almagest) proved to be a strong
influence on scholars throughout the Mediterranean and
Europe. As native of Seville, Aflah knew Moses ben
Maimon (Maimonides, 1135-1204). He developed a
theorem in spherical trigonometry that bears his
name, and created an instrument called the Torquentum
for making transformations between spherical coordinates.
His critique of Ptolemy's (c. 100-170) Almagest exerted an
impact on a number of thinkers, among them Ibn Rushd
(Averroës, 1126-1198).
Born in Seville in 1100 and died in 1150.
Gerolamo Cardano noticed that much material on
Regiomontanus spherical trigonometry was plagiarized the
work of the twelfth century Jabir ibn Aflah
By Antonio González
The Torquetum

15. Abraham Bar Hiyya
He was a mathematician, astronomer and philosopher
Hebrew . Born in Egypt in 1065, he lived in Barcelona and
scientifically trained in the Courts of Zaragoza where he held
various positions including Chief of the guard earning him the
nickname Savasorda .
Developed several scientific abstracts in Hebrew, from
Arabic sources, and translated numerous Arabic and Hebrew
into Latin works. Among his major works include
Foundations of intelligence and belief tower. The shape of
the earth, which is the first treatise in Hebrew on
astronomical geography, as well as Book of computing the
calendar.
It is one of those who were responsible for transmitting to
Europe 's great Jewish Andalusian Arabic science and , in
particular , of the Upper and Zaragoza . For example , the
quadratic equation and its solution have a very ancient
origin and were known as algorithms to solve it in Babylon
and Egypt. In Greece was developed by mathematician
Diafonto Alexandria. So their solution was introduced to
Europe by the mathematician Abraham bar Hiyya .
By Ricardo Manrique Esteban

16. Abraham Ben Ezra
By Julia García
He was born in Tudela (Taifa of Zaragoza) in 1092
and died in Calahorra (Kingdom of Castile) in 1167.
He was one of the most distinguished Jewish men of
letters and writers of the Middle Ages. Ibn Ezra
excelled in
philosophy, astronomy/astrology, mathematics, poet
ry, linguistics, and exegesis; he was called The
Wise, The Great and The Admirable Doctor.
Its importance is due to the Arab mathematical
spread across Europe. One of his most important
works dealing with the description of the decimal
place for values ​​of the numbers vary depending on
their position from left to right. Also dealt with the
zero and also translated the commentary of Al-
Biruni on the boards of Al-Khwarizmi on the
introduction of the current Indian figures in Arab
mathematics.
Ezra Calendar

17. Azarquiel, the Andalusian astronomer
Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī
was born in Toledo in 1029 and died in Seville in
1087. From humble beginnings, he worked as a
blacksmith, which led to the construction of
scientific precision instruments, as astrolabes, at the
request of Arab and Jewish astronomers.
Communication with these scholars and intelligence
of Al-Zarqali could lead to a remarkable
understanding of astronomical science self-
taught, which led him to create innovations from
astrolabe, as azafea.
His work mainly known through the translations made ​​in
astronomy specialists responsible for the actual scientific
work scriptorium of Alfonso X the Wise. Thus, between
1225 and 1231 also Toledo Jewish Yehuda ben Moshe
and Guillelmus Anglicus translated his Treatise on azafea
into Latin, which was poured in the years 1260 to
Castilian by the Toledo same Jew named in the prologues
of alfonsíes works Yehuda Fly Fly or the Coheneso.
By Alejandro Merino

18. Al-Qalasadi
Abu al-Hasan Ali bin Mohammed bin Ali al-Qurashi al-Basti
(Baza, Granada, 1412 - Beja, Tunisia Current, 1486), was one
of the most important mathematical granadís.
He studied philosophy, mathematics and science partition
inheritance, very important in the Arab tradition. Pilgrimage
to Mecca and he could always housed in a cultural
environment madrasas where they lived. He had many
disciples and wrote several works among which 12
Algebra, including:
-Treatise on Arithmetic and Algebra, translated into several European languages ​​and was a
major advance in the mathematics of his time. With it contributed to algebraic symbolism
using the Arabic alphabet characters as mathematical symbols, expressing the equations
with letters and short words that have symbolic value.
- Classification of Arithmetic Science, which was very popular in North Africa .
Finally al- Qalasadi used in both the arithmetic treated as in his writings on succession
partitions identical to modern symbolism to represent the fraction , the numerator over
the denominator meeting both separated by a horizontal line.
By Roberto de la Orden

19. This is our small contribution to the knowledge of the great mathematicians and
thinkers that existed in Al-Andalus, in an age when the study and development of
science in Europe was stagnant
On the other hand, keep in mind that in Arab schools or madrasas, not only studied
math. Teachers and students were true humanists, knowing all sciences, so we speak
of mathematicians who were doctors, philosophers and especially astronomers.
Keep in mind that for the Arab knowledge of the daylight hours were very important to
their prayers.
Other great humanist thinkers not as dedicated to mathematics were
Averroes, Maimónides and Said Al-andalusi.

20. Averroes
Abū l-Walīd Muhammad ibn Ahmad ibn Muhammad ibn
Rushd born in Cordoba on April 14, 1126 and died in
Marrakech on December 10, 1198.
It was an Andalusian philosopher and physician, a master of
philosophy and Islamic law, mathematics, astronomy and
medicine.
The Cordovan philosopher thinks differently Aristotle to
emphasize the role of sensory nerves in the brain and
recognize the location of some intellectual faculties as
imagination or memory.
Averroes places the origin of the human intellect in sensory
perception of individual objects and concrete end in
globalization. He tried to clarify how human beings think
and how the formulation of universal and eternal truths
from perishable beings is possible.
It was an important philosopher of thought
By Arturo Padilla

21. Maimónides
By Martín Angulo
Moshé ben Maimón o Musa ibn Maymun also called from the
Renaissance Maimonides was a physician, rabbi and Jewish
theologian of Al-Andalus in the Middle Ages. Was important
philosopher in medieval thought. Born in Córdoba (Spain), on
March 30, 1138, in the midst of a distinguished
family, paternally, of rabbinical judges, scholars and community
leaders, documented from the tenth century.
It started small and their biblical and Talmudic studies in the city
of Córdoba , but in 1148 a wave of Almohad fanaticism caused
his family had to pretend his conversion to Islam and change of
residence often Al- Andalus.
He lived in the city of Almeria , where he gave shelter in his house to his master Averroes
, until moving in 1160 with her children to Fez. There he lived for only five years, because of
the Almohad intolerance that forced them into exile , first for a few months in Palestine and
finally Egypt. Maimonides lived there the rest of his life with his family in the city of
Alexandria and later in Fustat (now Cairo , Egypt ), where he earned a living to practice
medicine in the court of the Vizier Saladin, and then in the vizier al- Fadl , eldest son of
Saladin.
The Guide for the Perplexed ( 1190 ) , poorly dubbed Guide the wayward , is the key to his
philosophical thought and exerted a strong influence on both Jewish and Christian circles
especially scholastics.

22. Said al-Andalusi
Abu- l -Qa'im ibn Said, called Said al- Andalusi
(Almería, 1029 - Toledo, July 6, 1070 ) was a
scientist, historian of philosophy and science and
Hispano- Muslim jurist .
The diagnosis was scientist in mathematics and astronomy. contributed in Toledanas Tables
and, with Azarquiel he perfected with more accurate estimates of access and movement
recess of the fixed stars , contrary to the Ptolemaic theory.
The only work of Said al- Andalusi that remains is Kitab al- Tabaqat uman (Book of the
categories of nations ), where he studied the universal development of philosophy and
science. He wrote in Toledo in 1068 , when the author was 39 years old . It demonstrates
objectivity, impartiality and critical approach to the subject . According to him there are
only eight "nations" with scientific contributions : Indians , Persians, Babylonians , Greeks
, Byzantines, Egyptians, Israelis and Arabs. Among these stands the Andalusian . It focuses
on mathematics , astronomy , medicine and human geography , and other fields of study. It
was used as a source for many other stories of science in medieval and modern times.
By Martin Escalona
As historian of science is an essential tool for the
study of ancient and medieval science source and
science in Al- Andalus.