European International Journal of Multidisciplinary Research
and Management Studies
12
https://eipublication.com/index.php/eijmrms
TYPE
Original Research
PAGE NO.
17-20
DOI
OPEN ACCESS
SUBMITED
08 January 2025
ACCEPTED
20 February 2025
PUBLISHED
11 March 2025
VOLUME
Vol.05 Issue03 2025
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
Uzbekistan
mathematicians and their
discoveries
Jorayeva Mohinur Yunus kizi
1st year student of Mathematics Education, Termez State Pedagogical,
Institute, Termez, Uzbekistan
Turayev Ruziboy Norovich
PhD, Senior Lecturer, Department of Mathematics and Informatics,
Termez State Pedagogical Institute, Uzbekistan
Abstract:
Mathematics is one of the most important
foundations of human development and one of the
sciences that has played an important role in the
development of civilization. The importance of
mathematics in the development of all sciences and
technologies is incomparable. Initially, this science
began with simple calculations, and later branched out
into such branches as complex algebra, geometry,
analysis, and number theory. Uzbekistan is one of the
countries that has produced great mathematicians in
the history of science. Scientists such as Muhammad ibn
Musa al-Khwarizmi, Abu Rayhan Beruni, Mirza Ulugbek,
Qazizoda Rumi, and Jamshid al-Koshi made a great
contribution to science not only in the East, but also in
the whole world with their discoveries. In this article, we
will talk about the lives, scientific works, scientific
achievements of great mathematicians, how their
discoveries are used today, and their significance today.
The purpose of this article is to highlight the
contribution of Uzbek mathematicians to science,
analyze their important discoveries and developments,
and show their place in the development of
mathematics. Through the article, readers will gain
information about the scientific heritage of Uzbek
mathematicians and their significance today.
Keywords:
Uzbek mathematicians, Muhammad al-
Khwarizmi, Ulugbek, Qazizoda Rumi, algebra, algorithm,
trigonometry, scientific heritage, mathematical analysis,
number theory, Central Asian scientists, modern
mathematics.
Introduction:
Qazizoda Rumi (1364
–
1436) was a famous
Uzbek mathematician and astronomer who made a
European International Journal of Multidisciplinary Research
and Management Studies
18
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
significant contribution to the scientific and cultural
development of Transoxiana. His scientific activities
were mainly associated with Samarkand, and he was
one of the main scientific collaborators of Mirzo
Ulugbek.
Life: Qazizada Rumi, whose full name was Sadriddin
Musa ibn Mahmud Rumi, was born in 1364 in what is
now Turkey. The nickname "Rumi" refers to his origin
from the Anatolian (Rumiya) region. He later moved to
Transoxiana and pursued his scholarly activities in that
region.
Scientific activity: He had a deep knowledge in the
fields of mathematics, astronomy and philosophy, and
made important discoveries in trigonometry and
astronomy in particular. Qazizoda Rumi Mirzo was one
of the main scientific leaders at the Ulugbek
Observatory. Among his students was the famous
mathematician and astronomer Ali Kushchi
Works: Sharh al-Mulakhas: "Sharh al-Mulakhas" is an
important scientific work on astronomy and
mathematics written by Qazizada Rumi, as a
commentary on the book "Al-Mulakhas fi al-Hay'a"
(Summary of Astronomy) written by Nasir al-Din Tusi
(13th century). This work is of great importance in the
scientific heritage of the Middle East and served as one
of the main guides for later astronomers and
mathematicians.
Content and significance of the work:
1. AstronomyThe work
"Sharh al-Mulakhas" includes astronomical knowledge
of that time, and it covers the following topics in detail:
- The movement of celestial bodies - A detailed
explanation of the stars, planets and the laws of their
movement is given.
- The shape and movement of the Earth - Based on the
geocentric model adopted at that time, there are
scientific analyses of the position of the Earth and the
structure of the universe.
- Solar and lunar eclipses - The mechanism of
occurrence of these phenomena and methods for
calculating them are described.
2. Trigonometry and mathematical aspects
The work also provides insights into trigonometric
methods necessary for accurate astronomical
calculations. In particular, the astronomical application
of the sine, cosine and tangent functions, calculation
methods used in Eastern mathematics, Geometric
models and their role in explaining the motion of
celestial bodies
Scientific significance of the work:
1. Influence on Eastern and European astronomy -
Through this work, Qazizoda Rumi further improved the
work of Nasir al-Din Tusi and later had a great influence
on the activities of the Mirzo Ulugbek Observatory.
2. Accurate development of astronomical tables - This
commentary was an important source in the
composition of "Zizhi Kuragoniy" by Ulugbek and his
team.
3. Being a source for the next generation of scientists -
Ali Kushchi and other famous astronomers used this
work of Qazizoda Rumi.
Sharh Ashkal at-
Ta’sis: "S
harh Ashkal at-
Ta’sis" is an
important mathematical work written by Qazizada
Rumi, which is a commentary on the book "Ashkal at-
Ta’sis" written by the famous scholar Mahmud
Zamakhshari (1075
–
1144). This work, by explaining
concepts in the fields of algebra, geometry, and
mathematical logic, had a great influence on the
development of medieval Islamic mathematics.
Content and significance of the work:
1. Origin of the workIn his work "Ashkal at-
Ta’sis",
Mahmud Zamakhshari outlined the basic principles of
algebra and geometry. This work is one of the important
parts of Islamic mathematics of the 9th
–
12th centuries,
in which: mathematical formulas, algebraic and
geometric problems, and solutions based on logical
arguments are presented.
However, since this work is short and concise in some
places, Qazizadeh Rumi wrote a commentary on it to
make it more understandable and comprehensive.
2. Content of the work
Qazizoda Rumi's "Sharh Ashkal at-Ta'sis" is based on
mathematical thought and theoretical principles, and
pays close attention to the issues of algebra, geometry,
and mathematical logic. This work made a great
contribution to the development of the Eastern school
of mathematics and served as a theoretical basis for the
scientific works of scientists such as Ali Qushchi and
Mirzo Ulugbek in later periods. The main content of the
work is discussed in more detail below.
1) Algebra and equations
Algebra is one of the main branches of mathematics,
and Qazizoda Rumi considered various algebraic
problems in this field and provided a theoretical basis
for their solutions.
a) Algebraic equations and their solution methods
Equations with one and two unknowns
–
Determining
the unknowns was important in medieval mathematics.
Qazizoda Rumi described methods for solving these
equations using various algebraic and geometric
methods.
Quadratic and higher-order equations
–
He revised Al-
European International Journal of Multidisciplinary Research
and Management Studies
19
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
Khwarizmi’s method
for quadratic equations and
presented new proofs based on it.
b) Properties of numbers and mathematical proofs
Prime numbers and their properties
–
Eastern
mathematicians paid special attention to the study of
prime numbers, as they play an important role in
algebraic structures.
Number theory
–
Qazizoda Rumi studied issues such as
the division of numbers, their even and odd types, and
the properties of complex numbers.
c) Mathematical ratios and proportions
Proportions
–
Qazizoda Rumi explained mathematical
ratios and their importance in physical and
astronomical calculations.
Useful Relative Relationships
–
For example, the
golden ratio and other special proportions have been
used in art and architecture since ancient times.
2) Geometry and Shapes
Geometry is one of the most developed areas of
Eastern mathematics, and Qazizoda Rumi presented
his deep knowledge in this field as a commentary.
a) In-depth analysis of triangles, rectangles, and circles
Euclidean Geometry
–
The principles of Euclidean
geometry are widely used to explain the basic
properties of triangles and other shapes.
Parallelograms and their properties
–
Qazizoda Rumi
compared and analyzed the properties of shapes such
as squares, rhombuses, and rectangles.
Circles and their lengths
–
Determination of the
number Pi (π) and calculations on the length of a circle.
b) Pythagorean Theorem and its Proofs
Proof of the Pythagorean Theorem by Islamic
Mathematicians
–
Qazizoda Rumi gave several proofs
of this theorem and explained how it is used in various
mathematical contexts.
Pythagorean Triples
–
with sets of numbers such as
(3,4,5), (5,12,13)operation and their properties.
c)
Trigonometric
calculations
of
Eastern
mathematicians
Sine, cosine and tangent - Qazizoda Rumi gave
explanations about these trigonometric functions and
expressed his opinion on their application in
astronomy and geography.
Spherical geometry - Special geometric rules used in
the study of the motion of terrestrial and celestial
bodies.
3) Mathematical logic and proofs
The concept of mathematical logic was of great
importance in Qazizoda Rumi's work. He tried to
improve the methods of proving mathematical theories.
a) Mathematical axioms and postulates
Euclidean axioms - Qazizoda Rumi revised the five basic
postulates of Euclid and analyzed their reliability.
Alternative axioms - He expressed his opinion on
alternative geometric axioms put forward by some
schools of mathematics.
b) Logical proofs and their structure
Various methods of proofs
–
Ways to prove
mathematical theorems using induction, deduction and
contrapositive hypothesis methods.
The rigor of mathematical proofs
–
Necessary conditions
for proofs to be correct and clear.
c) Methodological approaches to solving mathematical
problems
Geometric constructions
–
Problems solved using a
circle and a ruler.
Solving geometry problems with algebraic methods
–
Methods for solving problems based on the relationship
between algebra and geometry.
3. Scientific significance of the work:
1. Impact on the development of mathematics
–
"Sharh
Ashkal at-Ta'sis" contributed to the in-depth study of
algebra and geometry in the Middle Ages.
2. Impact on subsequent mathematicians
–
This work
was later studied by scientists from the Mirzo Ulugbek
Observatory, including Ali Kushchi, and served as the
basis for his work.
3. The connection between mathematics and
astronomy
–
Geometry and algebra were widely used in
astronomical calculations, so this work was also
important in the field of astronomy.
Collaboration with Ulugbek: Qazizoda Rumi Mirzo was
one of Ulugbek's scientific advisors and actively
participated in compiling the astronomical tables "Ziji
Kuragoniy". This table was one of the most accurate
astronomical calculations of that time, and was later
used by many European scientists.
Scientific legacy:
Qazizoda Rumi's work had a great influence on scientific
development in the Middle East and Central Asia. His
astronomical tables and trigonometric calculations later
played an important role in the development of science.
Conclusion:
Qazizoda Rumi did important work on
mathematical theories.
These great scientists left us an invaluable scientific
heritage. Their scientific works also serve as the basis for
today's technologies and modern mathematical models.
"Sharh al-Mulaxhas" is one of the important scientific
European International Journal of Multidisciplinary Research
and Management Studies
20
https://eipublication.com/index.php/eijmrms
European International Journal of Multidisciplinary Research and Management Studies
works that shows the rise of medieval Eastern science
to a high level. It made a great contribution to the
development of astronomy and mathematics at that
time, and was later studied in Europe.
The work "Sharh Ashkal at-Ta'sis" written by Qazizoda
Rumi was created to make the basic concepts of
mathematics easier to understand and develop. It
clearly expressed the theoretical aspects of algebra
and geometry, serving as an important guide for the
next generation of scientists.
Mathematics is an eternal science, and Uzbek
scientists left an indelible mark on its development.
REFERENCES
Berdikulov O. Great scholars in the history of science of
Uzbekistan - Tashkent: Science, 2000.
Karimov R. Eastern scholars and their scientific
heritage - Samarkand: Ma'naviyat, 2012.
Nasr S.H. Science and Civilization in Islam
–
Harvard
University Press, 1968.
Al-Khwarizmiy M. Algebra and its methods
–
Tashkent:
Fan, 1985.
Qori-Niyoziy
M. Mirzo Ulug‘bek and his scientific
school
–
Tashkent: Uzbekistan, 1963.
Scientific heritage in Uzbekistan: Qazizoda Rumi and
his works // Uzbekistan National Encyclopedia, 2005.
Rosen, E. Three Scientific Treatises by Qāḍīzāda al
-
Rūmī // Journal of
Near Eastern Studies, 1956.
Sayili, A. The Observatory in Islam and Its Place in the
General History of the Observatory
–
Ankara: Turk
Tarih Kurumu Basimevi, 1960.
Samkharov A. History and development of
mathematics
–
Tashkent: University Press, 1998.
Sarton G. Introduction to the History of Science
–
Baltimore: Williams & Wilkins, 1927.
