The history of mathematics began in prehistoric times with simple calculation techniques, then evolved significantly through the civilizations of Ancient Egypt, Babylonia, Greece, India, and the Islamic world, eventually giving rise to calculus and the abstract modern mathematics of the present day.
Prehistoric Era and Ancient Civilizations :
A.) Prehistory:
Early humans used simple counting tools, such as the Ishango bone and the Lebombo bone, approximately 20,000 to 35,000 years BCE.
B.) Ancient Egypt:
Utilized a numeral system for land measurement and the construction of pyramids, with well-known artifacts such as the Rhind Mathematical Papyrus (~1650 BCE).
C.) Babylon:
Utilized a base-60 numeral system which gave rise to the division of time (60 minutes) and the circle (360 degrees) and produced the Plimpton 322 tablet (c. 1900 BCE).
The Classical Era and Eastern Contributions :
A.) Ancient Greece:
Transformed mathematics into a science of logic and deductive reasoning through figures such as Pythagoras (triangle theorem), Thales, and Euclid (the Father of Geometry).
B.) India:
The introduction of the number zero and the decimal place-value system by scholars such as Aryabhata (476–550 CE) and Brahmagupta (598–668 CE).
C.) Islamic Golden Age:
Al-Khwarizmi (780–850 CE) pioneered the foundations of algebra and spread the Hindu-Arabic numeral system.
From the Modern Revolution to the Present Day :
A.) The Renaissance & the Scientific Revolution:
Fibonacci introduced a numerical sequence, while Isaac Newton and Gottfried Wilhelm Leibniz developed calculus in the 17th century.
B.) The 19th & 20th Centuries:
The emergence of non-Euclidean geometry, set theory, and the concept of a computing machine by Alan Turing.
The history of the origins of mathematics is also documented in several books at Harvard University, which include the following:
A.) A History in Sum (Author : Steve Nadis and Shin-Tung Yau).
B.) Dual at Dawn (Author : Amir Alexander).
C.) Greek Mathematical Works, Volume 1 and Volume 2
(Author : Ivor Thomas).
According to an article from BPIKA (Bureau for Innovation and Career Development) regarding the field of mathematics:
Long before the modern era an age characterized by the seamless global dissemination of knowledge mathematical developments were already flourishing in various regions. Among the oldest surviving mathematical texts are the Plimpton 322 tablet (Babylonian mathematics, c. 1900 BCE), the Rhind Mathematical Papyrus (Egyptian mathematics, 2000–1800 BCE), and the Moscow Mathematical Papyrus (Egyptian mathematics, c. 1890 BCE). Notably, all three address the Pythagorean theorem, which stands as one of the earliest and most widespread mathematical advancements, following basic arithmetic and geometry. The history of Babylonian mathematics encompasses the body of mathematical knowledge developed by the peoples of Mesopotamia a region known today as Iraq. It is termed "Babylonian mathematics" due to the pivotal role of the Babylonian region as a center for learning. A hallmark of this era is the sexagesimal (base-60) numeral system, which serves as the foundation for our modern division of time and space: 60 seconds in a minute, 60 minutes in an hour, and 360 (60 × 6) degrees in a full circle. Every historical period has consistently contributed to the evolution of new and useful mathematical concepts.
If you are familiar with Muhammad ibn Musa al-Khwarizmi, you likely know that he was one of the architects of mathematics truly the "Father of Mathematics." His extraordinary discoveries most notably algebra and the concept of zero served as a cornerstone for the advancement of mathematics at the time. Throughout history, from antiquity through the Middle Ages, there have been frequent bursts of creativity in the field of mathematics. Beginning with the Italian Renaissance in the 16th century, the evolution of mathematics became intertwined with new scientific discoveries, leading to an exponential growth that continues to this day. Knowledge constantly evolves alongside the times, giving rise to new concepts designed to explain the phenomena of each era and mathematics is no exception!
Education generally varied from one country to another. The Spartans emphasized moral education, while the Athenians focused on the refinement of both the physical and mental self. Mathematics was taught differently than it is today; specifically, geometry and arithmetic were treated as distinct subjects. The concept of arithmetic was further subdivided into calculation a skill taught to artisans and the middle class. Those with the time, means, and inclination could pursue further studies in the science of numbers. Boys began their education at home, under the guidance of their parents or a mathematics tutor. Their foundational education encompassed literature, music, and gymnastics, but included very little instruction in arithmetic or geometry.
Around the age of twelve, students would enroll in mathematics classes, where they delved further into grammar, logic, and rhetoric. While those from the working class generally concluded their formal education at this stage, students from the upper classes would go on to enroll as scholars at universities or academies established by figures such as Plato, Pythagoras, or Aristotle. Pythagoras founded a school in 514 BC; we owe a great deal to this institution, which advanced the study of geometry and various other academic disciplines. As a result of these pursuits, music came to be regarded as a mathematical science. Plato's Academy remained in existence for over 900 years. Because its primary objective was the development of future statesmen, Plato's perspective on mathematics was more circumscribed than that of Pythagoras. He maintained that the study of mathematics would foster clear and logical thinking qualities deemed essential for the politicians of that era.
He proposed that a student should study mathematics for their first ten years to facilitate a transition toward the rational and philosophical thinking necessary for success in politics. His academy was viewed as a bastion of 'pagan' thought and was ultimately closed by Emperor Justinian in 529 AD. Further evidence of the Roman authorities' control over Plato's pedagogical methods can be found in The Republic, in which he rejects the notion that only a basic study of mathematics is sufficient.
Much like the Greeks, the history of mathematics among the Romans began with basic education provided at home exclusively for boys. At the age of 12, these students would go on to receive formal instruction, which included literature, music, and basic arithmetic the latter taught using fingers and an abacus. Unless their social status or profession demanded it, Roman students generally did not pursue mathematical studies beyond what they had learned at home. Those who sought to apply mathematics further could attend classes led by a "Master of Mathematics." Such instances were rare, however, and represented an exception to the typical educational norms in Rome. Surviving documents from this period suggest that the teaching of mathematics was not universally welcomed or embraced, though it was considered necessary in certain specific cases.
Vitruvius advised architecture students to study optics, astronomy, law, geometry, and arithmetic. Galen recommended that aspiring physicians study medicine, rhetoric, music, dialectics, geometry, and arithmetic. Varro and Seneca also advocated for the study of geometry and arithmetic, though solely as a means to strengthen or deepen one's capacity for logical reasoning. In ancient Rome, professions involving logic, rhetoric, or oratory were considered far more noble than those concerned with numbers or the natural sciences. In fact, the upper classes looked down upon those with a "narrow perspective" individuals whose careers were tied to extensive mathematical or scientific knowledge.
Cassiodorus, a 6th-century Roman statesman, was deeply committed to education and championed the need for instruction within the Roman Catholic Church. He categorized learning into two broad domains: The Trivium, which concerns language and speech, and the Quadrivium the study of arithmetic, geometry, music, and astronomy. These divisions persist within the framework of modern education, though they have been renamed the humanities and the natural sciences; notably, contemporary philosophical education treats music as a facet of human culture rather than merely as a formal science. By the 9th century, many monasteries functioned as schools, providing education to new members of the clergy. While the Trivium remained a core component of the curriculum, the study and teaching of mathematics and the sciences were reserved for the highest centers of learning. The school associated with York Minster was one of the institutions in England where mathematics was taught. The Church served as the primary driver of education in Europe, though mathematical instruction remained quite limited. Furthermore, the onset of war caused the focus to shift away from academic pursuits until Gerbert of Aurillac rediscovered mathematical texts authored by Boethius. Upon becoming Pope in 999 AD, Gerbert produced his own copies of these documents and established them as essential components of ecclesiastical education. The study of mathematics subsequently gained prominence and remained a fundamental requirement in schools for the next five centuries.
During this period, significant advancements were being made worldwide in the study of numbers and their relationships including interest calculations, algebra, differential calculus, and factorization. New developments were incorporated into mathematics curricula as soon as they could be proven. In England, a religious movement that had broken away from Roman Catholicism was gaining momentum. This group sought to distance itself from associations with "pagan" influences and other such ideas, which led to a general disfavor toward the study of mathematics in the country.
The Renaissance era gave rise to new ideas about education. Beyond merely learning what one should do for a profession, the emphasis shifted toward students acquiring life skills. During this period, Euclid's Elements was translated into many languages and disseminated widely, thanks to the advent of the printing press. This meant that mathematics scholars in Germany, France, and Italy could use the same instructional material for their studies regardless of whether a teacher was present.
Despite the significant advancements made in the field of mathematics, the art of teaching mathematics in primary schools as well as the nature of national mathematics examinations has remained fundamentally unchanged since the time of De Morgan. Even private mathematics tutoring has largely reverted to methods reminiscent of ancient times, unless, of course, one chooses to teach mathematics online. Governments and relevant organizations have invested substantial resources into the professional development of teachers and the refinement of pedagogical methods. The core mathematics curriculum has also expanded to encompass the study of Mathematical concepts Algebra Geometry Calculus Trigonometry Various types of equations quadratic, linear, differential, parametric, and more.
From the academic perspective of scholars at University Muhammadiyah Yogyakarta (UMY), the history of the birth and development of mathematics is rooted in a paradigm of integrating knowledge within Islamic civilization a framework in which science (including mathematics) is not separated from religious values. According to research on the integration of science conducted at UMY's Center for the Integration of Science in Islamic Civilization (CISIC), mathematics emerged from the practical needs of early humans and evolved into a structured discipline through the convergence of various great civilizations, with significant, invaluable contributions from the Islamic world.
The Golden Age of Islam in Science and Technology, according to Rizka Maulana Saputra, S.Pd.I., M.S.I. (a lecturer at University Muhammadiyah Yogyakarta):
The golden age of Islam in the fields of science and technology can be mapped across several interconnected historical phases. The first phase was a formative period, spanning from the late 7th century to the mid-8th century CE, during which the Umayyad Caliphate established the foundations for administration, language, and cross-cultural engagement. The second phase was the classical golden age under the Abbasid Caliphate notably during the reigns of Caliphs Al-Mansur (754–775 CE) and Harun al-Rashid (786–809 CE), reaching its zenith under Al-Ma'mun (813–833 CE) with the establishment of the Bayt al-Hikmah (House of Wisdom) in Baghdad. The third phase represented a parallel golden age in the western reaches of the Islamic world, specifically in Andalusia (711–1492 CE), Sicily (831–1091 CE), and North Africa. The fourth phase was a subsequent period marked by significant achievements under the Seljuk, Ayyubid, and Mamluk dynasties, followed by the Ottoman, Safavid, and Mughal empires.
The golden age of Islam in the fields of science and technology can be mapped across several interconnected historical phases. The first phase was a formative period, spanning from the late 7th century to the mid-8th century CE, during which the Umayyad Caliphate established the foundations for administration, language, and cross cultural engagement. The second phase was the classical golden age under the Abbasid Caliphate notably during the reigns of Caliphs Al-Mansur (754–775 CE) and Harun al-Rashid (786–809 CE), reaching its zenith under Al-Ma'mun (813–833 CE) with the establishment of the Bayt al-Hikmah (House of Wisdom) in Baghdad. The third phase represented a parallel golden age in the western reaches of the Islamic world, specifically in Andalusia (711–1492 CE), Sicily (831–1091 CE), and North Africa. The fourth phase was a subsequent period marked by significant achievements under the Seljuk, Ayyubid, and Mamluk dynasties, followed by the Ottoman, Safavid, and Mughal empires.
Academically, Universitas Sang Bumi Ruwa Jurai (University Saburai) adheres to the universal historiographical consensus on mathematics as taught in various higher education institutions. It makes no unique or separate historical claims; rather, its formal curriculum divides the history of the emergence and development of mathematics into five major periods, aligned with the timeline of world civilizations. Institutionally, University Sang Bumi Ruwa Jurai (University Saburai) does not offer any specific or specialized academic program that presents an alternative version of the history of mathematics. The university focuses on fields of study such as Public Administration, Accounting, Law, and other disciplines within the social sciences and engineering.
Based on official historical documents from the University of Lampung (Unila), the history of mathematics at the university can be viewed from two perspectives: the emergence of mathematics as an academic discipline, and the chronological establishment of the mathematics institution or department at Unila.
Institutionally, the history of mathematics education at the University of Lampung (Unila) has evolved alongside the development of its faculties, as outlined below:
• 1968 (Initial Foundations through the Educational Track): Mathematics was first taught formally at Unila following the integration of the Tanjungkarang branch of the Institute of Teacher Training and Education (IKIP) Jakarta into Unila's Faculty of Education (FK). Within this faculty, a Department of Mathematics Education was established, with a primary focus on training mathematics educators/teachers.
• 1995 (The Genesis of the Faculty of Mathematics and Natural Sciences - FMIPA): The need to develop pure (non-educational) sciences became increasingly pressing. Pursuant to the Decree of the Minister of Education and Culture of the Republic of Indonesia No. 0334/O/1995, dated November 15, 1995, the University of Lampung officially established the Faculty of Mathematics and Natural Sciences (FMIPA). In this initial phase, the new faculty incorporated the Departments of Biology and Chemistry, which were transferred from the Faculty of Agriculture.
• 1998 (Establishment of the Study Program): To broaden the scope of pure sciences, the Director General of Higher Education at the Ministry of Education and Culture issued Decree No. 55/DIKTI/Kep/1998, dated February 23, 1998, which authorized the creation of a Mathematics Study Program (alongside a Physics Study Program) under the auspices of Unila's FMIPA.
• 1999 (Official Establishment of the Department of Pure Mathematics): Pure mathematics was formally institutionalized at Unila through the Decree of the Director General of Higher Education No. 12/DIKTI/Kep/1999, dated January 13, 1999. This decree marked the elevation of the Mathematics Study Program to the status of a full Department of Mathematics within the Faculty of Mathematics and Natural Sciences (FMIPA) at Unila.