# Relevance of Mathematics in Science

It has been observed that the cause of unwillingness among bright students to pursue a carrier in science is the abysmally low quality of teaching and fear of the subject mathematics in our educational institutions. Even in competitive exams for KAS/IAS/IPS candidates rarely opt this subject for entrance test. We cannot afford to neglect this subject, owing to its relevance in scientific knowledge and also to overcome the deficiency of mathematics teachers in our institutions.

Mathematics is fundamental to science because it provides the language, tools, and frameworks necessary for scientific inquiry, analysis and communication. Its relevance spans across various scientific disciplines, impacting both theoretical and experimental aspects. From the early days of civilization to the cutting-edge research of today’s, mathematics has consistently played a crucial role in the development of scientific knowledge.

**Mathematics in Ancient Civilizations:- **The use of mathematics dates back to ancient civilizations such as the Egyptian, Babylonians and Greeks. Just like language, mathematics is instructive to human beings. Counting comes naturally to us. Simple shapes like squares, triangles and circles are grasped intuitively.

Therefore it is no surprise that most cultures and Civilizations have had some achievements in mathematics. In ancient times mathematics dealt primarily with numbers (arithmetic) and shapes (geometry) or a generalization of both these (algebra). These early cultures developed and applied basic arithmetic, geometry and algebra for various practical purposes such as astronomy, agriculture, engineering, trade & commerce and geography.

** ****(i) Egyptian Mathematics:- **Use of elementary mathematical concepts to understand natural phenomenon and for architectural purposes (i.e.; pyramid) can be traced to pre-historic times. The samples of cave paintings, pottery and textiles from the ancient past indicate that the early civilizations had a well developed feel for design, symmetry, ratio, and magnitude. The earliest preserved record of mathematical history dates back to the advanced civilizations of Egypt and Babylonia (present day Iraq) in the third Millennium BC.

Two old documents that were discovered in the 19th century are; (i) Rhind Papyrus preserved in the British Museum and (ii) Golenishchev Papyrus lodged in the Moscow Museum of Fine Arts. The Rhind Papyrus lists 84 and Moscow Papyrus 25 specific mathematical problems. These documents reveal that the Egyptians had developed a numeration system based on successive power of ten. For instance if the symbol C represents 10 and! represented 1 then CCC!!!! would represent 34.

Using the appropriate symbols for the new numbers, addition and subtraction could be done. Similarly, multiplication of numbers, fractions and other problems were solved by Egyptians. Golenishcev papyrus contains a problem about finding the volume of a truncated pyramid. They had also discovered working rules for solving problems relating to mapping, surveying, measurement & weights, area of common figures like; squares, rectangle, triangles, trapezium etc.

They also knew the method of finding the volumes of solid objects like; bricks, cylinders and pyramids. To measure distances they employed the concept of similar triangles.

** ****(ii) Babylonian Mathematics:- **The mathematical information of this civilization is available from the records on baked clays; the tablets of which have survived and are kept in various museums of the world. They gave a fair idea of the status of the Babylonian mathematics which was relatively more advanced than the Egyptians (their contemporaries). They followed the approach of saxagesimal system based on the number 60; and had devised wedge shaped symbols ( I ,U) to represent the numbers one and ten.

The first 59 numerals were expressed using these symbols much like the Egyptian method of enumeration. There after, the place value system was used to represent higher numbers. This necessitated the use of powers of the number 60. Some Babylonian tablets dating back to 2000 BC contain tables of squares of numbers up to 59 and cube of numbers up to 32. The Babylonias had some idea of the relationship between the sides of a square and its diagonal that led to the Pythagoras theorem.

They had devised approximate methods to find the value of the diagonal of a rectangle whose sides are given. Using the identity of squares and the method of solving linear equation in two variables, the Babylonians could also find the positive root of any quadratic equation and solve some cubic equations also.

They could also sum arithmetic and geometric progressions. In the later period astronomers extensively used the sexagesimal system invented by the Babylonians. Even today we use it while dividing the angles into degree, minutes & seconds; and time into hours and seconds.

**(iii) Greek Mathematics:-** The early Greek mathematics (8th century BC to 4th century BC) was similar to that of previous civilizations. It was essentially practical mathematics connected with the measurement of land and also with the trade and Commerce carried by the Phoenician merchants. The transition from practical to general mathematics began around the 5th century BC. Greeks were able to prove the Pythagoras theorem, introducing the concept of axiom, deduction and proof.

The famous Pythagoras after the name of Greek mathematician Pythagoras, laid the ground work for geometry. Among many ancient Greek mathematicians few notable were; Thales, Democritus, Euclid, Archimedes, Apollonius Hipparchus, Diophantus and Menelaus, who all have contributed significantly to the Greek mathematics. Euclid in around 300 BC compiled thirteen volumes, of the mathematical knowledge that existed at that time in Greek. These volumes known as the Elements are the principal source of our knowledge of pre-Euclidean geometry and arithmetic in Greece.

Euclid captured the knowledge generated in Greece from about 5th century BC to about 3rd century BC, which include; the propositions, theorms and corollaries, the properties of numbers, geometrical figures and geometrical constructions. In these propositions properties of triangles, circles and other planer figures are explored . Much of these geometrical studies are taught in educational institutions even today.

Greece carried out studies on the geometry of conic section (parabola,eclipse and hyperbola). This class of work was referred to as solid geometry. Geometrical constructions was a major achievement of Greek scholars. Euclid's "Elements" systematized the knowledge of geometry of the time and remained a definitive reference for centuries, Archimedes, also made significant contribution to geometry, calculus and the understanding of Pi.

These advancements in Greek mathematics (geometry) led the scientists to seek applications in Physical Sciences. Euclid applied these tools to study the problems in optics; Archimedes to investigate Centre of Gravity in mechanics; Hipparchus worked on earliest sine tables and laid the conceptual foundation of trigonometry.

The geometrical studies of the Greek mathematics found application in astronomy. Models of the universe with the earth at the centre and planets fixed to rotating concentric spheres were designed. The influence of Greek mathematics war partly the cause of rapid rise of mathematics in the 17th century.

**(iv) Ancient Indian Mathematics:- **During the Rig Veda period (1500 BC -700 BC), when the Aryan groups who had come from Soviet Central Asia and Iran, were always on the move and in constant strife with each other or with the local non-Aryans. As a result there was no advancement in science & technology.

Their technology was limited to the construction of chariots, iron tools and weapons of War. The Rigvedic period was followed by Yajurvedic period that lasted for 300 years (i.e; 700 BC- 400 BC). Knowledge of the metallurgy of iron, copper, silver and tin continued to be developed by the Aryans till the beginning of Maurya period. Besides many developments in various fields of science; like in chemistry, botany, physiology, medicine and astronomy.

There was also significant advancement in mathematics. Detailed description of the geometrical theorems and axioms are available in a text called Sulvasutra which dates around 600-300 BC. In arithmetic numbers in multiples of 10 going upto as high powers of 10, as 10^{12} were known and used. All the arithmetic operators on numbers were also known Sulvasutras, that contain several instances of addition, subtraction, multiplication, division & squaring of fractions.

Indian subcontinent had a long rich tradition of scientific thought much before the Europeans. Their scientific achievement was known to the Europeans large through the efforts of Arab in the middle ages. The golden age of Indian science was during the rule of Gupta Emperors and Harshvardhana (4th to 7th centuries). During this period considerable original work was done in mathematics and astronomy.

Astronomy has formed part of Indian intellectual traditions since the time of Vedas (C.1500 BC) in which earlier references to astronomical studies can be found. These have been described in texts called "Sidhantas" which refined and built up the knowledge in the vedic and the late vedic period. The Indian astronomy of this period recorded accurate observations of the sun, moon and planets. To make few ancient astronomers and mathematicians, Aryabhata, Varahmihira, Brahmagupta, Bhaskara-I Bhaskhara-II were famous for their works on astronomy, algebra and decimal systems.

According to the idea of Aryabhatta Earth rotates and heavens are still; eclipses are caused by shadows of earth or moon. Varamhira was of the opinion that the Earth is motionless and the sun, moon and the planets move around it. Eclipse are caused by the Shadows of earth or moon. Brahmagupta presented the idea that eclipse was caused by Rahu and Ketu; earth is motionless and the sun, moon and the planets move around it.

Bhaskara-I carried his works based on the knowledge contained in Sidhantas. Bhaskara-II wrote first book on mathematics using decimal systems . The developments in science suffered a set back soon after the decline of Gupta period. Hereafter there were a few advances made solely by individual efforts.

In the medieval period many commentaries appeared on the works of earlier scholars. Around this time the Arab scholars translated many of the Indian works on astronomy and mathematics into Arabic and Persian. These translations found their way to Europe. Likewise, the Arabic translations of ancient Greek works on mathematics and astronomy transferred to India.

This cross fertilization of Ideas was facilitated largely due to the works and efforts of the Arabs. The influence of Persian and Arab Science on Indian workers is evident in the astronomical instruments and observatories constructed at Jaipur and Delhi in India.

*by: Prof (Dr) Mohammad Aslam Baba, Former Principal/Dean Engineering and Technology, Cluster University Srinagar*