Introduction to Mathematics

Mathematics originates from a Greek word ìmathemaî which means science, learning, etc..  Mathematics is an abstract science, although its application is seen in practically each and every sphere of our lives. It is the basis of all the other sciences. 

The oldest known mathematical treatise, dating between 2000 and 1700 B.C. comes from Egypt and is known as Ahmes Papyrus. The document contains rules for finding volumes of barns and areas of fields. Fractions and whole numbers also appear to be mentioned. Equations similar to algebra with unknown quantities are mentioned also. It is a great wonder that about thousand years earlier, the Egyptians had built their pyramids. This shows that the Egyptians knew a lot of advanced mathematics.

Progress of language in written form helped a great deal for scientific ideas to be developed and recorded. Framework of time, a system of counting, a calendar were in place by about 2000 B.C. in Babylonian and Mesopotamian civilizations. In these early civilizations, science and mathematics had flourished a great deal. The Babylonians used two systems of counting, one based on 10, capable of running into the hundreds of thousands, and the other based on 60 for mathematical and astronomical purposes. From the latter we get hours into sixty minutes and minutes into 60 seconds. Similar is true with the measurements of angles into minutes and seconds of an arc. Around 600 B.C., the Chaldeans, established near the Caspian Sea, named five planets, Mercury, Venus, Mars, Jupiter and Saturn. Together with the Sun and the Moon, they formed early basis of a week consisting of seven days. Even civilizations of the Indus Valley were fairly advanced in mathematics and astronomy around this time.

The word geometry comes from Greek words (ge : earth, metron : measure). Pythagoras was one of the early Greek mathematicians (6^th century B.C.) whose Theorem of Pythagoras concerning squares of the sides of a right-angled triangle is well known.  Pythagoras could tell the heights, distances, or how far a boat was from the coast, by using his knowledge of the right angled triangles.

Amongst the oldest known Indian mathematicians is Aryabhatta, who lived in Kusumaputra in Bihar around 470 A.D.  Aryabhatta wrote ìAryabhatiyaî in which he has explained concepts of astronomy, spherical trigonometry, arithmetic, etc.  The concept of numbers including zero was in use during his time.  

In the early part of the 20^th century, Indian mathematician Srinivas Ramanujan became very famous because of his work with the number system. 

There are many branches of mathematics. Arithmetic of counting, adding, subtracting, etc. is the simplest form of mathematics we come across in our every day lives. Geometry, Algebra are other branches of mathematics. Higher mathematics involves number theory, Algebraic Geometry, Calculus, Differential Geometry, etc. The list is endless. Every branch of engineering deals with mathematics. Fluctuations and predictions in the stock market depend on the statistical models, whose basis is again mathematics. Entire weather forecast involves complicated non-linear mathematics that needs large computers to solve the multi-parameter equations.  Launching a space shuttle, keeping it in a specific orbit; launching an artificial satellite and parking it in a fixed orbit around the earth or the sun, etc. needs very complex mathematical equations.  It is said even animals are qualitatively aware of numbers. A lion knows ìoneî deer from a herd of ìmanyî deer. In some experiments, humans have been able to teach chimpanzees some amount of arithmetic. It is said that the concept of aesthetics and beauty also can be explained in terms of symmetry and a number series!

Thus there is no escape from mathematics. As one learns mathematics, one learns to appreciate its powers of prediction and applications. It is good to remember that the entire structure of the universe is based on the foundations of mathematics!  

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