It is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain. - Albert Einstein.
Invention or Discovery?
Mathematics was always present in nature, waiting to be discovered. In fact, it is present everywhere in the universe. But math, as a subject, is dreaded and scary for many. Even thinking about calculations, theorems, algebra, geometry, permutations and combinations gives goosebumps to some people.
Mathematics as a science is not a discovery by a single person. It is a joint effort which was started by the Babylonians and Egyptians, way back in 3000 BC. There are important contributions from the Greeks, Indians, and others, which have helped develop mathematical concepts, abstracts, formulae, etc. The discovery of various constants, laws, and theorems is based on the invention of the numerical system. All of these numbers give physics, chemistry, and all the other sciences a much-needed backbone, which supports and gives them a definite measure.
Why is it a Discovery?
The concepts of mathematics have always been in nature. The shapes, symmetry, sizes, and quantities, have always been an integral part of natural phenomenon.
The principles of symmetry and balance are seen in almost all living things. Many living things, including human beings, show symmetry in their anatomy. For example, the body structures of mammals are such that, the left and right side of their anatomical structures are perfect mirror images of each other. This kind of symmetry can also be seen in the placement of leaves on branches. This is called bilateral symmetry.
The other type is radial symmetry, a classic example of which is a circle. You can divide the circle in many parts by drawing lines, and each part will be equal to the others. Asymmetry is also a part of the universe, and makes up complex structures like the Big Bang, and various animals like the sponges, which do not exhibit any balance or similarity in their structures.
A branch of mathematics, geometry describes shapes. We find so many shapes in nature. Celestial bodies like the Moon, Earth, and planets, are spherical in shape. They revolve in an elliptical orbit around the Sun. Mountains, some fruits like strawberries or pineapples, and tress like the Christmas tree, are conical in shape. The cells that a honeycomb is made up of are hexagonal in shape.
The Fibonacci sequence or the Golden ratio is one of the basic fundamental sequences of the universe. It is omnipresent, and its practical applications are found in many structures or patterns in the cosmos. The sequence was put forth by Leonardo Fibonacci during calculation of the offspring produced by a pair of rabbits in a course of one year.
The sequence starts as - 0,1,1,2,3,5,8,13,21,34,55,87... and so on and so forth. The logic behind this sequence is that, each number is a sum of the two numbers that come before it. The ratio is called Phi, which equals numerically as 1.61803, which can be seen in various biological structures and other objects.
All the above-mentioned phenomena are an integral part of the universe, and of mathematics as well. We have just discovered these phenomena and named them. However, there are a few inventions that took place which helped develop mathematics as a science.
Some Inventions in Mathematics
After the beginning of trade in ancient times, a need for counting was developed. The human hand was the first device used to count the number of quantities. After the number ten, rocks, pebbles, shells, or other natural markers were used to count. Many, few, nothing, infinite,, etc., are associated with the counting of terms in mathematics. Before the advent of the numerical system, these were the terms that described quantities. Then developed the Hindu-Arabic numerical system, which gave rise to abacus and accounting.
The invention of the numerical system greatly advanced and developed mathematics. Eminent mathematicians like Euclid, Pythagoras, Archimedes, Plato, etc., built up mathematics as a concept. Various geometrical theorems, algebraic concepts and formulae, differential integration, and calculus, logarithms, decimal point, graphical representation, geometrical instruments like the protractor or ruler, digital languages, and mathematical signs were invented, which helped mathematics scale new heights and evolve as a science.
Many concepts and practices in mathematics were invented; however, mathematics was a remarkable discovery that changed the face of all the other sciences, and pioneered the way for new approaches and advancements to explain and explore the universal facts, concepts, and pragmatisms.