Meaning and Nature Of Mathematics
* “Mathematics is the Science of number and Space”
* “Mathematics is the Science of Measurement, quantity and Magnitude.”
These definitions clearly indicate that Mathematics is an accepted Science which deals with the quantitative aspect of our life and knowledge.
* Mathematics has been recognized as one of the Central Strings of human intellectual activity throughout the centuries.
* The Word “Mathematics” has been used in two distinct and different senses.
i.e. One as a method used to solve the problems of quality, space, order etc. and the second as a set of laws or generalizations of truths that are discovered.
* Mathematics is a tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.
* In other words, as in mathematics we find results at the abstract level with the help of process of reasoning, therefore mathematics may be regarded as a science of abstract forms.
* As expressed by Hindi Mathematicians, “Mathematics(Ganita) means the Science of Calculation.”
From the above opinions we include that Mathematics is a Science of Quality and Space. It deals with the questions and problems involving size, portion, area, time interval, distance etc. It is also a science of calculation involving the use of number and symbols.
* It deals with the relationship between magnitudes. It deals with Numerical part of Man’s life.
In this way it is a Systematic, organized and exact branch of science, which deals with abstract concepts.
NATURE OF MATHEMATICS
1) Mathematics, like everything else that man has created, exists to fulfil certain human needs and desires.
2) The dominant intellectual interest of mankind shows that, mathematics appeals very powerfully to mankind.
3) It involves man’s high cognitive powers.
4) It has its own language-signs, symbols, terms and operations etc.
5) It has its own tools like intuition, logic, reasoning, analysis, construction, generality and individuality etc.
6) It helps in drawing conclusions and interpreting various ideas and themes.
7) Mathematics is the science of inductive -deductive reasoning.
Inductive-reasoning means when a particular property is true in a sufficient number of cases, then we conclude that it will true for all similar cases.
Deductive-reasoning is based on axioms, postulates, self-evident truth, undefined terms and definitions.
8) “Mathematics is a way to settle in the mind as habit of reasoning.”
9) Mathematics can be used in two distinct and different senses i.e. (i) The truth that are discovered and (ii) The methods used to learn truth.
10) Mathematics is of two types- Pure and Applied Mathematics
Pure Mathematics deals with theories and principles without regard to their application to concrete things.
Applied Mathematics is the practical side of pure mathematics.
That is why each and every invention and discovery in the field of physical, biological or social sciences owe much to applied mathematics.
* “It is the science of number and space.”
* “It is the science of measurements, quantity and magnitude.”
* Rationality, accuracy, originality of thinking, certainty of results, transfer of learning in terms of similarity to the reasoning of day to day life and verification are the vital components of mathematics.
* Mathematics is an expression of the human mind reflects the active will, the contemplative reason and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.