The document discusses the differences between pure and applied mathematics. Pure mathematics is the abstract, theoretical study of mathematical structures and relationships, while applied mathematics uses mathematical methods to solve problems in the physical world. Many concepts that were originally developed through pure mathematics, such as complex numbers, later found applications. The relationship between pure and applied mathematics is interdependent, with problems in applied mathematics driving developments in pure mathematics and vice versa.

1. Haritha B S
Mathematics
Semester 1
Mount Trabor Training
College, Pathanapuram

2.  Pure Mathematics is the study of the essential
structures of Mathematics.
 It involves systematic and deductive reasoning, deals
with exact statements, concepts and theories which
are disconnected from perception.
 It treats only theories and principles without regard to
their application to concrete things.
 It consists of all those assertions as that, if such and
such proposition is true of anything, then such
another proposition true of that thing.
 It is developed on an abstract self contained basis
without any consideration of its possible application, if
any.

3.  Applied Mathematics is the application of Pure
Mathematics in the real world.
 It considers those parts of Mathematical theories
that have certain direct or practical application to
objects or action in the material world.
 Principles of Applied Mathematics have been used
to investigated phenomenon such as heat, sound,
light, mechanics, astronomy, navigation…
 It helps in solving the intricate problems of the
physical world like weight of earth, determine the
paths of planets, solve complicated problems of
business in the international world…

4.  Applied Mathematics act as a bridge between Pure
Mathematics with Physics, Chemistry, Mechanics…
 Many theories and structures of Pure Mathematics
later on find many applications which were not known
at the time of their invention.
 Eg: Complex numbers were developed for the point of
view of Pure Mathematics, but now Complex number
are widely used and they find application in electricity,
radio,…

5.  Study of problem in applied leads to development in
Pure Mathematics, theories developed in Pure leads to
Applied Mathematics.
 Interdependent and interrelated.
 Relationship between Pure and Applied Mathematics
has been summarized by Synge in the following words:
i. A dive from the world of reality into the world of
Mathematics.
ii. A swim in the world of Mathematics.
iii. A climb from the world of Mathematics into the
world of reality carrying the prediction in teeth.