There are two ways in which
maths has become so effective in our age. The first is through its relationships
with science, the second is through its connection with human reasoning. Math
method is reasoning of the highest level know to man, and every field of investigation-be
it law,politics, psychology, medicine or anthropology-has felt its influence and
had modelled itself on maths to some extent ever since its creation. In order
to gain a more comprehensive view of the relation of maths to the sciences, let
us analyze the various ways in which maths has been serving scientific investigations.
1.Maths has been supplying a language for the treatment of the quantitative problems
of the physical and social sciences. Much of this language has taken the form
of math symbols. Symbols also permit concise, clear representation of ideas which
are sometimes very complex. Scientists have learned to use math symbols whenever
possible.
2.Maths has been supplying science with numerous methods and conclusions.Among
the important conclusions are its formulas, which scientists have accepted and
used in solving problems. The use of such formulas is so common that the contribution
of maths in this direction has not been fully appreciated.
3.Maths has been enabling the sciences to make predictions. This is perhaps the
most valuable contribution of maths to the sciences. The ability to make predictions
by math by math means was exemplified in the most remarkable way in 1846 by the
two astronomers Leverrier and Adams. As a result of calculations, they predicted,
working independently, that there must exist another planet beyond those known
at the time. A search for it in the sky at the predicted place and time revealed
the planet Neptune. Prediction has played a part in every math solution of a quantitative
problem arising in the physical and social sciences.
4.Maths has been furnishing science with ideas to describe phenomena. Among such
ideas may be mentioned the idea for functional relation; the graphical representation
of functional relations by means of coordinate geometry; the notion of a limit;
the notion of infinite classes which helps us to understand motion. Of special
importance are the statistical methods and theories which have led to the idea
of a statistical law. The description is not complete without mentioning the fact
that for many physical phenomena no exact concepts exist other than math ones.
Maths has been supplying a language, methods and conclusions for science;enabling
scientists to predict results; furnishing science with ideas to describe phenomena
and preparing the minds of scientists for new ways of thinking.
It would be quite wrong to think that maths had been giving so much to the sciences
and receiving nothing in return. Physical objects and observed facts had often
served as a source of the elements and postulates if maths. Actually, the fundamental
concepts of many branches of maths are the ones that had been suggested by physical
experiences. Scientific theories have frequently suggested directions for pursuing
math investigations, thus furnishing a starting point for math discoveries. For
example, Copernican astronomy had suggested many new problems involving the effects
of gravitational attraction between heavenly bodies in motion. These problems
had stimulated the further activities of many scientists in the field of differential
equations.
Math language is precise and concise, so that it is often confusing to people
unaccustomed to its forms. The symbolism used in math language is essential to
distinguish meanings often confused in common speech.Math style aims at brevity
and formal perfection.
The student must always remember that the understanding of any subject in maths
presupposes clear and definite knowledge of what precedes. This is the reason
why "there is no royal road" to maths and why the study of maths is
discouraging to weak minds, those who are not able to master the subject.
The language of maths consist mostly of signs and symbols, and, in a sense, is
an unspoken language. There can be no more universal or more simple language,
it is the same throughout the civilized world, though the people of each country
translate it into their own particular spoken language. For instance, the symbol
5 means the same to a person in England, Spain, Italy or any other country; but
in each country it may be called by a different spoken word. Some of the best
known symbols of maths are the numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition
(+), subtraction (-), multiplications (*), division (/), equality (=) and the
letter of the alphabets:Greek, Latin, Gothic and Hebrew(rather rarely).