contribution of mathematicians.pdf

Contribution of mathematics

1. CONTRIBUTIONS OF GREAT MATHEMATICIANS

Introduction
The height which the mathematics is occupying today and the progress which
it has made through the age is all due to the dedicated and sustained work of its
great students. A large number of them have immortalized themselves by their
memorable contribution to their subject. Mankind will remember them forever with
gratitude. Their lives and deeds will continue to inspire the students and scholars.
These were geniuses whose works will benefit the human race throughout its
existence.

Aryabhata
Aryabhata was the first of the great Hindu Mathematicians. He lived from 475
A.D to 500 A.D in or near the present city of Patna. He wrote an arithmetic including
under this heading arithmetic and geometric progressions, quadratic equations and
indeterminate equations. He also computed arithmetical tables which contained a
table of sines. His work in mensuration was crude and in this respect, it somewhat
resembled that of the Egyptians.

Contribution
1) Aryabhata invented a notation system consisting of alphabet numerals. Digits
are denoted by alphabet numerals in this system.

2) Although earlier to Aryabhata, the method of extracting square root was evolved
by Jain mathematicians, yet Aryabhata is known for giving its simple and clear
explanation.

3) Aryabhata put more appropriate uses of the decimal system.

4) He gave almost all the formulae for knowing area of different figures like area of
a square, rectangle, triangle, rhombus, circle and volumes of the spheres and
cones etc.

5) He tried to point out the construction of different geometrical figures –triangle,
quadrilateral, circle.

6) He for the first time in the world gave the value of ??????.

2. 7) He has given a method of addition, subtraction, division and multiplication of
simple and compound algebraic quantities (integer as well as fractional). He
mentioned the algebraic formulae like (�+�)
2
=�
2
+2��+�
2
��� ��=
(�+�)
2
−(�
2
+�
2
)
2
.
8) He tried to give a rule for summing an arithmetic series after p
th
term.

9) He tried to solve indeterminate linear equations like ��±��=� �� �ℎ� ���ℎ��
of the fractions which is substantially the same as the method in use today.

10) His contribution in geometry are commendable. Also famous Pythagoras
theorem seen different form in his work.

11) Aryabhata paid considerable attention to trigonometry and his introduction of
sines was a noteable improvement upon the clumsy half-chords of Ptolemy.

12) Aryabhata in addition to mathematics was also the master of astronomy.



C.F.Gauss
Carl Friedrich Gauss was born at Brunswick, Germany. He is a famous
Astronomer, Physicist and a Mathematician. Every work Gauss produced was an
event in history of Mathematics and sciences and hence he lives everywhere in
mathematics and sciences.

Contributions
1) At the age of 19 years on 30
th
March, 1796 he invented the process of
constructing a polygon of 17 sides with the help of a ruler and compass only.

2) In 1799 his first book ‘Disquisitions Arithmeticae was published. It brought the
following things into time light: -

I. Proofs of the following algebraic facts were first seen in this book.
a. Every integral rational equation in a single variable has atleast one
root.
b. Every equation will have as many roots as the highest power of the
unknown.

II. He presented a total picture of the number system through this book.
Besides negative, positive, rational and irrational numbers he firmly dealt
with imaginary numbers.

III. He for the first time, used the symbol ‘ⅈ’ for expressing imaginary quantity
√−1. ??????ℎ� ������� �??????�� 4+2√−1 or 4+2ⅈ were named as complex

3. number by him and he introduced the world with the characteristic of such
numbers


3) He brought something new in the calendar system by becoming successful to
know the exact date of Easter and his birthday.

4) At the age of 24 he turned towards astronomy. He computed accurately the
orbits of some newly discovered planet and satellites.


5) He spent the valuable ten years of his life in Geodetic researches. He did so
many researches in the subjects Differential geometry, Theory of surfaces,
Statistics etc. In the theory of probability, he was the originator of the famous
law “Gaussian Law of Normal Distribution of Errors”.

6) He was a Master of Mathematics of motions and growth that had been
developed by Newton and Leibnitz, so much so that he shares with Lagrange
and Laplace a foremost place among the founders of modern mathematical
analysis.


7) He was one of the first to the study what is known as the non Euclidean
geometry that is now associated with the name of Nikolas Ivano Vitch
Lobachivsky of the University of Kazan.

8) Three of the problems which Gauss considered in his work on surfaces
suggested general theories of mathematical and scientific importance. The
method Gauss invented in the branches like measurement of curvature, the
theory of conformal mapping and the applicability of surfaces were general
and of wide utility.

9) Gauss won lasting fame for his scientific researches into magnetism and
electricity. In this connection he demonstrated the possibility of sending
telegraphic signals from Gottingen to a neighbouring town and thus played a
part in developing the ideas on which such famous scientists as Galvani Volta
and Ampere had been working.