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HISTORY OF CALCULUS
Dr Aarti Kaushik
Associate Professor, Dept. of Applied Sciences

Calculus is one of the foundation stones of the Modern Euclid and his predecessors
Mathematics. It is a branch which is focused on limits, developed the method of exhaustion in
continuity, derivatives, integrals and infinite series. There is 5th century BCE as a way to compute
a controversy between Newton, Leibniz and their followers the area inside a circle by filling the
on who discovered Calculus first, called the Leibniz-Newton circle with a sequence of polygons with
Calculus controversy. The accepted historical version is that an increasing number of sides and a
Newton and Leibniz discovered Calculus independently. But, corresponding increase in area. This
the fact is that different people developed different parts of method could also be called a part of
calculus at different times and at different places. Some of integral calculus. In 3rd century BCE,
them knew nothing about the others. Most of the things Archimedes (c. 287-212 BC) developed the concept of
Leibniz and Newton did were known before them, but some infinitesimals and employed the method of exhaustion to the
things were new with them. point where he could compute the volume of a cone, sphere,
The invention of calculus is much like the invention of etc.
radio which cannot be attributed to one inventor only. The
invention of radio started when electromagnetic equations
were first formulated in its present form by Oliver Heaviside
though some attribute it to Maxwell. This was followed by
Hertz's work on radio waves. Many other inventors like
Jagdish Chandra Bose, Nikola Tesla, Reginald Fessenden,
Alexander Popov, Edwin Howard Armstrong and Oliver
Heaviside contributed significantly in this area. Then,
Marconi utilized the works of all these great inventors and
won the Nobel Prize in Physics along with Karl Ferdinand
Braun in 1909. In the same fashion, modern Mathematicians
credit Leibniz and Newton for inventing calculus, but they
did not invent derivatives, integration, Taylor series, or even
the Fundamental Theorem of Calculus.
As early as c.?1820 BC, calculations of volumes and Bhaskara II (1114-1185 AD), an eminent Indian
areas, a major problem of integral calculus, can be found in mathematician and astrologer, discovered “Calculus” in its
the Egyptian Moscow papyrus , but the formulas were only proto-form centuries ago. In Siddhanta Shiromani, which is
given for concrete numbers and they were not derived by an astronomical treatise preliminary concepts of infinitesimal
deductive reasoning. It is believed that Babylonians have calculus, differential calculus and integral calculus are found.
discovered the trapezoidal rule while doing astronomical Evidence suggests Bhaskara was acquainted with some ideas
observations of Jupiter. of differential calculus. Bhaskara also goes deeper into the
'differential calculus' and suggests that the differential
coefficient vanishes at an extremum value of the function,
indicating knowledge of the concept of 'infinitesimals'. There
is also evidence of an early form of Rolle's Theorem in his
work. He was also aware that when a variable attains the
maximum value, its differential vanishes.
Archimedes used the method of exhaustion to compute From the fourteenth century to the sixteenth century
the area inside a circle

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