Today morning I tried to “discover” the history of calculus and searched the web . I expected to find something starting from Newton and Leibnitz .
But I was wrong . The history or more appropriately the idea dates back to the Greeks ! These dudes were crazy .
After inventing the naural numbers ( 1,2,3 etc ) the greeks thought
of more interesting problems . The Greek philosopher Zeno proposed that
motion was impossible . He said that to go from a place A to B you would
first have to reach the midpoint of AB . Lets call this C . Inorder to
reach C from A you would first have to reach the midpoint of AC etc .
Thus there would be infinite midpoints between A and B and u can never reach
B ! The proposition was crazy but the idea was great . This was the first
time someone had thought of infinities , infinite points between 2 points and
infinitisimal distances .
In 370 BC some Greek Mathematicians thought of a tool called
” The method of Exhaustions” . The method is : to find the area of a
figure put smaller figures in it to completely fill the given figure.
This will help you find the area .
This method was first used by Arichmedes to find the area of
a parabola. He put a triangle in the parabola . The filled the remaining
area with smalller triangles and thus calculated the area .
So historically integration was invented before differentiation .
In the 16th century Kepler and another dude Cavelieri thought of
any area composed of an infinite no of infinitisimal rectangles .
Fermat invented a method to solve problems related to maxima and
minima of curves . This was the beginning of differentiation .
However the real inventors of Calculus as a subject were
Newton and Leibnitz . They independently combined all the abovementioned
tools/methods to form a subject . They were the first to realize that
differentiation and integration were opposites of each other . They
were the first to form a notation for differentiation and integration .
Newton actually invented calculus while trying to make his
theory of gravitation . He had an intution that the mass of a sphere can
be assumed to be concentrated at the centre to find the gravitational force
outside the sphere . But he needed a proof . He invented calculus and
got the proof .
There was a bitter rivalary between Newton and Leibnitz over the
question of who invented Calculus . Both parties fought long and hard .
They attacked each other personally . In the end England cut itself
off the mathematics of the continent . The English mathematicians refused
to use the dx/dt notation for differentiation and lazy S notation for
integration because they were invented by leibnitz .
Meanwhile in the continent during the 18th and 19th century began
a age of great mathematical discoveries powered by this great technique
called Calculus .