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 .