Generations of scientists and mathematicians had tried their hand unsuccessfully at solving Newton's problem (for the technically minded, the problem was coming up with a mathematical formula to predict the fluid dynamics of a flying object taking into account the combination of forces including gravity and air friction).

That was until Indian-born Shouryya was on a school trip to Dresden University, and heard the professors mention the problem, and saying it was unsolvable.

Hearing this, Shouryya said "Why not? I didn't believe there couldn't be a solution."

So he got to work on it, and wouldn't give up until he had solved it and published his work.

Does he think it was genius that got him there? No. In fact, almost the opposite.

"I think it was just schoolboy naivety."

FOOD FOR THOUGHT: Name three things in your business or life that you written off as "impossible". Now, like Shouryya, don't believe it. Get busy. Take a fresh look at the problem. Trust your instincts. Muse, contemplate, dream.

If you need to get your creative juices flowing, try this.

The problem Shouryya solved?

Let (x(t),y(t)) be the position of a particle at time t. Let g be the acceleration due to gravity and c the constant of friction. Solve the differential equation:

(x''(t)2 + (y''(t)+g)2 )1/2 = c*(x'(t)2 + y'(t)2 )

subject to the constraint that (x''(t),y''(t)+g) is always opposite in direction to (x'(t),y'(t)).

Finding the general solution to this differential equation will find the general solution for the path of a particle which has drag proportional to the square of the velocity (and opposite in direction). Here's an explanation how this differential equation encodes the motion of such a particle:

The square of the velocity is:

x'(t)2 + y'(t)2

The total acceleraton is:

( x''(t)2 + y''(t)2 )1/2

The acceleration due to gravity is g in the negative y direction.
Thus the drag (acceleration due only to friction) is:

( x''(t)2 + (y''(t)+g)2 )1/2

Thus path of such a particle satisfies the differential equation:

( x''(t)2 + (y''(t)+g)2 )1/2 = c*(x'(t)2 + y'(t)2 )