June 30, 2012
16-Year Old Solves a 350-Year Old "Impossible" Math Problem

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A few months ago, 16-year old Shouryya Ray blew the mind of mathematicians and the media by solving two "unsolvable" particle dynamics problems first posed by Isaac Newton 350 years ago.

How did he do it?

Explained Shouryya: "When it was explained to us that the problems had no solutions, I thought to myself, 'Well, there's no harm in trying."

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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 )

Posted by Mitch Ditkoff at June 30, 2012 11:00 AM

Comments

THE ABSTRACT OF MY PAPER,"FORMULATION OF A NEW EQUATION OF TIME" WAS PUBLISHED IN THE PROCEEDING OF THE WEST BENGAL STATE SCIENCE AND TECHNOLOGY CONGRESS ORGANIZED BY DEPTT. OF SCIENCE AND TECHNOLOGY,GOVT. OF W.B.,INDIA A FEW YEARS AGO.IT'S A NEW EQUATION OF SIDEREAL TIME BASED ON DOPPLER'S EFFECT OF LIGHT AND A SINGLE VARIABLE,'g' OF THE CELESTIAL OBJECT. I AM A FREE-LANCE RESEARCHER IN MATHEMATICS,PHYSICS AND ASTRONOMY HAVING PUBLISHED PAPERS IN INDIA,USA AND UK.

Posted by: Bablu Dey [TypeKey Profile Page] at July 7, 2012 06:40 AM

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