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January 05, 2011
It has defeated some of the greatest mathematicians and scientists of the last 400 years who have devoted hundreds of thousands of hours to prove it is not mere conjecture.
It all started innocently enough, (if cannonballs are ever innocent), when Sir Walter Raleigh simply wanted to know the ultimate way to pack cannonballs in the hold of his ship.
In 1611, German astronomer Johannes Kepler, best known for figuring out planetary motions, responded by saying just pile them up the same way that grocers stack oranges.
Namely, in the folds of another sphere below.
Now if you or I were asked, without knowing it was called face centered cubic packing, we might have said something like, "Yeah, I think that's probably the best way."
But when Kepler said it, it was genius.
It apparently takes more geniuses to prove it, which is the only way a conjecture can become a theorem.
(For example, the dropped piece of toast always falling on the buttered side down is mere conjecture, although I would award it theory like status.)
If you can ever squeeze drama out of this obsessive desire to prove Kepler right, author George Szpiro does it with, "Kepler's Conjecture: How Some of the Greatest Minds in History Helped Solve One of the Oldest Math Problems in the World."
Turns out there are endless ways to pack spheres in a Euclidean space and over the last four hundred years those minds went through all of them.
And now they're, well sort of "cheating" by using computers.
In 1953 Hungarian, László Fejes-Tóth showed that given sufficient computing power the problem could be solved.
Now, the American mathematician, Thomas Hales has either done it, or we're not quite sure, pending further scrutiny.
So what is finally the point in proving Kepler's conjecture so it can land in the prestigious Annals of Mathematics?
Is it as Albert Einstein said:
"Curiosity has its own reason for existing."
Or is it as Sir George Mallory said:
"Because it is there."
I know this group knows how to pack many astute answers into a rectangular box.
At least that would be my conjecture, which should take at least one day to prove.
Goldbach's Conjecture singnet.com Take a look at an interesting article we found.
Euler's Mathematical Contributions suite101.com Take a look at an interesting article we found.
What is Kepler's conjecture knowledgerush.com Take a look at an interesting article we found.
Which conjecture should be elevated to theory?