Posted on 03/25/2005 8:50:03 AM PST by bedolido
A number puzzle originating in the work of self-taught maths genius Srinivasa Ramanujan nearly a century ago has been solved. The solution may one day lead to advances in particle physics and computer security.
Karl Mahlburg, a graduate student at the University of Wisconsin in Madison, US, has spent a year putting together the final pieces to the puzzle, which involves understanding patterns of numbers.
"I have filled notebook upon notebook with calculations and equations," says Mahlburg, who has submitted a 10-page paper of his results to the Proceedings of the National Academy of Sciences.
The patterns were first discovered by Ramanujan, who was born in India in 1887 and flunked out of college after just a year because he neglected his studies in subjects outside of mathematics.
But he was so passionate about the subject he wrote to mathematicians in England outlining his theories, and one realised his innate talent. Ramanujan was brought to England in 1914 and worked there until shortly before his untimely death in 1920 following a mystery illness.
Curious patterns Ramanujan noticed that whole numbers can be broken into sums of smaller numbers, called partitions. The number 4, for example, contains five partitions: 4, 3+1, 2+2, 1+1+2, and 1+1+1+1.
He further realised that curious patterns - called congruences - occurred for some numbers in that the number of partitions was divisible by 5, 7, and 11. For example, the number of partitions for any number ending in 4 or 9 is divisible by 5.
(Excerpt) Read more at newscientist.com ...
I am still trying to figure out why the name “Democrat” changes to “Democratic” depending on usage.
“Republican” never becomes “Republicanic”.
Any help with this one?
But what did he actually prove! That there is a way to generate or define a very large set of numbers subject to certain operations that we didn't know existed even though we invented the numbers and operations in the first place. It may allow us to make use of the "finding" but does it lead to a greater understanding of numbers as numbers? It is like proving in Chess that a player playing White who never makes a mistake will always win when playing against an opponent who also never makes a mistake, given the existing rules of Chess. If true, what does it say about chess, except that Chess is a game where a player playing white who never makes a mistake.... (Plot of War Games, as I recall.)
:-) Whoohooo! Glad you liked it. Thanks for the link. Its been a while since I read that.
ping
I read that article about the number 137... had to go read 20 blonde jokes just to feel intelligent. Strange just how much we know and how much there is to know. Some people know more of the little a man can learn... others just read Dilbert and complain about a lack of nookie.
I wish I knew what he was talking about... but my brain hurts now. back to writing java using BEA/Weblogic getting rid of Cross-Domain and replacing it with Struts.
LOL! Thanks.
Understood. :-)
That it applies to all prime numbers, not just those tested. We could get a supercomputer crunching on this, showing the pattern works on prime numbers thousands of digits long, but it still wouldn't prove that this works for all prime numbers.
I am most definitely not a good enough mathematician to fully understand the implications of this. However, this shows something predictable about prime numbers. Most modern cryptography related to prime numbers. Maybe this discovery will result in making it easier to factor large numbers into their primes, which could effectively break most of the cryptographic schemes used today.
Just switch to another base and that number will go away. :^)
LOL, exactly. It obviously wasn't created to be a mystery, it just is a mystery. Take 2 advil and post again tomorrow.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.