Mathematician untangles legendary problem

[C1ay]

Karl Mahlburg, a young mathematician, has solved a crucial chunk of a puzzle that has haunted number theorists since the math legend Srinivasa Ramanujan scribbled his revolutionary notions into a tattered notebook...

 

The father of modern number theory, Ramanujan died prematurely in 1920 at the age of 32. The Indian mathematician's work is vast but he is particularly famous for noticing curious patterns in the way whole numbers can be broken down into sums of smaller numbers, or "partitions." The number 4, for example, has five partitions because it can be expressed in five ways, including 4, 3+1, 2+2, 1+1+2, and 1+1+1+1.

 

Ramanujan, who had little formal training in mathematics, made partition lists for the first 200 integers and observed a peculiar regularity. For any number that ends in 4 or 9, he found, the number of partitions is always divisible by 5. Similarly, starting at 5, the number of partitions for every seventh integer is a multiple of 7, and, starting with 6, the partitions for every 11th integer are a multiple of 11...

 

More....

 

The article also discusses some patterns he''s found that hold true for all primes. It looks intriguing.

[Turtle]

___Interesting indeed! Moreover, my Katabatak Function is a similar 'crank' & I have developed it much in the same manner as Ramanujan. I believe further it has similar significance in advancing Number Theory. While it was Ramanujan who uniquely 'saw' the patterns, it is now others who have rigorously characterized them. As it is I who have uniquely 'seen' Katabatak patterns, I have put them forward for anyone to characterize.

___I hope I don't have to go the route of Ramanujan or Fuller, or a host of others, ie die before anyone takes notice. Que sera sera. ;)

[Tormod]

No, that would be very nice if you didn't die on us, Turtle.

[Turtle]

___GETE Not that I'm planning on it any time soon, just that life has a way of throwing curves. In the case of Ramanujan (who I never saw called 'Father of Number Theory' before) he did all his work on his own on scrappy little paper & only by chance did he come to the attention of Western mathematicians. The irony is that the recognition is what killed him; they found him & brought him to England where he took ill & died.

___I mentioned Buckminster Fuller, who was ridiculed & belittled no end for his ideas, particularly his prediction of a 4th form of carbon & its exact molecular arrangement. We now called this form by his name & it's in no small measure out of guilt I hope.

___Anyway, whether I'm like these guys or not, I think I am so I'm thinking Hypography & the web are a way to circumvent the perils that have taken so many others. All of my scrappy little drawings & equations might have been lost if I was suddenly struck by a meteor or car or any number of unpredicatable ends. What sense would any heirs make of it anyway; none.

___No, I think it's better to just give this stuff out & not try to hold it away for some unknown future. I rely on the idea that people here will poke a stick into any weak point if they can, & that I provide no such purchase or quickly remedy the breech. I also, being a cynic, rely on the stealers to disiminate the work. Indeed, the thiefs attention is a high badge of honor inasmuch as who better knows the value of things.

___In keeping this diatribe in line with the thread, I bow to all those legendary problem proposers; to paraphrase Leanardo of Pisa, "the best part is having the idea, carrying it out is secondary". ;)