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Ramanujian's Deathbed Problem Cracked
Jake's Mom sends word of the serendipitous solution to a decades-old mathematical mystery. Researchers from the University of Wisconsin have unraveled a major number theory puzzle left at the death of one of the twentieth century's greatest mathematicians, Srinivasa Ramanujan. From the press release: "Mathematicians have finally laid to rest the legendary mystery surrounding an elusive group of numerical expressions known as the 'mock theta functions.' Number theorists have struggled to understand the functions ever since... Ramanujan first alluded to them in a letter written [to G. H. Hardy] on his deathbed, in 1920. Now, using mathematical techniques that emerged well after Ramanujan's death, two number theorists at the University of Wisconsin-Madison have pieced together an explanatory framework that for the first time illustrates what mock theta functions are, and exactly how to derive them."
The summary didn't refer to Ramanujan as "the Indian math guy" this time! Great work! (Don't ask how I remember that one.)
...
Although, it could do with one less "i"
Apology to Ubuntu forum.
Spell error in story title! Its Ramanujan, without the 'i'.
There's gotta be a Scientology joke in there somewhere
[Fuck Beta]
o0t!
Guess the wiki still needs to be updated
--
"I want to work in Theory -- everything works in Theory!" -- John Cash, id
Ramanujan was so amazing. His work on integer partitions was enough to be revolutionary, yet he hardly stopped there--all before dying at such a young age.
"Nature doesn't care how smart you are. You can still be wrong." - Richard Feynman
The mock theta functions are special functions that describe of host of phenomena, the most interesting of which is probably its relation to modular forms. There has been a great deal of controversy as to how these functions should actually be defined in the abstract sense and for the most part any serious attempts at figuring them out have involved using nothing more than the functions that Ramanujan himself wrote down in a notebook right before he died. It will probably be some time before this "solution" appears in a final, published form so don't get your hopes up unless you have connections to number theorists close to the activity. If you are at a university you can look up scads of articles on the topic from JStor, or just browse the bounded periodicals in the library.
This is cool and all, but the real kicker will be if Peter Sarnak from Princeton proves the Riemann Hypothesis (rumor has it he is on the way to doing so).
From what I've read about Ramanujan, what I still can't understand is how a guy from a poor background with little to no formal schooling is able to just sit around and write in a notebook and come up with the equations he did. I just have to wonder what it was in nature that made him so more adapted to mathematics than the rest of us mere mortal humans. This guy was on a completely different level. Mozart comes to mind when I think of him.
Both TFA and wiki mention that these functions keep cropping up in real world problems from chemistry and physics.
So... uh, which ones?
See, this is why I switched majors from physics. Any time I look at an infinite series, my head starts to hurt.
The next Slashdot story will be ready soon, but subscribers can beat the rush and slashdot the links early!
3) Become really, really famous.
I propose:
3) Become really, really famous while at the same time guaranteeing you will never ever have sex with a conscious human female.
Seven puppies were harmed during the making of this post.
I did not know uou guys developed it in the first place? you live and learn
You never catch me alive
It appears that Ken is holding a seminar at UW on March 29 2007 (http://math.uwyo.edu/DEPTCOLLOQ.asp#Mar%2029). We will probably have to wait until then for any details.
You seem to have missed a step, the infamous x)???.
This seems to be a simple case where if we solve the equation:
X=?
?="Answer"
"Answer"="Implement Joke Correctly"
Therefore, X="Implement Joke Correctly"
QED
Proof by very large bribes. QED.
Both PP and GPP should be modded Funny.
Both PP and GPP being moderated Redundant
is clearly an indication of a lack of caffeine.
You are being MICROattacked, from various angles, in a SOFT manner.
Some of the papers being described can be found PDF on web page of Kathrin Bringmann (one of the two authors):http://www.math.wisc.edu/~bringman/. While it doesn't include the very latest, it includes some from last year on the topic.
"I have discovered a truly marvelous demonstration of this proposition that this margin is too narrow to contain."
The only problem I've ever heard about people having on their deathbeds is that they are dying.
Knowing Google's lust for data collection, the Soviet Union is still alive and well inside the psyche of Sergey Brin....
not totally offtopic but i would like to recommend this amazing book (the man who knew infinity) to anyone interested in reading his biography. its one of the best biographies i've ever read.
fifteen jugglers, five believers
You mean there was even MORE math after "Integration by Parts"? Sheesh you guys need to get a life :P
Seven puppies were harmed during the making of this post.
As a young mathematician-in-training (just finished my undergrad degree), it disappoints me to see the kind of coverage the maths community gets.
It takes a near-century-old problem to be solved to pop a maths story on slashdot - and TFA holds no details. To get on any kind of mainstream news, the Poincare conjecture needs to be solved, and then we get "Perelman proved a rabbit was a sphere".
Mathematics at universities worldwide is being dumbed down for the pursuit of the cashed-up Engineering student. Mathematicians get no kind of acclaim for their work - even compared to other 'unglamourous' pursuits. People these days don't seem to appreciate the debt they owe to mathematics.
What's it going to take for mathematicians to get some mainstream coverage? A sex scandal?
There are 10 kinds of people in this world: those who understand binary, and nine other kinds of people.
Silly, it's between Illinois and Ohio.
"The first rule of intelligent tinkering is to save all the pieces." --Aldo Leopold (Paraphrased)
How will I intellectually masturbate?
Simple. Redefine the universe's parameters such that intellectual masturbation is no longer necessary, and place yourself in the appropriate set. You're a mathematician. You can do ANYTHING. Duh!
Seven puppies were harmed during the making of this post.
Ease of understanding & teaching.
I really think the reason why a lot of people are bewildered with math (& thus ignore it) is that they were never really able to approach it properly. Mathematics has a tendency in university to not explain itself properly. Things that I found rather simple in the end were just never explained clearly, were incomplete explanations, assumed you knew & understood concepts from other, unrelated courses, or were given "pseudo-explinations" that kind-of explained something but not properly, giving potential incorrect understandings that could be disastrous later (think high school math).
The entire cutter mentality that math classes can tend to be in university don't help much either (what is probably the #1 reason why people drop their hard science/engineering/comp sci courses?? Probably MATH!)
Once I figured whatever a concept really meant in math, I realized reading the textbook after the fact (sometimes several courses later) they use terms and concepts that aren't explained at all or they use really obtuse english sentences while simply defined symbolic language could easily show the concept. Actually most of it I found rather simple & clear in the end once I got to understand it but found that the textbook just explained it, badly or with huge gaps in their explinations.
There are smooth operators that act on imaginary numbers right by the corner. Then it gets really kinky. Consider improper integrals, strip functions, etc.
Computers make very fast, very accurate mistakes
I'm terribly sorry to be ignorant of what those are, but could somebody please give some links and references? The article itself say nothing at all. Bad article.
I resent that mockery, you insensitive... oh, I thought you said deride.
I have no idea when you checked, but PNAS offers a number of tracks for submission, all of which are refereed (though cynics might think that some are refereed more stringently than others). The information is displayed for all to see at their information for authors page.
It's easy - just have a good writer release a few Bible Code books.
- Bible code for children
- Bible code for dummies
- Bible code howto
India has had a long standing history in mathematics much of which predates that in the Islamo-christian tradition.
......
Formal mathematical schooling among Brahmins was particularly important among people in Tamil Nadu and Kerala, two of the sea-faring communities in India. Ramanujan belonged to the Iyengar tradition of mathematics (although many people related Iyengars to Yoga...) from Tamil Nadu.
Among other contributions of Indian mathematics include
Pre-ACE
The decimal system and the number zero
Inductive reasoning and the inductive method
Fractions
Equations
Mathematical tables
Binomial theorem
Pythogorean theorem
Area calculations
Conic sections
Irrational numbers
Boolean Logic
Null Sets
Transformations and recursions
Number theory
Trignometry
Formal language and grammar theory
Post ACE (pre renaissance)
Cubic and Quartic Equations
Pi as an infinite series
Geometric and Harmonic series
Series theory
Permutations and combinations
Cardinal numbers
Transfinite numbers
Set theory
Fibonnacci series
Derivative
Rolles theorem
Differentiation
Limits
Differential and integral calculus (predating Leibnitz and Newton by 200 years)
For a laundry list see
http://en.wikipedia.org/wiki/Indian_mathematics
Some of these brahmanic schools were far more advanced than European schools. Ramanujan had good schooling from a tradition steeped in mathematics. He was Europe's first direct exposure (as opposed to published books that were translated) to Indian mathematics hence the cult status.
Imagine a Narayana Pandit or a Chitrabhanu from the Kerala schools in Europe in 1500 AD spouting Calculus and Reimann's theorem (two well known theorems in India at that time)... they too would have been declared as geniuses.
-S
Technically, since the intestinal tract runs from mouth to ass in one go, a rabbit should be considered a torus.
You're leaving out the nasal cavity and nostrils. These also lead to the throat and the rest of the intestinal tract. Thus a rabbit is identical to a pretzel.
When our name is on the back of your car, we're behind you all the way!
Here is a link to a more informative article: http://www.telegraphindia.com/1050411/asp/knowhow/ story_4560152.asp
So get creative.
IANAL but write like a drunk one.
I've often thought that the grammatical structures of the various languages, profoundly affects the way people think. There has always seemed to be an unusually high number of Indian mathematicians, German/Scotts engineers, Irish poets, etc. IS this just playing into stereotypes, or does the way that words are strung together affect the thought patterns, making it easier to do, or create certain things. Clearly there are some economic issues - to create math, all one needs is a paper and pencil, but I think there is more to that. Moreover, if everyone starts to speak the same language, or if some languages die out, will we lose a group of people who may be talented in a useful area?
..........FULL STOP.
Mock Theta Soup.... *gargle*
There have been studies that support your theory.
...sometimes, in order to hurt someone very badly, you have to tell that person terrible lies. - PA
Alcohol and mock theta functions don't mix. You should never drink and derive.
What if the Hokey Pokey really is what it's all about?
You fail at life. Or at least at using the preview button. And yes, I am hitting the Preview button.
You all have Oo.o and Firefox, so get World Wind.
I didn't realize math was so naughty. This gives the name, Norbert Weiner, more meaning.
Did you notice the Google ads on this page? "Sympathy gifts," "Living wills," "Estate planning." I looked aroung the page to figure out why Google picked these ads. It must be because of the word "deathbed" in the article!
That that is is that that that that is not is not.
Slashdot text boxes are huge. You should have said you couldn't get all the symbols and numbers past the lameness filter ;)
qntm.org
This might lead to even better cryptographic encoding functions. See the relationship between elliptic functions and cryptography here.
DNA is a Turing machine. You, however, being dynamic and emergent, are not.