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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.)
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Although, it could do with one less "i"
Apology to Ubuntu forum.
Guess the wiki still needs to be updated
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"I want to work in Theory -- everything works in Theory!" -- John Cash, id
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).
But...but....with the "i" it almost anagrams to "marijuana"!
As a republican I feel it my responsibity to manufacture criminals. People need punished!
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.
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.
I think you imagined the "i"
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.
Ramanujan was already a complex guy.
Trying to Wick rotate him would be a pretty negative thing to do.
Reality must take precedence over public relations, for nature cannot be fooled.
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.
India has had a long standing history in mathematics much of which predates that in the Islamo-christian tradition.
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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