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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."
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).
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.
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