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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."
Spell error in story title! Its Ramanujan, without the 'i'.
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
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).
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.
To answer this very loosely, parts of these functions are bounded by geodesics with cusps at the corners, and this means that any geodesic structure of this type (certain types of chemical structures and a slew of phenomena in relativistic physics) can be partly described by those pieces of these functions and that it is possible that these functions represent a certain type of generalization for these structures, allowing scientists to better describe some existing structures with similar modular forms and even some that exist only in thought.
Not quite.
He did not have advanced learning in math.
even though he went to school, in the end he was so enamored with maths that he stopped studying everything else, which cost him high. He was unable to get through to college. Thus, his knowledge was limited and was from primarily two books he found in the library.
Hardy once even mentioned that his greatest regret was that Ramanujan did not have the higher learning that would have avoided him rediscovering many - many theories. On one count, 1/3 of his discoveries were re-discoveries
He won prizes at school for his maths prowess, and went to university on a scholarship. He lost the scholarhip due to his obsessive inability to do other aspects of the curiculum that were not maths related, or which were offensive to his Brahman beliefs. There was never any doubt that he was mathematically gifted, and his mother promoted him intensively. There seems to be a myth that he was an illiterate peasant who happened to stumble on a maths book came from, but I don't know where it came from.
You know what they say about opinions. They're all fabulous!
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
Ramanujan's family was NOT poor. His father was among the first rung of urban middle-class professionals, who've just moved from their villages as (colonial) India's cities started expanding, finding employment as a minor clerk somewhere. His mother was very educated, and often sang in the local temple, thus earning some petty, but useful, cash in the process.
They weren't well-off, but they weren't poor either. Ramanujan had no absolutely pressure whatsoever to find an actual job while he was sitting in the verandah of his Sarangapani Street house, and writing his fantastical proofs in that mystical notebook of his. (In fact, he got married while he was jobless, a prospect that is unimaginable even in still-arranged-marriage-friendly contemporary India).
More than mere navel gazing.
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