Ramanujian's Deathbed Problem Cracked 205
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."
Spelling error (Score:4, Informative)
Bloody lack of details... (Score:5, Informative)
Guess the wiki [wikipedia.org] still needs to be updated
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"I want to work in Theory -- everything works in Theory!" -- John Cash, id
Ramanujan keeps getting more impressive... (Score:3, Informative)
Re:Lack of information (Score:5, Informative)
This is cool and all, but the real kicker will be if Peter Sarnak from Princeton proves the Riemann Hypothesis [wikipedia.org] (rumor has it he is on the way to doing so).
Ken Ono's seminar (Score:5, Informative)
Re:Real World Uses? (Score:4, Informative)
Re:Ramanujan (Score:3, Informative)
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
Re:Ramanujan (Score:4, Informative)
the man who knew infinity (Score:5, Informative)
Re:Ramanujan (Score:3, Informative)
Ramanujan is mentioned in the movie Good Will Hunting [wikipedia.org] and that is how he is presented. That's the first time I heard of him. I'm sure people just use that myth because it's not too far from the truth and makes a much better story.
Re:Ramanujan (Score:3, Informative)
And yes there were instances during his life when he struggled for money, even to eat.
I'm not saying rich or poor makes you smart. I'm saying being poor tends to keep you from being discovered by the rest of us. The immense contributions of Ramanujan could have been lost to us all if Hardy had not taken the chance to bring a total unknown to Cambridge.
Re:Bloody lack of details... (Score:5, Informative)
Arxiv doesn't appear to carry the paper, and only two papers in it relate to mock theta functions at all. One of them is a transformation formula for second-order mock theta functions [arxiv.org] and the other talks about mock theta functions as quantum invariants [arxiv.org], whatever that means. A glance at the paper suggests that mock theta functions relate to a key element in topology, but my maths isn't nearly good enough to tell you exactly what is being described.
Re:Credibility? (Score:2, Informative)
Re:Ramanujan (Score:4, Informative)
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).
Re:Mock theta functions? (Score:1, Informative)
Indian mathematicians (Score:5, Informative)
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 [wikipedia.org]
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
Non-Torroidial Rabbits (Score:3, Informative)
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 [wikipedia.org].
More informative article (Score:2, Informative)
Re:Indian mathematicians (Score:1, Informative)
That would be a fair assessment if Ramanujan was merely stating things that other Brahmins knew, or if he had not rediscovered much of higher mathematics by himself. Since he was stating theorems (he did not often provide proofs for his own work) that nobody else in the world would know were true until decades after his death, it's not unfair to call him a genius. To give you some idea of his insight, he wrote down about 3,000 theorems in his lifetime - one of my undergraduate professors (David Bressoud) did his PhD thesis on the proof of one of the unsolved theorems from Ramanujan's notebooks.