## Ramanujian's Deathbed Problem Cracked 205

Posted
by
kdawson

from the mock-theta-soup dept.

from the mock-theta-soup dept.

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."*
## Good job! (Score:5, Insightful)

Although, it could do with one less "i"

## Re:Good job! (Score:5, Funny)

Armeniancreated a math problem?!"## Re:Good job! (Score:5, Funny)

doesseem like good work, but realistically we won't know how important it is until it appears as a deus ex machina device on NUMB3RS.## Re: (Score:2)

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One of the best comments I've read here in quite some time.

## Re:Good job! (Score:4, Funny)

"Hm, it seems this perp is following a pattern

[long and vague digression on Ramanujan's work that conveys nothing other than "it's complicated"]

[condescending reference to the hot chick's heritage]

"So that implies that he'll strike *here* next."

[catches perp]

****

Is that about right?

## Spelling error (Score:4, Informative)

## Re:Spelling error (Score:5, Funny)

## Re:Spelling error (Score:5, Funny)

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I think you imagined the "i""i" is a classic example of why you mathematicians and we programmers will NEVER get along

int i;

for(i= 0; i MAX; i++){}

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ifloating around somewhere.Those guys are complex.

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I think you imagined the "i"enter the existentialist theories...

## Re:Spelling error (Score:5, Funny)

Trying to Wick rotate him would be a pretty negative thing to do.

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## Curiously enough (Score:5, Funny)

There's gotta be a Scientology joke in there somewhere

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## Re:Curiously enough (Score:4, Funny)

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## Bloody lack of details... (Score:5, Informative)

Guess the wiki [wikipedia.org] still needs to be updated

--

"I want to work in Theory --

everything works in Theory!" -- John Cash, id## 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.

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There goes my Mock Theta Function solving hobby.

## Ramanujan keeps getting more impressive... (Score:3, Informative)

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I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."- Godfrey H. Hardy (1877-1947)

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## Ramanujan (Score:5, Insightful)

## Re:Ramanujan (Score:5, Interesting)

Math, being theoritical, does not require a lot of external resources (like laboratories etc.)

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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 dis

## Re:Ramanujan (Score:5, Insightful)

Might it be that education structures the mind to follow the known paths? Perhaps by not knowing the 'usual' solutions, you can come up with a more elegant and deep solution?

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When approaching a problem, I often avoid learning too much about how others have done it before I try to think of a way to solve it. Sometimes I come up with the same thing as widely accepted practice, and sometimes I come up with something that's significantly worse than widely accepted practice, and sometimes I come up with something better. That latter is much less likely to happen if I fully educate myself on other people's solutions first.

I do not think education is bad, and I'm not anti-intellect

## Re:Ramanujan (Score:4, Informative)

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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.

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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

## Re:Ramanujan (Score:5, Insightful)

At the same time, Hardy acknowledged that "on the other hand he would have been less of a Ramanujan, and more of a European professor, and the loss might have been greater than the gain." (From Hardy's article in "The American Mathematical Monthly" 44.3 (1937), p. 137-155.)

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Mozart comes to mind when I think of him.How? Mozart was very privileged. When his father saw a little musical talent in him, he threw plenty of resources to develop that talent including "instruction in clavier, violin, and organ." Wiki-link. [wikipedia.org] This was all at the age of 3 mind you, one has to take into consideration the amount that you can condition a human being to excel in a certain area if you train them from such an early age.

## Re:Ramanujan (Score:5, Insightful)

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Yes, but think of all the Hitlers we're also missing out on. We'd better play it safe and hold them down. Besides, they only discover things I don't care about or don't want to hear.

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Whenever someone says something like this (which is pretty frequently) it occurs to me, it's sad to think that

human beingslanguish among the world's millions of underprivileged children...But I guess the one-in-a-million starving, uneducated supergeniuses would affect us more :-P

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Okay, I'll play

Tough question. It's widely known that the intelligence distribution of women tends less toward both extremes, so a factor of 2 increase in geniuses is a very liberal upper bound.

On the other hand, if these geniuses have fewer children than they otherwise would, their genes will fail to be passed on. Since intelligence has a substant

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just that the education system has a strong tendency to indoctrinate those [Democratic] valuesYou know, I have heard this many, many times, mostly as an indictment of the educational system. I'm not saying the educational system doesn't have problems, but I always found this to be a weird thing for Republicans to point out. "Educated people tend to vote Democrat." It

couldreflect some sort of bias in the educational system, or it could simply reflect a bias of informed, intelligent people towards Dem## Re: (Score:2)

You've missed my point entirely. I'm not saying "educated people tend to vote Democrat". I'm trying to say that the education establishment has a strong influence over curricula, and is not above pushing their own agenda. It's an entirely different thing.

The fact that the education establishment is strongly Democrat-leaning is undeniable. That th

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## 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'tpooreither. 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).## Language effects on the brain may affect thought (Score:2)

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He was in and out of foster homes throughout childhood. He ended up taking up menial jobs at a local university to be around math. But he lost his job when he almost went to jail for assault and battery and hitting a cop. But luckily one of the professors at the university noticed he solved some "unsolvable" problem on a chalkboard and got him paroled.

He skips out on his parole, but Robin williams saves him by telling him it isn't his fault and he ends up driving cross-

## Real World Uses? (Score:2)

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.

## Re:Real World Uses? (Score:4, Informative)

## Ken Ono's seminar (Score:5, Informative)

## Obligatory (Score:5, Funny)

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Don't forget :

I have a discovered a truly marvelous demonstration of this proposition beneath your current threshold

The next truly marvelous demonstration will be ready soon, but subscribers can beat the rush and see it early!

## the man who knew infinity (Score:5, Informative)

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Ramanujan is the only person I've ever considered as an idol. That book is the reason. I've been to countless places after I first read the book; I still carry my dog-ear-ed copy wherever I go.

In fact, I think I'll re-re-read it again tonight; always good to look back on your heroes' stories and see where you are since you first read about them. (Not far away, I'm afraid, in my case).

## Disappointing (Score:5, Insightful)

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?

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## Ease of understanding & teaching. (Score:5, Insightful)

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.

## Re:Ease of understanding & teaching. (Score:5, Insightful)

Not in the sense that the curricula should be dumbed down in any way - this would not work out well in the long run.

But there definitely is a streak of the beloved "if it was hard to code, it should be hard to understand" mentality to be found in mathematics.

Introductory math courses at universities usually do not have concepts of such bewildering complexity on the curriculum, that they should be considered to be as "hard" as they turn out to be for everyone.

However, they still are the bane of undergrads everywhere, and sometimes I wonder if the obtuseness of these courses is not just an in-joke perpetrated by the mathematicians.

If you are not smart enough to "get it" in the arcane way the stuff is being presented, you woul not hack it further down the road anyway - at least not in pure math, and they are not inclined to have pity on anyone who could not have gone down that road in the first place.

Or so the reasoning might go, when mathematicians are amongst themselves...

Note that the remarks in this posting mostly apply to the teaching of the kind of "working math" that an engineer might use, which (to put it mildly) can still be pretty involved in terms of complexity, but always has a goal-oriented quality to it that pure math does not necessarily share. This residual "grounding in reality" usually makes the teaching of even advanced concepts much easier - a potential bonus that (at least in my opinion) is not used nearly as often as it could be.

A.

## Re:Ease of understanding & teaching. (Score:5, Interesting)

I can relate to that. I studied math at a famous university for a couple of years before I dropped out. Here are some of the things I remember:

We started with over 100 students in the first year. By the third year, the number had dropped to less than 10 students. Half of those dropped out later. The professors were proud of this fact.

Each lecture took three hours, with one fifteen minute break. You were only allowed to ask questions in the last 15 minutes of the lecture.

Professors only took the trouble to learn students' names when they entered third-year courses.

I once wrote a research paper for one of the professors for a first-year course. In the very last paragraph of the paper I wrote a little joke. The paper was marked "A", then the "A" was crossed out, "C-" written below it, with an arrow pointing to the joke.

Math students had access to the faculty mainframe (this was in the early 1980s), but did not get instruction on how to use it, as opposed to physics students. The reasoning was that math students either should not need computers for their work, or should be smart enough to figure it all out by studying the manuals.

Professors often supplied example excercises. Students were encouraged to make these excercises and supply their answers to the professor. However, these answers were NEVER corrected, so that after a while students simply did not bother anymore.

Professors were notorious for not preparing lectures, and working out examples as they were going along, often failing to prove what they wanted to prove. One particularly telling incident was when a professor was working out a complex proof, starting at the top left of one of the two four-piece blackboards in the hall, and chalking down, very fast, formula after formula. I was trying to follow his proof, but, of course, was always several lines behind. But I thought I did understand it, and was approaching to where he was. When he was at the bottom-right of the second blackboard, he paused, and kept staring at the last line he had written, muttering to himself. While I was approaching this last line (making lots of notes, because OF COURSE these proofs weren't in the textbooks or anything), he started scanning back. After doing this for about five minutes, he suddenly walked over to the first board again, changed a plus into a minus in one of the first lines, then made lots of changes in the rest of what he had written, and finally wrote "Q.E.D." at the bottom-right. Then he closed the blackboards and sent us on our way.

Through this experience I thought I simply was not good enough at math. But when I switched to computer science, where math courses were taught by computer scientists, I passed with flying colours, usually as the best of the class. Not because the courses were easier, but because they were taught better.

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Who gave you the right to criticize communication skills, Mr. Random Comma Guy?

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That's the inevitable backlash from exaggerating the importance of math to other fields. Speaking for computer science, there is a lot of CS that can be done without good math knowledge. If you make math a required subject, you will either hamper (otherwise) good computer scientists in getting degrees, or you will have to dumb down the math curriculum. I claim that both of these are happening.

## That would undoubtely help. (Score:2)

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I can just about guarantee that if you can explain why this solution matters, your post will go to +5 on the moderation scale.

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Take that, non-mathematical pundits and biologically unaware mathematicians!

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## Non-Torroidial Rabbits (Score:3, Informative)

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 [wikipedia.org].

## Mock functions... (Score:3, Funny)

I resent that mockery, you insensitive... oh, I thought you said

deride.## Re: (Score:2)

Thet a good joke...

## Has to be said... (Score:2)

## How to popularize math (Score:3, Funny)

- Bible code for children

- Bible code for dummies

- Bible code howto

## 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

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BCE = Before Christian Era

Basically a politically correct way of saying A.D (Anno Dominus = Year of the Lord) since not everyone believes in the christian "Lord"

-S

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era.## Re: (Score:2)

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Isn't it insulting to say "

I know what you're thinking, but Indians aren't stupid! They're as smart as we are! Look at all this stuff they've done!" ?Or maybe it's "

Look at all these great Indians! I'm an Indian just like them, therefore I'm one of them!" Except being a good mathematician has nothing to do with your race, there's just not that big of a difference between races.If this guy had a beard would you post all t

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## More informative article (Score:2, Informative)

## Google Ads relevant to "deathbed" (Score:2)

## 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).

## some of the good drs' papers (Score:2)

## Re:Lack of information (Score:5, Funny)

## you left math too early (Score:5, Funny)

## Re: (Score:2, Troll)

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.

## Re: (Score:2)

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

## Re:How to solve a mathematical mystery (Score:5, Funny)

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!

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Both PP and GPP being moderated Redundant

is clearly an indication of a lack of caffeine.

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