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."

Comments

Good job!

[UbuntuDupe]

The summary didn't refer to Ramanujan as "the Indian math guy" this time! Great work! (Don't ask how I remember that one.)

Although, it could do with one less "i" ...

Ramanujan

[theurge14]

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.

Re:Ramanujan

[OldManAndTheC]

It's sad to think that geniuses may languish among the world's millions of underprivileged children who lack access to education. When you think of the potential impact of a single person of the caliber of Mozart, Ramanujan, etc., our civilization could be missing out on some truly wonderful things.

Re:Ramanujan

[MrBoombasticfantasti]

Still, that means that 2/3 of his discoveries are new and original!

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?

Re:Ramanujan

[rxmd]

Quoted from Hardy "So the real tragedy of Ramanujan was not his early death at the age of 32, but that in his most formative years, he did not receive proper training, and so a significant part of his work was rediscovery..."

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.)

Re:Ramanujan

[be-fan]

And how many potential geniuses do we miss out on when we teach 50% of our population to prioritize making babies over perusing their talents and goals?

Re:Ramanujan

[jahudabudy]

just that the education system has a strong tendency to indoctrinate those [Democratic] values

You 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 could reflect some sort of bias in the educational system, or it could simply reflect a bias of informed, intelligent people towards Democrat. If I were trying to support the Republican party, I think I would try to downplay this particular trend. Then again, what do I know about political maneuvering?

Disappointing

[grimdawg]

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?

Ease of understanding & teaching.

[Anonymous Coward]

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.

Re:Ease of understanding & teaching.

[muecksteiner]

You have a very good point about math generally not being taught as well as it could be.

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.

[langarto]

Looks like your university was crap, no matter how famous it was.

Re:Ease of understanding & teaching.

[Ibag]

Teaching mathematics is difficult. Many people can only think about things in terms of concrete examples, but even when math is trying to generalize a real world concept, it generally does so by using abstract looking definitions (which are made using precise terms, often employing a symbolic language). People generally don't care about these abstract ideas, though. They either want to know what a concept "means" or exactly how to use it. Often times, there aren't any good examples that illustrate exactly what something is, and which people could soundly base their understand on. Moreover, before university, many teachers don't understand what they are actually teaching, so they can't impart any real insight.

If you were told to explain a toolbox to a group of people, without being allowed to pull in outside material (like wood or nails), and the people were looking for some sort of deep appreciation for a screw driver, you would probably have difficulty even if you were a professional carpenter. No cries of "You will need to know this later!" will make people pay attention, and you will be hard pressed to find something that will actually help people understand.

What needs to be done is that people need to learn to think at an early age, become comfortable with abstract ideas, and the people teaching children about math need to understand what they are saying (so that they don't then say something wrong which forever taints someone's thinking). That way, when people get to college, they won't have to drop engineering classes because they don't like math.

Re:Indian mathematicians

[ChrisMaple]

Some nationalities (and more importantly, some cultures) have a history of making contributions to various aspects of civilization out of proportion to their numbers. It is both interesting to find these correlations and important to find cause-and-effect relations if they exist. Getting annoyed because people point them out, and flaming them, is not a contribution.