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Classic Math Puzzle Cracked
Posted by
timothy
on Tue Mar 22, 2005 07:23 PM
from the numberology dept.
from the numberology dept.
An anonymous reader writes "This is cool - if mind-bending. A century ago, a self-taught math genius from India noticed some patterns in how numbers can be created by adding other numbers. Now a grad student has finished the job showing that the patterns apply to all prime numbers, not just some. There's more on the Indian math guy here."
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Srinivasa Ramanujan? (Score:5, Informative)
Re:Srinivasa Ramanujan? (Score:5, Insightful)
My thoughts exactly. I wonder, will the next article about relativity reference "some German physics guy"? Or, for that matter, should we be on the lookout for articles about an operating system software codes invented by a Finlandish computer guy?
--MarkusQ
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Re:Srinivasa Ramanujan? (Score:4, Insightful)
Maybe it's time that we pulled in Indian editors to /., perhaps they could help push quality up a notch.
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Re:Srinivasa Ramanujan? (Score:5, Funny)
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Re:Srinivasa Ramanujan? (Score:4, Insightful)
[Gets out bullhorn:]
It is very obvious that the submitter was CONSCIOUSLY referring to Ramanujan as "some Indian guy or something, Idontrememberhisname" in a tounge-in-cheek way, a technique frequently used by those of us who possess an actual sense of humor. Please do not be alarmed or otherwise let this information affect your propensity for righteous indignation in the future. That is all.
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Re:Srinivasa Ramanujan? (Score:5, Funny)
This will in turn reduce productivity in India so much that America becomes competitive again! Brilliant!
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Does this remind anyone of Bill and Ted's? (Score:5, Insightful)
and:
"If I was a short French dude from the past where would I go?"
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Re:Srinivasa Ramanujan? (Score:5, Insightful)
Most
Also, the fact that the link to the bio was included seems to indicate that "anonymous reader" does know and care who "the Indian math guy" was.
I apologize in advance for the following rant:
The sad thing is that much of readership of
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Re:Srinivasa Ramanujan? (Score:4, Insightful)
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Re:Srinivasa Ramanujan? (Score:5, Interesting)
There was another genius like this, only he was a musical genius. There was an African-American slave in the mid-1800's who could play nearly anything on the piano after hearing it once or twice. He was a 'field slave', not a 'house slave'. He used to sneak up to the plantation manor house and listen to visiting musicians play Bach and Mozart on the piano. He was caught one night playing Bach on piano in the manor house and only escaped being whipped to death by his unbelievable talent. He also had the ability to sit down at the piano and play any chord that someone else had just played. He could do by ear.
His 'master', the plantation owner, took him on concert tours around the US, even to the North where this black genius was not a legally-owned slave and would have been able to receive politcal asylum and freedom. But he always returned to the plantation with the 'master', as he was illiterate and uncomfortable among the northern wealthy gentry.
I know that this guy existed; he was a genius whose type of talent appears only in one of ten million people, but I have no idea what his name was. Maybe some Slashdotters who are seriously into African-American musical history could let us know.
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Better example of unexpected genius (Score:4, Interesting)
Mir Sultan Khan arrived in England in 1929 as manservant to an Indian Maharaja, and immediately took the European chess world by storm (the Wikipedia article [wikipedia.org] compares him to Morphy). He convincingly defeated all the great players of that era -- Alekhine, Capablanca, Euwe, Rubenstein, more, but when the American master Reuben Fine visited the maharaja's digs in London, Khan was the waiter who served the meal. In 1933, the maharaja left England and Khan was taken back to India: no more tournament chess for him.
His story is not the same as the story of Blind Tom, in spite of cetain similarities. There is no indication that Khan's owner/employer exploited those remarkable talents, and the talents were in fact measurably remarkable. In the case of Blind Tom, one is tempted to think of S. Johnson's remark: "Sir, a woman's preaching is like a dog's walking on his hind legs. It is not done well; but you are surprised to find it done at all." [from Boswell's Life of Johnson]
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Re:Don't kid yourself. (Score:4, Insightful)
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Re:Don't kid yourself. (Score:4, Insightful)
That said, my guess is that the poster had copied the URL of the story and couldn't remember how to spell Ramanujan, and just used some shorthand which came off as a slight where one wasn't intended. The myriad of inevitable offshoring jokes are much more offensive than the (correct if somewhat lame) description of Ramanujan as an "Indian math guy."
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Good Will Hunting (Score:4, Informative)
If you took number theory or some high level mathematics courses and never heard about Srinivasa Ramanujan it would be akin to studying relativistic physics and never hearing about Albert Einstein .
Most people probably heard about Ramanujan recently from the movie "Good Will Hunting" [imdb.com]. Where they refer to Ramanujan by name several time during the movie, although they totally butchered his name and made me cringe every time they said it. The movie is based on a Ramanujan type character, in Hollywood fashion though. Where a young good looking confidant and outgoing Matt Damon with the physique of a construction worker plays the math genius. Ramanujan was shy, introvert, awkward and not in the best physical health.
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Re:Don't kid yourself. (Score:4, Insightful)
Funny that your parochial flamebait happens to be true. Ramanujan was definitively smarter than either of them.
Not to put down Big Al, but he only had a small armful of memorable discoveries spread over the decades of his career. OTOH, Ramanujan pumped out astonishingly brilliant stuff pretty much every day of his sadly brief adult life.
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Re:Don't kid yourself. (Score:5, Informative)
You are kidding, right? Sure, as Einstein grew older, he produced less and less, but here's what he did in 1905 alone:
"A New Determination of Molecular Dimensions" (Einstein's doctoral dissertation) (30 April 1905)
Buchdruckerei K. J. Wyss, Bern, 1906.
Also: Annalen der Physik, 19(1906), pp. 289-305.
This is Einstein's doctoral dissertation, submitted after much delay to the University of Zurich. In it he uses available physical data on the diffusion of sugar in solution and the effect of dissolved sugar on the solution's viscosity to determine the size of sugar molecules and Avogadro's number. The analysis makes the kinetic theory of heat more definite, in so far as it provides a measure of the real size of molecules, so that they cannot be dismissed as easily as useful fictions. It is the least impressive of Einstein's work of 1905 although, curiously, the most cited.
"On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." (Brownian motion paper) (May 1905; received 11 May 1905)
Annalen der Physik, 17(1905), pp. 549-560.
In this paper Einstein reports that the kinetic theory of heat predicts that small particles suspended in water must execute a random motion visible under the microscope. He suspects this motion is Brownian motion but has insufficient data to affirm it. The prediction is a powerful test of the truth of the kinetic theory of heat. A failure to observe the effect would refute the theory. If it is seen and measured, it provides a way to estimate Avogadro's number. The domain in which the effect is observed is one in which the second law of thermodynamics no longer holds, a disturbing result for the energeticists of the time.
"On the electrodynamics of moving bodies" (special relativity) (June 1905; received 30 June 1905)
Annalen der Physik, 17(1905), pp. 891-921.
Einstein develops the special theory of relativity in this paper. His concern, as he makes clear in the introduction, is that then current electrodynamics harbors a state of rest, the ether state of rest, and the theory gives very different accounts of electrodynamic processes at rest or moving in the ether. But experiments in electrodynamics and optic have provided no way to determine which is the ether state of rest of all inertial state of motion. Einstein shows that Maxwell-Lorentz electrodynamics has in fact always obeyed a principle of relativity of inertial motion. We just failed to notice it since we tacitly thought that space and time had Newtonian properties, not those of special relativity.
"Does the inertia of a body depend on its energy content?" (E=mc2) (September 1905; received 27 September 1905) Annalen der Physik, 18(1905), pp. 639-41.
Written as a brief follow-up to the special relativity paper, this short note derives the inertial of energy: all energy E also has an inertia E/c2.
"On a heuristic viewpoint concerning the production and transformation of light." (light quantum/photoelectric effect paper) (17 March 1905)
Annalen der Physik, 17(1905), pp. 132-148.
While the victory in the 19th century of the electromagnetic wave theory of light over Newton's corpuscle view is undeniable, Einstein shows that its success is incomplete. The theory gives incorrect results for the analysis of heat radiation. He looks at the thermodynamic properties of high frequency heat radiation and finds that this radiation behaves just like a collection of many spatially localized units ("quanta") of energy of magnitude hf (h=Planck's constant, f=frequency). He proceeds to show how this quantum view of light makes sense of several experiments in electrodynamics and optics, the best know being the photoelectric effect. He then described the paper as "revolutionary."
And these were on wildly different apsects of physics -- Brownian motion, Relativity, Statistical Mechanics, Photoele
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Re:Don't kid yourself. (Score:4, Interesting)
I wouldn't want to put him down.
But I agree that Ramanujan was a phenomenon. He was so completely different from any of his contemporary mathematicians that there is really no comparison.
He was discovered by the west when he sent a manuscript to Hardy, a famous English mathematician. Hardy almost discarded it, since much of it was stuff he had seen before (though Ramanujan had rediscovered it independently), but it also contained 120 thereoms no one but Ramanujan had ever seen before.
Later, when he came to England, Ramanujan filled notebooks with thousands of theorems, though not, apparently with proofs. I think proving Ramanujan's thereoms is still a major occupation of academia.
Interestingly, there is a similar story involving Einstein. Bose, who was an unknown Indian physics instructor, sent an unsolicited manuscript to Einstein which eventually led to the theory of Bose statistics, or Bose-Einstein statistics and the Bose condensate.
Crackpots from all over the world were sending Einstein manuscripts, and Bose's manuscript looked a lot like one of these. But Einstein read it anyway, and saw that Bose's ideas had merit. Ultimately, it seemed that Bose only had the one really good idea in him, and after collaborating with Einstein on the one paper, he went back to India and continued teaching. Apparently he was an especially good teacher.
MM
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Re:The really annoying part. (Score:5, Informative)
I just moused over, and it's in the freaking URL.
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ramanujan (Score:5, Informative)
Also at physorg [physorg.com].
It all deals with the Partition function [wolfram.com].
Ramanujan Biography (Score:5, Informative)
It's really interesting. Ramanujan was doing all this brilliant number theory on his own in India, and he decided to start sending his ideas around. He contacted several brilliant mathematicians, none of whom could figure out what he was talking about, largely because Ramanujan had some peculiar ways of expressing things. Finally Ramanujan contacted G. H. Hardy (at Cambridge), who saw his potential. Hardy invited Ramanujan to come to Cambridge right away, but couldn't get him to come because Ramanujan was a devout Hindu, and felt that he would be permanently "polluted" were he to leave India. Eventually, Ramanujan came to an agreement with his mother and went to spend time with Hardy, who spent a great deal of time helping Ramanujan convert his raw ideas into a more traditional, presentable form for maths journals. Ramanujan had a tough time in Cambridge, because he really didn't fit in. Eventually, he became very sick (tuberculosis, I think), and died. My understanding is that serious mathematicians are continuing to gather many new ideas in number theory from Ramanujan's notebooks, which are published by Springer-Verlag [amazon.com].
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Interesting (Score:4, Funny)
Why is this important to us? (Score:4, Informative)
Know your math department (Score:5, Insightful)
Well, then don't go to the Pure Math department when you're asking questions about Applied Math! Don't go to the C&O department, and ask about Statistics, and don't go the Actuary Science department, and ask about Accounting! Yes, they're all within the Math Faculty, but you have to pick your department correctly, or you won't get the answers you want! Sheesh! You wouldn't go to a French professor, and get all annoyed that they didn't speak ancient greek, would you? They're in the Arts Faculty, but Ancient Greek belongs to the Classical Studies department, and French belongs to Romance Languages department.
There is a lot of mathematics out there with real world applications: modeling for physics and engineering, non-linear statistical methods for stock market analysis, all sorts of new crypographic methods and applications, graphical rendering engines; tons of stuff.
Typically, pure math is far in advance of real-world applications: most of the mathematics we use today had no "real world" application when it was first concieved of. Field theory was considered "useless" when it was created, but it forms the heart of both modern cryptography, and of error correcting codes. These two, in turn, have become crucial to the success of our banking and telecommunications industries.
New insights into eliptic curves are yielding a new form of cryptography; the discrete logarithm problem forms the basis of another. Ten years ago, quantum computing was a matter of purely speculative mathematics; today, it exists as an experimental science.
Imaginary numbers were so named because no one figured they had real world uses: today, they're taught as a practical matter for electrical engineers to use in their electronics calculations. Taylor series approximations take the guesswork out of sin and cosine calculations, polynomial interpolation techniques allows computation of a "curve of best fit" for arbitrary scientific data, and every modern engineer is now aquainted with Fourier's transform. Some of Benoit Mandlebrot's notions about fractals were used to create JPEG compression, in common use on the Internet. Wavelet theory is currently being developed to attempt to improve on current methods.
Math is pushing ahead very fast; the real reason you don't usually see it is because it's often right at the heart of things; deep inside our hashing algorithms, hidden in a cryptography library, working behind the scenes as the statistical underpinnings of a successful greylist design that keeps spam away. It's in the boolean algebras that were used to design an efficient circuit layout, and in the iterative methods used to compute a new airfoil design. It's everywhere.
--
AC
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Re:Know your math department (Score:5, Informative)
Gauss [wikipedia.org] did quite a lot of things in math, but inventing imaginary numbers was not one of them. These numbers were known long before him and their name was coined by Rene Descartes, as a quick glance at wikipedia [wikipedia.org] would reveal. Incidentally, Descartes named the numbers imaginary exactly because he did not believe they could "exist."
Gauss was french
Gauss was one of the greatest german mathematicians, my friend.
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True story (I may post it again sometime) (Score:4, Funny)
The applicant gave a very interesting presentation. I got lost during the first 5 minutes when he was still giving background, but it was still interesting. His presentation was on - assuming that I remember any of the very little that I may have understood - some specific behaviors of the infinite boundaries of n-dimensional manifolds.
The best part was when he said, "In case you think that this is just esoteric and 'out there,' I want you to know that this stuff has real applications in topology."
There were about 6 other grad students and 15 math faculty there and I think I was the only one to notice how funny that was, so I'm sorry if you don't get the joke.
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Re:Why is this important to us? (Score:5, Interesting)
Compression algorithms map one huge number (consider an entire file as one huge number) to another. They "work" because most huge numbers of interest in a given domain aren't valid; random ASCII is gibberish, not English, so we remap that "random" looking stuff to stuff of more interest. This allows us to pack the interesting things much more tightly into the small numbers.
But for every number we shorten, we must also lengthen a number. Real-world algorithms do clever things to minimize the real-world impact of this fact, so you don't see it, but it's obvious if you think about it. If you have a sequence "1 2 3 4 5 6 7 8 9 10" which maps back to 1-10, for every number you pull down (move 8 -> 2), another number moves up.
No matter what you do, you can't create a magical compression algorithm that can be the "DNA" of all other numbers. You didn't say this directly, but a lot of people have this idea floating around in their head and I sort of "smell" it in your post.
(Proof: Suppose you have a compression algorithm that always shortens a number, and the corresponding decryption function. (Note we don't assume anything about the nature of the algorithm other than the compression, so it applies to all such algorithms, no matter how fancy the math.) Of the binary numbers 00, 01, 10, 11, each is therefore shortened to 1 bit. But there are only two possibilities for that one bit, and it has to cover 4 numbers. This is not possible for a decompression function by definition of "function". Therefore, contradiction, and there is no such compression algorithm.
I left the terminology a little fuzzy to try to prevent Math Overload; mathematicians should be able to fill in the blanks fairly easily.)
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Vaguest post I've ever seen (Score:5, Informative)
That's got to be the worst write up I've ever seen on /.
This statement implies that the genius is famous because he noticed that there is/are pattern(s) in how you can add up numbers to get other numbers . . . that statement is so vague that the discovery could be incredible or intuitively obvious.
Quoted from one of the links is a much better explanation below:
One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. The problem of finding p(n) was studied by Euler, who found a formula for the generating function of p(n) (that is, for the infinite series whose nth term is p(n)xn). While this allows one to calculate p(n) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula (though they only proved it works asymptotically; Rademacher proved it gives the exact value of p(n)).
Dissappointing (Score:5, Insightful)
I thought this was news for nerds, sure maybe not everyone knows who Ramanujan was, but a good proportion should, at least enough that you don't have to demean him with a vague description.
Re:Dissappointing (Score:5, Insightful)
Seemed disrespectful to me - specially for a guy who's probably brighter than 99% of anyone in
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Ramanujan was one of the greats of mathematics. (Score:5, Informative)
I believe that the American Mathematical Society wrote up a nice review of his lost or last notebook a few years ago.
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Re:Dissappointing (Score:4, Interesting)
IMO:
He could not have worked in India. He needed a lot of personal tutoring and contact with first-rate mathematicians, and there haven't been many mathemeticians as first-rate as G. H. Hardy.
Whether the early death was worth (to the world or to Ramanujan) the growth (to math, to Ramanujan, and to Hardy) that came from the Ramanujan-Hardy collaboration, I don't know.
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yeah (Score:4, Funny)
yeah, I saw that too. Like, how if you have a 4, and add a 1, you get a 5. It's pretty cool.
meth (Score:4, Funny)
ah crank [wikipedia.org].. is there anything it cant do?
Na-hee-na-na-jar (Score:5, Funny)
It's not that difficult."
"Yeah, well at least your name isn't Michael Bolton."
Re:Na-hee-na-na-jar (Score:4, Funny)
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Discoverer? (Score:5, Interesting)
It is interesting that the New Scientist article basically attributes the idea of studying number partitions to Ramanujan, yet the linked article on him mentions that Euler had studied the problem before, and given a partial solution...
Obilgatory story (Score:5, Interesting)
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."
(London 1940).
Re:Obilgatory story (Score:5, Informative)
9^3 + 10^3 = 729 + 1000 = 1729
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Re:Obilgatory story (Score:4, Funny)
by uniqueCondition (769252) on Tuesday March 22, @07:45PM (#12018209)
GH Hardy (he wrote A Mathematician's Apology) speaking of Ramanujan:
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."
(London 1940).
A funny co-incidence happened about 10 years ago that brought this story to mind when I moved back from A2 to Detroit. Our new phone number ended in 1729. Of course my GF complained that it would be hard to remember since it was such an un-interesting phone number!
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How incredibly sad (Score:5, Insightful)
Russell (Score:5, Informative)
The coolest reference on Hardy's reaction to Ramanujan's initial letter is seen in a letter that was sent by Bertrand Russell to an acquaintance. It goes something like:
"Saw Littlewood and Hardy in a considerable state of excitement. They claim to have discovered a second Newton, a Hindu clerk working in Madras for 20 pounds a year...It's all secret now, of course. I feel excited to know this"
From: Ramanujan: Letters and Commenary
Bruce C. Berndt and Robert L. Rankin.
American Mathematical Society-London Mathematical Society.
Numbers were there before the big bang (Score:5, Funny)
Mystery Illness? (Score:5, Informative)
He didn't die from a "mystery illness", he died from tuberculosis (or as it was called back then, the consumption).
In other news... (Score:5, Funny)
(I think you get the point)
Don't forget Pi... (Score:5, Informative)
That's the first thing I thought of when I saw the article text, and I was kind of disappointed it wasn't about that particular aspect of Ramanujan.
Indian math guy!?? (Score:5, Insightful)
some guy??????? (Score:4, Insightful)
Have some decency. Recognize genius and respect it. What have you accomplished? Even 1/10th of what any respected scientist has? Don't you expect people to call you by your name and not "hey you"? Why not give the same respect to others?
I'm also surprised that the Slashdot editors let this story be published without correcting it!! What, are story submissions now governed by a perl script?
RANT OFF.
Re:What's in a name? (Score:5, Insightful)
The summary didn't name Karl Mahlburg, the subject of the article, either.
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Re:You could at least use his name in the article (Score:4, Funny)
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Also suggests a low number of Indian maths guys (Score:4, Interesting)
India has a very long history of mathematics. eg. Pythagoras theorom was proven in India long before Pythagoras was even born.
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