Slashdot Mirror
Classic Math Puzzle Cracked
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."
you mean Srinivasa Ramanujan
Due to financial difficulties, the light at the end of the tunnel has been turned off.
More on Ramanujan at St. Andrews
Also at physorg.
It all deals with the Partition function.
The Indian mathematician outsourced this to a US grad student
"I'd rather be a lightning rod than a seismometer." -Ken Kesey
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)).
That Ramanujan is refered to as `that Indian math guy'...
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.
a self-taught math genius from India noticed some patterns in how numbers can be created by adding other numbers.
yeah, I saw that too. Like, how if you have a 4, and add a 1, you get a 5. It's pretty cool.
"We would not have expected that the crank would have been the right answer to so many of these congruence theorems"
ah crank.. is there anything it cant do?
"Na-hee, na-na-jar. Na-hee-na-na-jar.
It's not that difficult."
"Yeah, well at least your name isn't Michael Bolton."
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...
Repton.
They say that only an experienced wizard can do the tengu shuffle.
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).
"The more you know, the less sure you are." - Voltaire
The summary didn't name Karl Mahlburg, the subject of the article, either.
... that Ramanujan gets referred to on slashdot as the "Indian math guy" and is followed by jokes on outsourcing. You can read about him at http://scienceworld.wolfram.com/biography/Ramanuja n.html
or read the book "The Man who knew infinity" by Robert Kanigel.
He had remarkable contributions in number theory, all made
with very little formal training. His story cannot be explained
in any other way but supreme in-born genius (he himself explained it by inspiration from the goddess Namagiri).
The attitude to math in the general populace is one of total
avoidance. I had hopes that the average slashdotter was different.
I believe that the American Mathematical Society wrote up a nice review of his lost or last notebook a few years ago.
"sweet dreams are made of this..."
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.
"how numbers can be created by adding other numbers"... that sounds more like the observation of an American presidency guy.
He didn't die from a "mystery illness", he died from tuberculosis (or as it was called back then, the consumption).
My digital rights don't need management.
"A decade ago, a self-taught computer genius from Finland [...] There's more on the Finish computer guy here."
(I think you get the point)
The Pi symbol /. uses for Math articles is very appropriate in this case, because Ramanujan also came up with a formula for the numerical representation of Pi
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.
Show me on the doll where his noodly appendage touched you.
Ramanujan was one of the greatest mathematical geniuses of the 20th century. there are some people on./ who could do with some basic education.
When I was a PhD math student, I often annoyed professors by asking them about real-world applications, and usually got vague answers like the one quoted.
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
No.
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.)
"All you've learned was that Ceasar was a salad dressing dude."
and:
"If I was a short French dude from the past where would I go?"
These posts express my own personal views, not those of my employer
NOT in the same league as Einstein or Linus Torvalds
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.
His name is in the first sentence.
I just moused over, and it's in the freaking URL.
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."
Dude, I think I can see my house from here.
Not to put down Big Al, but he only had a small armful of memorable discoveries spread over the decades of his career.
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
"That's not even wrong..." -- Wolfgang Pauli
A wonderful biography of Ramanujan is, "The Man Who Knew Infinity: A Life of the Genius Ramanujan", by Robert Kanigel
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.
If you watch TV news, you know less about the world than if you just drank gin straight from the bottle.
By the same token, "German guess guy" is Heisenberg, "Italian nuke guy" is Fermi and "Slashdot condescension guy" is whoever bespoke "Indian math guy," referring to Ramanujan. Mathematics, made of pure thought, advances meteorically faster than the dull material world, let alone the moral, spiritual or (shall we call a spade a spade?) ethological world of semi-sentient apes and slash dotters. Ramanujan lived in a future virtually all of us cannot even imagine, and his name is revered, not because we understand him, but because he thought the future beautiful.
``Tension, apprehension & dissension have begun!'' - Duffy Wyg&, in Alfred Bester's _The Demolished Man_
What's up with that? So they only have names when they're American scientists? Do you know how much Srinivasa Ramanujam contributed to math??? Just because YOU don't know them does NOT make them any less deserving of the respect they SHOULD get from everyone for their contribution to the field!! Or are you just another one of those hicks who respects people based on their nationality and on rubbish like "if i don't know them, they're not worth knowing"?
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.
Find a job you like and you will never work a day in your life.
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 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]