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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.
"Andrews says the methods used to arrive at the result will probably be applicable to problems in areas far afield from mathematics. He and Mahlburg note partitions have been used previously in understanding the various ways particles can arrange themselves, as well as in encrypting credit card information sent over the internet."
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)).
Straight from the horses mouth... http://www.news.wisc.edu/10833.html I saw that a few days ago during the Nanotechnology article; I never thought of submitting it.
Would you kindly mod me +1 insightful?
Not really. It only works if you are Muslim and male there. Pakistan actually has laws which include rape as a punishment for women, and the system also encourages killing of non-Muslims by specifically (in the code of law) making the killing of a non-Muslim a minor crime compared to the killing of a Muslim. I can provide links to both horrific laws if you want. That is not very intellectual or nurturing. Islam has absolutely no place in law, and any country that governs by Islamic law is declaring a war on those who don't worship the Muslim god. That is rather anti-intellectual. The same goes, of course, for any government that forces any religion on its people, including Christianity.
Don't blame Durga. I voted for Centauri.
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..."
9^3 + 10^3 = 729 + 1000 = 1729
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.
I was going to mention the Robert Kanigel book as well. It's a great book. You've beaten me to the punch.
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.
Only the civil code is non-uniform. This deals with marriage, divorce and inheritance, for instance.
A murder is a criminal case, and it is uniformly treated in the Indian Penal Code, irrespective of the usual divisions.
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.
His name is in the first sentence.
I just moused over, and it's in the freaking URL.
The best general reading about applied math in the context of Ramanujan's work and life are in G.H. Hardy's A Mathematician's Apology and Robert Kanigel's The Man Who Knew Infinity. Both are excellent reads for non mathematicians.
Almost as interesting is looking into how much human coaching AM took to come up with the results - its not all that clear how much human intervention was involved, but I've certainly heard AI researchers cast a nasturtium or two on AM (and its successor Eurisko) because the results were essentially unreproducable.
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.
Thanks for the FUD, asshat. Ramanujan died of tuberculosis.
Gauss 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 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.
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". 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.
Wikipedia has its own version of the blind slave pianist:
http://en.wikipedia.org/wiki/Blind_Tom
-- Juanco