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69 Comments
- Gr00ver, on 09/22/2009, -1/+31▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲▲
- rotorbladesmoke, on 09/22/2009, -0/+26There isn't a comment witty enough to eclipse the sheer nerdpower coursing through this article.
- juliusthecat, on 09/22/2009, -0/+22Digg needs more of this and less politics / celebrity news.
- Osirus1156, on 09/22/2009, -0/+153Ds Max -> MeshSmooth -> MeshSmooth -> MeshSmooth -> Awe 3Ds Max crashed.
- RealmDown, on 09/22/2009, -1/+14I disagree. None of the angles in this article are obtuse.
- eihwaz, on 09/22/2009, -0/+12 "Old problems like this may seem obscure, but they generate a lot of interesting and useful research as people develop new ways to attack them."
- etx313, on 09/22/2009, -0/+10zbrush->subdivide->subdivide->subdivide->subdivide->subdivide->subdivide->subdivide->subdivide->subdivide
- daliminator, on 09/22/2009, -0/+9Yes... computer very power. Is good max.
- stuwanker, on 09/22/2009, -0/+9I can't really speak to practical applications, but I don't think we need computations on the order of this magnitude for any real world problems.
As far as the theory is concerned, think of this like a mathematical experiment. We have certain conjectures that we think are true--this Birch and Swinnerton-Dyer Conjecture (BSD), for example, or the connections between number theory and something called random matrix theory (which is used in physics and probability) that Rubenstein references. These computations help us determine whether these conjectures make sense or not. If the number match up, cool; if not, then we have to tweak things in our conjectures or possibly throw them out. Presumably the numbers that were calculated are consistent with Tunnell's result, and this fact would be consistent with the truth of BSD. (In fact, if the numbers were not consistent, then BSD would be false, and we'd be reading THAT story right now, as the Clay Institute would be paying someone $1,000,000 for the result.) Similarly, Rubenstein says that the numbers do match up with the predictions he gets from random matrix theory. Furthermore, in some number theoretic problems (e.g., my research), the ability to do so many computations with so many large numbers can actually allow us to PROVE things.
So, yeah, theoretically, it's neat. - xcpleprechaun, on 09/22/2009, -2/+10If mathematicians from North America, Europe, Australia and South America resolve the first one trillion cases of an ancient mathematics problem and nobody is able to understand them, does it really matter?
- rogeris, on 09/22/2009, -0/+7What is the practical purpose of a violinist?
- rossisdead, on 09/22/2009, -0/+6I don't think Diggers know much about gays and triangles.
- iseth, on 09/22/2009, -0/+6Distributed Computing is the term you're looking for.
- rkthoadan, on 09/22/2009, -0/+6Here... ∆
- kaelyiesta, on 09/22/2009, -0/+6I know the question is rhetorical but I'll answer anyway, as it also is the same answer I'd give to the question of 'practical application' of this mathematical conclusion.
The purpose is exercise, in a sense. Working to achieve is the natural desire of humans. Even as a child, one rarely leaves their mind at rest, instead they find ways to push themselves even when it's just playing. The natural state of mankind isn't to do nothing. - stuwanker, on 09/22/2009, -0/+6Presumably they mean regular sized handwriting. Let's say each digit takes up 1/2 cm. Then the numbers we're dealing with could have as many as 150 billion digits.
That's a lot. - Nitrodist88, on 09/22/2009, -4/+9So, does anyone know what this really means? What are the practical applications?
- Recyclable, on 09/22/2009, -0/+5Not for cryptography and many other applications :/
- geesamba, on 09/22/2009, -0/+4You're right, it's not a trillion triangles. But closeness of numbers is very much on the relative scale.
- LaughingMan89, on 09/22/2009, -0/+3Which is why it would've been nice to see a little blurb about the method of computations themselves.
- Origin415, on 09/22/2009, -0/+3All the prime numbers, meaning all the numbers within that sequence which are prime. Clearly you cant add 8 to a prime number and expect it to be prime.
- Origin415, on 09/22/2009, -0/+3Never ask a mathematician about practical applications.
Rather, pure mathematicians work on problems which are 'important'.
That said, the triangles themselves are neither, but advances in algorithms could be both. - Chinzon, on 09/22/2009, -1/+4Since they got rid of 7. Didn't you get the memo?
- etx313, on 09/22/2009, -1/+4Well that was very negative of you.
- Origin415, on 09/23/2009, -0/+2Of course I meant in general, theres no reason that p+8 needs to be prime if p is prime. In fact exactly one of n, n + 8, and n + 16 has to be divisible by 3, for all n.
- Scotty87, on 09/22/2009, -0/+2Sure I did!
- zadadka, on 09/22/2009, -0/+2Didn't Scotty punch up these numbers to establish the parameters for a ship to ship transport at warp?
- hfactor, on 09/22/2009, -0/+2"proved that all the prime numbers in the sequence 5, 13, 21, 29, ..., are congruent"
What sequence? Since when is 21 prime? - inactive, on 09/22/2009, -0/+2Think of the hard drives.
- m0og0o, on 09/22/2009, -0/+2Maya > Poly Smooth > set divisions to 9001.
- rogeris, on 09/22/2009, -0/+2Hooray math!
- cuoops, on 09/22/2009, -0/+2source - http://www.aimath.org/news/congruentnumbers/
- EarlOfLade, on 09/22/2009, -0/+2It just shows his ignorance about mathematics I guess. Most of what is interesting in mathematics, happens in a very narrow area.
Just because the numbers used, increase in value, doesn't make the problem more interesting or difficult except for cases were one are looking for large numbers, primes, fibonacci numbers etc were the problem is, these days, more of a logistics issue and computational power issue than a theoretical problem. - krellor, on 09/22/2009, -0/+2So, did they actually have a clever way of multiplying large numbers, or did they just make massive swap files on the hard drive? That is what I'd actually be interested in, methods of multiplying to decrease the space rather then making massive use of hard drive space. Heck, I've got a program to do math with massive numbers that could use hard drive space easily enough. Is that all they did?
- stuwanker, on 09/23/2009, -0/+1No, they were searching for congruent numbers less than or equal to a trillion.
- stuwanker, on 09/22/2009, -0/+1@ygugsa295: That's why math is so powerful: mathematicians strive to (and succeed in) proving things in great generality. Additionally, the arguments used to prove something in general reveal a lot more about the theory than calculations showing that the first n cases are true. These revelations point the discipline in new directions, oftentimes in places where we never would have thought to look if we were content to just figure out a couple of cases.
------------------
@EarlOfLade: "It just shows his ignorance about mathematics I guess." And you just showed yours.
For every area of mathematics, there is someone who finds that area interesting--that's why that area got developed in the first place.
And although some problems do not get more difficult when you increase certain parameters, for example linear algebra, there are other cases which get absurdly more difficult a numbers increase. For example, consider the roots of polynomials with integer coefficients. Understanding the arithmetic and algebra of said roots becomes markedly more difficult as the degree of the polynomial increases. A full understanding of this theory is not a logistics problem right now--it is a theoretical problem. We know what we think the answer looks like, but we're nowhere near solving it. - laserbeem, on 09/24/2009, -0/+1Fascinating story. You very quickly got me "beyond my depth" with your article, but it was intersting nonetheless. I think what really struck me is that people have been wrestling with this for thousands of years, and we're still messing around with it. Thanks for sharing.
- wunderdog, on 09/22/2009, -0/+1Why are they using the term 'right-angled triangle' and how is that different from a right triangle?
- Yeyui, on 09/22/2009, -1/+2More likely, it is a journalists desire to be understood.
- Suricou, on 09/22/2009, -0/+1If you used turbosmooth you might get another iteration out of it.
- inactive, on 09/22/2009, -3/+4yeah, seriously, what font are they using, and what size? 20000pt wingdings?
- eers2snow, on 09/22/2009, -0/+142?
- firebhaal, on 09/23/2009, -0/+1..▲
▲.▲ - stuwanker, on 09/22/2009, -0/+1It's useful because they're doing explicit computations with some pretty intricate mathematical objects. The specific results they achieve are useful in seeing whether the real data match up to the predictions made by various conjectures. The general method of calculation is useful in doing explicit computations with these objects in applications where the theory is already known.
- copysmith, on 10/01/2009, -0/+1I majored in math in college, and this was beyond me. I wonder what real, tangible practical applications this has. I can understand the excitement amongst mathematicians (they're not an easily excitable bunch), so it makes sense that they're all a-twitter over their accomplishment.
Congrats to you brainy types. Well done, and may soon solve many other similar problems. - bullrassler, on 09/23/2009, -0/+13,11. Also 5,13 and so on. But I think the explanation in your first sentence is correct.
Or did you mean you can't repeatedly add 8 to a prime number and expect the result to always be prime... - VVCephei, on 09/23/2009, -0/+13DS Max > Editable Mesh/Poly > Select all faces > Tessellate > Tessellate > Tessellate > Your 3D model now looks like a Picasso.
- Origin415, on 09/22/2009, -0/+1∆_1 ∆_2 ... ∆_1,000,000,000,000
There, 1 trillion. -
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