So good, in fact, that they can solve a problem that mathematicians have been trying to crack for thirty years in just two days.
Such is the case of a problem solved only a few months ago called the Boolean Pythagorean triples problem. A mathematician named Ronald Graham first offered a $100 prize to anyone who could solve it in the 1980s, and no one was able until May of this year. The Stampede supercomputer at the University of Texas did the job, which just so happens to be the largest-ever math proof in the history of ever: 200 terabytes.
Stampede, our heroic supercomputer
So, what's the essence of this colossal and seemingly intractable math problem? Well, you probably remember the unsuitably-named Pythagorean theorem from middle school: a^2 + b^2 = c^2. The integers a, b, and c in the Pythagorean theorem are known as Pythagorean triples. The problem asks whether it's possible for each of the positive integers can be colored either red or blue so that a combination of the Pythagorean triple can satisfy the Pythagorean theorem without having any of the integers be the same color.
In May, researchers at the University of Texas had Stampede attempt to solve the problem, and it spent two days working it out. (Now just imagine how long it would take a human, or an army of humans.) Stampede determined that yes, this is attainable. Another program even checked Stampede's resulting 200 terabyte proof and found it to be sound.
Answering the question posed by the Boolean Pythagorean triples problem only raised a veritable legion of different questions, however. For example, the question remains of just why it's possible for all of the integers to not have the same color. Also, it's apparently only possible to color the integers differently for 7,824. After the 7,825th integer, it just becomes impossible. Why is that?
I think perhaps this just speaks to our own relative lack of understanding of how the problem really works. But, like any science, it'll probably take dozens of minds and years of collaboration before humanity as a whole has really increased and improved our knowledge base. Really makes me wonder how long it would've taken people to figure the problem out without the use of a supercomputer, though.
Sources
- World's Largest Math Proof Solved. And It Takes Up 200 Terabytes. From Futurism.com
- Image Representation of the Problem's Solution. From Nature.
- Photograph of Stampede
One of the many interesting topics relating mathematics to computing. One of my favourites have to do with calculating the largest mersenne primes (the biggest one right now is 2^(74,207,281) − 1. Cant even imagine how anybody would solve for a number that is longer than 22 million digits.
ReplyDeleteComputers also had a lot of impact with a similar problem: the Fermat's last Theorem. The Theorem ask if x^n+y^n = z^n for n >= 3 has a real integers solution. Mathematicians took centuries to solve this problem until Andrew Wiles solved it in the 90s. Wiles used computers to understand the problem, which eventually led him to conclude that x^n+y^n = z^n for n >= 3 has no real integers solution.
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