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October 30th, 2007, 04:08 AM   #11
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Maybe you should read up on it before criticizing.
Ah, OK, I see what their point of view is now. As long as everything is proven, it's all well and good by me. Personally, I am a fan of brute force computation, so it suits me pretty well as long as the results are proven.
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October 30th, 2007, 05:19 AM   #12
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Originally Posted by Infinity
Ah, OK, I see what their point of view is now. As long as everything is proven, it's all well and good by me.
It's not all proven -- although much of it is, and often the results suggest new directions for proofs. The whole idea is to let the data guide you (in a 'smart' way based on good heuristics, not blindly) rather than relying only on proofs. It's more reliable than science (which also uses experiments, but not nearly as many) but not as reliable as traditional mathematics. Of course I can't recall a result in experimental mathematics that has turned out wrong...

Edit: I think this can be compared to the difference between pseudoprimality tests and primality proving. For a large number, a series of Frobenius pseudoprime tests might show that it was prime with 'probability' 1 - 10^-500 in a few hours. A proof of the primality of the number would take decades. The pseudoprime tests discover the primes, while ECPP just gives a proof of what you already know. Experimental mathematics states as its goal to discover what is not known, to guide the way for later proofs. Of course when they can prove results they do, but that's not their purpose as such.
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