Absolute proof a scarce commodity, even in math

From Discover, January 2004, p. 36.

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Mathematicians Face Uncertainty

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This will surely be remembered as the year mathematicians finally had to agree that their prized notion of absolute proof is an unattainable idealan excellent goal to strive for, but achievable only in relatively simple cases. Moreover, they were forced to make this adjustment under the harsh glare of the media, following three major news stories about so-called mathematical proofs.

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Early in the year, American mathematician Daniel Goldston and his Turkish colleague Cem Yildirim announced a proof of the twin prime conjecture, which says there are an infinite number of prime numbers differing by two, such as 3 and 5, or 11 and 13. Although experts around the world initially agreed that the new proof was correct, a few weeks later an insurmountable error was discovered.

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The above is a trucated version, from Discover Financial ServicesA full, online version is available free, if you are a Discover subscriber. You just have to register as such.I'll get this much up now. I'll try to follow up with a bit more later.Mooseps: The "Discover's Guide to the Top 100 Science Stories of 2003" index page can be found at Discover Financial Services

I'm a bit confused about the topic. It made me think that someone had managed to extend the Incompleteness Theorems to a lower level.And the introductory paragraph is unacceptable. It is confusing the fundamental concept of proof with the human-based process of presenting a proof. It seems to have been written solely for shock value.If there is a proof of twin primes, then it exists whether or not a person makes a mistake in presenting it. When the proof of Fermat's Greater Theorem was first presented, it also had a flaw. But they found it, retracted the proof, fixed it, and represented it. The particular proof of twin primes may not be as amenable to adjustment, but that is no reason to make it seem as if the situation is hopeless.------------------
Rrhain
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