
 Wikipedia-size maths proof too big for humans to check - graeham
http://www.newscientist.com/article/dn25068-wikipediasize-maths-proof-too-big-for-humans-to-check.html#.UwTuA3gRq8M
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archgrove
So, to me, proofs have two purposes. The first is to just say "This theorem is
true". The second is to give some insight into the problem. I have no problem
with such a proof satisfying purpose one; I may not be able to check it
myself, but I can build a chain of trustworthiness all the way back to a
program that I _can_ check myself. In such a chain, the truth of the final
result is not, to me, in dispute.

Alas, such a proof throughly fails the second test. I can't see how to gain
insight into the problem from such a proof, beyond just it validating previous
thought chains of the form "If X were true, then I could deduce Y". It doesn't
reveal more about the structure of the problem, or other results in the space.

It's no doubt useful (and all credit to the authors), but in terms of
generating new mathematics, I'm dubious. Perhaps people more versed in this
specific sub-field can tell me if I'm wrong?

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brador
Imagine if we could program a computer with all known mathematical truths.
What curiosities would it discover that we have yet to find?

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arbitrage
Perhaps an infinite number. However, like a tree falling in the woods ... if
humans (or some other intelligence) can't understand it, has anything actually
been discovered? Or is it more like a computer algorithmically solving a
jigsaw puzzle?

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wlievens
What what? And, what the hell is an infinite number?

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ColinWright
[https://hn.algolia.com/?q=proof#!/story/past_week/0/maths%20...](https://hn.algolia.com/?q=proof#!/story/past_week/0/maths%20proof)

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Dylan16807
Those submissions never got traction or comments, why link them?

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ColinWright
Because sometimes older submissions end up getting some discussion, even when
more recent submissions have more comments.

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saurik
[http://www.reddit.com/r/math/comments/1y5v15/if_no_human_can...](http://www.reddit.com/r/math/comments/1y5v15/if_no_human_can_check_a_proof_of_a_theorem_does/)

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twocows
"Wikipedia-sized" Is it really? They say in the article that the text of
Wikipedia is a 10GB download, but that has to be compressed (and compression
on plaintext, which comprises most of Wikipedia, is extremely efficient). I'm
guessing (but have no proof) that their 13GB file was raw data.

A minor thing, but comparisons like this always drive me nuts. Just say "13GB
proof too big for humans to check." Then there's no confusion.</sillyrant>

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VLM
A lot of its name games. 10 gigs of possibilities tested is actually pretty
short for something like OGR-27. We're probably going to prove OGR-27 in a few
weeks (or has it already been announced?) and I'm fairly certain a list of all
possible rulers checked would exceed 10 gigs. Yet you can report OGR-26 in
only 26 small numbers, or I guess you could draw a graphic pix using 492
pixels or whatever.

So is OGR-27 merely 27 numbers aka a 1-d pixel "graph" probably around five
hundred something pixels, or is it really zillions of gigs of rulers all of
which are longer than the OGR?

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judk
"Wikipedia" is displacing "encyclopedia" and "Library of Congress" as a unit
of measure!

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igravious
Uh, and football field. The output of this proof if laid end to end would fill
37 regular sized football fields.

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snird
"The set-theoretical axioms that sustain modern mathematics are self-evident
in differing degrees. One of them – indeed, the most important of them, namely
Cantor's axiom, the so-called axiom of infinity – has scarcely any claim to
self-evidence at all". John P. Mayberry

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adiM
From the linked Wikipedia article:

> All experiments were conducted on PCs equipped with an Intel Core i5-2500K
> CPU running at 3.30GHz and 16GB of RAM.

Why are these experiments not being conducted on a more powerful computer or a
cluster?

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alephnil
As already mentioned, it only took six hours. To make it run on a cluster or
supercomnputer, you must parallelize the algorithm, which will take
considerably longer time, even if it is easy. Then they likely have to apply
for access, which also take time. Then it is easier to just run it on an
available computer.

