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The only thing we need for a simulation is the ability to approximate the solutions as well as we want. And the numerical methods do give us that.

The Wikipedia page about the Church-Turing-Deutsch thesis is garbage, I'm sorry for linking to that. I was in a hurry with a mobile phone and didn't read it, just went with blind trust in Wikipedia. A proper essay about the subject, written by a respected researcher, is here.

This excellent blog article describes a technique developed by Judea Pearl decades ago to do exactly this. Would be interested to understand how this is different/better.

Looks great, much like I imagined studying Comp Sci ought to be. Ok one can get the book and use the materials for self-learning, but is there a list of institutions using the course for credit?

So many great courses and great teachers around now. Pity they didn't get all this together way back in my day. I've just been working my way through http://michaelnielsen.org/blog/quantum-computing-for-the-determined/ and am astonished at the simplicity and lucidity of Nielsen's teaching.

And it would also help the readers understand the article, a good referee report is quite illuminating. However, this has already been tried out by Nature in 2006

http://www.nature.com/nature/peerreview/

and didn't work so well. Apparently, scientists are somewhat reluctant to openly criticise each other's work. But there's PLoS ONE that is alive and well, giving us some hope.

Michael Nielsen has a fine essay about this in his blog:

http://michaelnielsen.org/blog/the-future-of-science-2/

For anyone interested in the details, you can find a lot more on this wiki, where a lot of mathematicians are weighing in on the proof and its potential flaws. Mathematicians are gathering from all over to examine this paper because it's so interesting. Even if one of the serious objections that have been raised so far kills it, it contains some novel ideas that will get people thinking.

They've also been gathering the news coverage and such, so it's probably the best place to find up-to-date information about this proof. It seems to have sparked quite a lot of interest for a paper that hasn't even been properly published.

The paper was preliminary to begin with. It is currently withdrawn in order to fix minor typos and because currently "enough unresolved issues with the paper exist to foster a healthy sense of skepticism". This is a good thing for now.

The original discussion was in a Google Doc but has since moved to a wiki.

Info: Previous post explaining the proof more clearly
Paper (not wort reading for most of us)

As of about a year ago, a new kind of collaborative math project known as "polymath" is emerging. These research projects are completely open for any interested scholar to drop in and make contributions to the problem at hand. The technical infrastructure is based on well-known tools such as wikis and forum discussions

The very first such project successfully explored a new approach to the density Hales-Jewett thorem--a significant problem in combinatorics--in about six weeks of effort, with a fully preserved record of about a thousand contributions from dozens of participants.

See Polymath Wiki for the details. This new contribution from the AIM will provide a focus point for such efforts and encourage similar massively collaborative projects.

And of course, the emerging field of computer-verified mathematics is also dependent on massive collaboration, in order to translate existing results into a fully-formalized form that computes will understand and verify as correct. A wiki-based project could be a great help there as well.

I'm sometimes bothered by the stress on studies being "verified" by something like a peer-review process.

This is a misunderstanding. The role of peer review is not to verify anything. To the contrary, there are many situations where a reviewer will not be able to verify results with resonable effort. Think LHC experiments, Mars probes, etc.

Peer review is really just a spam filter. Reviewers can check whether a publication has novel aspects to it, whether it is relevant to the journal or conference, whether it is presented in a comprehensible manner, whether releated work is properly cited, and so on. A paper that has passed the peer review process is not verified, it is only deemed useful.

There are people who claim otherwise and unfortunately some of them are scientists. Overstating the capabilities of peer review makes sense if one attempts to use science in politics (which isn't wrong per se) and attempts to close political debates on the sole ground of scientific considerations (which is usually wrong).

Recommended reading:

• Three myths about scientific peer review (where one commenter adds a link to this article quoting reviewer comments on famous computer science papers)
• How Are the Mighty Fallen

in Michael Nielsen's blog.

I'm sometimes bothered by the stress on studies being "verified" by something like a peer-review process.

This is a misunderstanding. The role of peer review is not to verify anything. To the contrary, there are many situations where a reviewer will not be able to verify results with resonable effort. Think LHC experiments, Mars probes, etc.

Peer review is really just a spam filter. Reviewers can check whether a publication has novel aspects to it, whether it is relevant to the journal or conference, whether it is presented in a comprehensible manner, whether releated work is properly cited, and so on. A paper that has passed the peer review process is not verified, it is only deemed useful.

There are people who claim otherwise and unfortunately some of them are scientists. Overstating the capabilities of peer review makes sense if one attempts to use science in politics (which isn't wrong per se) and attempts to close political debates on the sole ground of scientific considerations (which is usually wrong).

Recommended reading:

• Three myths about scientific peer review (where one commenter adds a link to this article quoting reviewer comments on famous computer science papers)
• How Are the Mighty Fallen

in Michael Nielsen's blog.