On 05 Mar 2014, at 17:09, Telmo Menezes wrote:




On Fri, Feb 21, 2014 at 9:10 PM, John Clark <johnkcl...@gmail.com> wrote: On Wed, Feb 19, 2014 at 1:13 PM, Telmo Menezes <te...@telmomenezes.com> wrote:

> If no human can check a proof of a theorem, does it really count as mathematics?

Good question, sometimes I wonder if we're getting close to that point. When Andrew Wiles proved Fermat's Last Theorem it took another world class mathematician nearly a full year to understand it and say it was correct. If I had a valid proof of the Riemann Hypothesis but would take as much brainpower for you to understand it as it took for me to write it is that really a proof, would there be any reason you should to bother to look at it? You might as well forget about me and start working on it from scratch.

True, but as you usually say, reality doesn't care... It is already the case for science that, for one to have a good general understanding on how things work, one has to trust numerous experiments and proofs that one cannot possibly have the time to verify.

A somewhat related issue is the failure so far to build a machine with human-level intelligence. One possibility is that the necessary algorithms are just too complex for a human brain to grasp. But then, maybe we can evolve them artificially. In which case we will end up creating something that we have no hope of understanding.

Maybe we're hitting an explanatory wall...

There is one at the start. We live on the border of it. It can be a bit between boring and frightening. But any "other person" by itself is an explanatory wall,



I'll let you know how my intelligence-augmentation experiments go:
https://en.wikipedia.org/wiki/Transcranial_direct-current_stimulation

:)


Artificial artificial paradise. Take care :)

Bruno



Cheers,
Telmo.


  John K Clark




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