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Apr 22, 2011 at 2:03 comment added user9072 Sorry, to write a third comment. I now edited my answer to (I hope) express more clearly what I wanted to say. Finally, I would like to appologize if my original crude formulation should have been disrespectful towards AKS. This was certainly not my intention.
Apr 22, 2011 at 0:15 comment added user9072 (cont.) the paper also contains a discussion of improvements of the bounds for the exponent (which I mentioned but of which I unfortunately failed to mention that some of them were already in the AKS-paper) that do involve these results. But they are not necessary for what is I believe the main point of the paper, namely that Primes is in P.
Apr 22, 2011 at 0:06 comment added user9072 I am the unknown giving the other answer. Not sure if I was misunderstood, but it was in no way my intention to somehow belittle the progress that AKS was (as I hoped to convey with a later sentence to that extent). On rereading the phrasing 'AKS did not use...number theory' in my asnwer I see that it is misleading and I will change this. But, what I beieve to be true and wanted to say is that the main proof in 'Primes is in P' does not use these number theoretic res. and succeeds in showing that Primes is in P essentially from 'nothing' (which to me makes the result even better); (cont.)
Apr 21, 2011 at 23:31 history answered Gil Kalai CC BY-SA 3.0