tag:blogger.com,1999:blog-3722233.post6870657438011112341..comments2024-08-02T16:56:41.757-05:00Comments on Computational Complexity: Intelligent Comments on Bill's G.H. Hardy/Avi W post that we did not post.Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3722233.post-13319199053151376302024-05-22T15:22:27.918-05:002024-05-22T15:22:27.918-05:00(Bill) Agree. The phrase ``chllenging the status q...(Bill) Agree. The phrase ``chllenging the status quo'' means different things in different context, however you are of course correct. There is an interesting (well--- I think so anyway) difference between what I meant and what you meant. <br />I thought of `challenging the status quo' as more like thinking that FLT was FALSE or that P=NP. You think of it as more like thinking that FLT can be solved soon or that (say) P vs NP can be resolved soon. And YES, my view is to narrow. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84794904853321770502024-05-17T22:14:15.658-05:002024-05-17T22:14:15.658-05:00To say that Wiles did not "challenge the stat...To say that Wiles did not "challenge the status quo" is IMO to take an overly narrow interpretation of the phrase "challenge the status quo." Challenging the status quo is not just about disproving conjectures. Before Wiles, the status quo was, "Fermat's Last Theorem is intractable, and by extension the Shimura-Taniyama-Weil conjecture is intractable." Wiles challenged this conventional wisdom and introduced new ideas, proving a very important special case of STW. Most truly groundbreaking new ideas challenge the status quo by drawing attention to an area that the status quo was neglecting as being unfruitful.Timothy Chowhttp://timothychow.netnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-33063738129396989872024-04-29T22:20:15.114-05:002024-04-29T22:20:15.114-05:00Terry Tao gave a talk (linked from his blog) at th...Terry Tao gave a talk (linked from his blog) at the JMM recently, entitled <a href="https://www.youtube.com/watch?v=t_plilnbAtM" rel="nofollow">"Correlations of Multiplicative Functions"</a>. In it, he says that for many (most?) number theory problems, mathematicians have a good idea what conjectures are probably true -- but proving them is much much harder. (Shades of the P v. NP problem, I guess.)<br /><br />I don't know enough complexity to understand Avi's work (except for having heard of expander graphs). But it sounds like he's come up with brilliant proofs, and this isn't undercut by the proofs being of things which people already expected to be true...<br />Josh Burdickhttps://www.blogger.com/profile/12231348292069164630noreply@blogger.com