tag:blogger.com,1999:blog-3722233.post9189092087066523247..comments2021-09-14T11:25:32.611-05:00Comments on Computational Complexity: Publicity for P versus NPLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3722233.post-43415680356942246412009-10-09T10:06:03.330-05:002009-10-09T10:06:03.330-05:00Since Lance has brought this into the light for so...Since Lance has brought this into the light for so many more people and because he does NOT use capital letters, I suggest we follow the Nobel committee in terms of standards and give him a Turing Award for his P-vs-NP work!a NOBEL readernoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85454339324748474432009-10-08T17:18:00.702-05:002009-10-08T17:18:00.702-05:00Saugata Basu's post accurately describes what ...Saugata Basu's post accurately describes what increasing number of systems engineers and biologists are discovering too.<br /><br />Namely, no matter what your field of research, if you raise your mathematical framework one level of abstraction, then (with surprising generality) you'll find yourself doing algebraic geometry and/or category theory.John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-92163404666106486102009-10-08T15:49:13.136-05:002009-10-08T15:49:13.136-05:00Don't worry. The field of algebraic geometry, ...<i>Don't worry. The field of algebraic geometry, though mainstream, is still esoteric to the vast majority of active research post-tenure mathematicians.<br /></i><br /><br />I want to make two comments.<br /><br />1. The "esotericity" of algebraic geometry mostly refers to Grothendieck's vast unrealized program of building a theory of motives. However, the kind of math involved in the program of Mulmuley et al., has to do with representation/invariant theory and classical algebraic geometry tracing its roots from Frobenius, Schur, Schubert and so on and is not esoteric et al. It is difficult, interesting and deep, but as down-to-earth as other "non-esoteric" branches of mathematics.<br /><br />2. If one thinks (as a few of us do) about the P/NP question as a question over arbitrary structures, then the classical, real, complex versions of this questions are really facets of a more universal algebro-geometric problem -- and in this sense it is really a question of algebraic-geometry, and so its solution would involve some kind of algebraic geometry. The approach of Mulmuley et al. is one such -- but that is not the sole reason why it might be useful to learn algebraic geometry to attack this problem.Saugata Basuhttps://www.blogger.com/profile/13295092939775521282noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-80333031158293003122009-10-08T12:57:08.617-05:002009-10-08T12:57:08.617-05:00If ever the mathematicians made jokes about us... ...<i>If ever the mathematicians made jokes about us... :)))</i><br /><br />Don't worry. The field of algebraic geometry, though mainstream, is still esoteric to the vast majority of active research post-tenure mathematicians.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-5212425343051025962009-10-08T11:29:16.110-05:002009-10-08T11:29:16.110-05:00I think TSP and VLSI design, while easy to state, ...I think TSP and VLSI design, while easy to state, are traditional, but not ideal as examples of hard problems we can't solve. Practitioners routinely solve these quite well. Scheduling and bin packing are probably better examples where the heuristics don't come close to (provable)optimality. Breaking of crypto and perfect game playing strategies would be other press-friendly consequences of P=NP.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-7180651006738639032009-10-08T11:28:36.829-05:002009-10-08T11:28:36.829-05:00An esoteric branch of mathematics known as algebra...<i>An esoteric branch of mathematics known as algebraic geometry</i><br /><br />Actually, algebraic geometry is a mainstream branch of mathematics. <br />But never mind, it's just the "New york Times", nothing serious.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-52281470169671553222009-10-08T10:08:07.404-05:002009-10-08T10:08:07.404-05:00I like the last sentence: "It’s a bit scary b...I like the last sentence: "It’s a bit scary because we have to start learning a very difficult mathematical field."<br /><br />If ever the mathematicians made jokes about us... :)))Mihaihttps://www.blogger.com/profile/11599372864611039927noreply@blogger.com