tag:blogger.com,1999:blog-3722233.post2754344269552524293..comments2023-10-03T22:38:16.743-05:00Comments on Computational Complexity: When did Math Get So Hard?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-3722233.post-83278435347041261742021-11-02T09:43:52.632-05:002021-11-02T09:43:52.632-05:00"Mathematicians are programmers ... the only ..."Mathematicians are programmers ... the only problem is that they are using the wrong programming language" :-)Marzio De Biasihttps://www.blogger.com/profile/18441670787376943932noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-2211550405283107772021-11-01T23:13:11.005-05:002021-11-01T23:13:11.005-05:00I understand 90%--- of the work done on The Muffin...I understand 90%--- of the work done on The Muffin Problem :-) <br /><br />One measure of how hard math has gotten is to have two parameters x,y<br /><br />If x% of the people can understand y% of mathematics, then when<br />x is small and y is small, math has gotten hard. <br /><br />gasarchhttps://www.blogger.com/profile/03004932739846901628noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-28043576048561087042021-11-01T23:03:33.473-05:002021-11-01T23:03:33.473-05:00@Bill: My question is whether von Neumann would ag...@Bill: My question is whether von Neumann would agree with this;<br />supposedly, he was one of the last giants to understand a large<br />portion of mathematics. I keep forgetting the famous quote that<br />states the percentage (20%?).<br />Even Terence Tao seems to have a threshold when dealing and posting about certain topics in modern mathematics -- there's one area particularly, that he has not touched on. So understanding where the threshold is and why it indeed represents such a challenge maybe not a bad approach.<br />EGnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-2109368421514196662021-11-01T17:24:31.094-05:002021-11-01T17:24:31.094-05:00 I Do listen for as long as I am not totally lost,... I Do listen for as long as I am not totally lost, but when I get totally lost I might proofread a paper, or work on a problem set, or make up a HW, or ... And the odd thing is that NOBODY in math things this is rude or inappropriate. They do the same at their Monday Colloquiums where very few people understand the talks. gasarchhttps://www.blogger.com/profile/03004932739846901628noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-5426852730932015152021-11-01T17:10:08.878-05:002021-11-01T17:10:08.878-05:00How do you sit through a foreign language movie if...How do you sit through a foreign language movie if you do not understand anything while the movie is about three to five people sitting in a room and standing in front of them is the leading actor doing most of the dialogue with some slides? Coffee?Anonymoushttps://www.blogger.com/profile/15215802322939426847noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58999412164349660082021-11-01T13:50:57.418-05:002021-11-01T13:50:57.418-05:00If you think that P!=NP (which is my guess, and se...If you think that P!=NP (which is my guess, and seems like the conventional wisdom), then proofs are generally going to be easier to check than find. (And presumably to "understand", although that's not exactly the same as "checking", I guess.)<br /><br />In which case, even if we rely on future math AIs (or smarter people) to find proofs, at least there is a window in which we'll understand the proofs, even if we can't find them ourselves.<br /><br />I think that's (kind of) reason for optimism. (Although I guess at some point, even checking the proofs becomes difficult also.)Josh Burdickhttps://www.blogger.com/profile/12231348292069164630noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-87131591735084689032021-11-01T13:43:24.605-05:002021-11-01T13:43:24.605-05:00That might be a good way of getting out of being o...That might be a good way of getting out of being on committees!<br /><br />But to be fair, as Dean's Rep its not my job to understand the material, though I would like to. Has math gotten so hard and abstract that this is impossible? NO- I often DO ask the student<br /><br />``Tell me what problems, perhaps from a long time ago, and perhaps no longer as connected to your research as you would like, motivated work in your field.''<br /><br />gasarchhttps://www.blogger.com/profile/03004932739846901628noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-934503493680094852021-11-01T12:42:51.916-05:002021-11-01T12:42:51.916-05:00I would refuse to serve on a committee if the cand...I would refuse to serve on a committee if the candidate could not spend the first 5 minutes motivating their work in a way I could understandAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-64291000424636100332021-11-01T11:02:02.424-05:002021-11-01T11:02:02.424-05:001) If so then I doubt UMD is unique in this.
2) An...1) If so then I doubt UMD is unique in this.<br />2) Another reason that I didn't list is that Math has been around so long that it requires so much prereq knowledge to understand things. So it may not be obscurse, just beyond my knowledge base.<br />3) To directly answer your question- might depend on what `obscure' means<br />gasarchhttps://www.blogger.com/profile/03004932739846901628noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-54577334333172756032021-11-01T05:36:35.925-05:002021-11-01T05:36:35.925-05:005) With the web and more people working in math, n...5) With the web and more people working in math, new results come out faster so its harder to keep up.<br /><br />This seems to be the most relevant to me. Together with the fact that math and CS seem to have a culture that allows them to really thrive in that environment. I wonder more how math and CS could help adjacent fields to thrive similarly.Jakitohttps://www.blogger.com/profile/08235089048981338795noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32863963130675637872021-11-01T04:50:26.539-05:002021-11-01T04:50:26.539-05:00Along the same lines as what J said, often there a...Along the same lines as what J said, often there are no incentives to make your research intelligible, and there can even be perverse incentives to make your research unintelligible. Jared Diamond wrote an interesting article on this topic back in 1997. http://timothychow.net/discover-jared-diamond-19970501.pdfTimothy Chowhttps://www.blogger.com/profile/15157353087847193176noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-59662690869093647512021-11-01T03:51:41.726-05:002021-11-01T03:51:41.726-05:00I suspect that mathematicians looking at the solut...I suspect that mathematicians looking at the solution of the Connes embedding problem may be wondering when computer science got so hard.Pascalhttps://www.blogger.com/profile/14201150679841329835noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-10508574001296233502021-10-31T17:06:47.793-05:002021-10-31T17:06:47.793-05:00Are math doctorates at UMD about creating somethin...Are math doctorates at UMD about creating something so obscure and complex that it will be seen as a new contribution?Jnoreply@blogger.com