tag:blogger.com,1999:blog-4987609114415205593.post4719583428871219215..comments2022-01-19T03:06:39.163+00:00Comments on M-Phi: The beauty (?) of mathematical proofs -- empirical predictions Jeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-4987609114415205593.post-90100552018649011742019-08-21T03:15:14.872+01:002019-08-21T03:15:14.872+01:00Thanks for sharing, nice post! Post really provice...Thanks for sharing, nice post! Post really provice useful information!<br /><br />An Thái Sơn với website <a href="http://www.google.lt/url?q=http://anthaison.vn" rel="nofollow">anthaison.vn</a> chuyên sản phẩm <a href="http://www.google.lt/url?q=https://www.youtube.com/watch?v=l0oyXccR7ZE" rel="nofollow">máy đưa võng</a> hay <a href="http://www.google.lt/url?q=http://anthaison.vn/sp/may-dua-vong-tu-dong-ts/" rel="nofollow">máy đưa võng tự động</a> tốt cho bé là địa chỉ bán <a href="http://www.google.lt/url?q=https://mayduavong.me/dia-chi-mua-may-dua-vong-tu-dong-gia-re-uy-tin-tai-tp-hcm/" rel="nofollow">máy đưa võng giá rẻ</a> tại TP.HCM và giúp bạn tìm <a href="http://www.google.lt/url?q=https://mayduavong.me/nen-mua-may-dua-vong-tu-dong-loai-nao-tot-nhat-gia-bao-nhieu/" rel="nofollow">máy đưa võng loại nào tốt</a> hiện nay.ngocnhunghttps://www.blogger.com/profile/16359547746753655080noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-18296113138544119852017-10-18T15:48:29.947+01:002017-10-18T15:48:29.947+01:00شركة الصفرات<a href="http://elsafrat.com/" rel="nofollow">شركة الصفرات</a>شركات خدمات منزليةhttps://www.blogger.com/profile/10701655500050294149noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-57871618268774195152016-01-27T01:42:07.769+00:002016-01-27T01:42:07.769+00:00You don't overcome challenges by making them s...You don't overcome challenges by making them smaller but by making yourself bigger<br />_________________________<br />I find a interest game, join us now!: <a href="http://www.csgo4skin.com/" rel="nofollow">CSGO Skins</a> and <a href="http://www.csgo4skin.com/" rel="nofollow">Buy CSGO Skins</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-2095979236056981562016-01-08T19:31:44.119+00:002016-01-08T19:31:44.119+00:00I read your final series post and its give us good...I read your final series post and its give us good idea how to solve math equation with proofs and how to find equation answer with proofs thanks for sharing <a href="http://www.onlinesummarizer.com/" rel="nofollow">online article summarizer</a> .Allen jeleyhttps://www.blogger.com/profile/10312119051975318074noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-28857407706312048742015-11-08T14:41:44.987+00:002015-11-08T14:41:44.987+00:00Packing "computer-assisted proofs" all i...Packing "computer-assisted proofs" all in the same box (the box containing "proofs that are typically viewed as ‘ugly’") might not be a good idea. There are nowadays remarkably different categories of computer-assisted proofs in the market: the well-known ones that proceed by <i>exhaustive checking</i>, those that are based on <i>model generation</i>, those based on <i>proof generation</i>, those that are just meant to allow for <i>formal verification</i>, those that take advantage of off-the-shelf <i>decision procedures</i>. These categories may not all have identical measure on a given (stereotypical? ideal?) mathematician's aesthetic ruler.<br /><br />By the way, <a href="http://www.ams.org/notices/200811/" rel="nofollow">here</a> you can find some very good reading on "formal proofs".Joao Marcoshttps://www.blogger.com/profile/03826725315002161720noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-47339230492394836882015-11-03T20:21:58.099+00:002015-11-03T20:21:58.099+00:00Well, that's music to my ears of course :) The...Well, that's music to my ears of course :) The example you give illustrates precisely the audience-relativity of the notion of explanatoriness (and beauty) when it comes to proofs.<br />But ultimately most of this should be investigated rigorously rather than being settled on mathematicians' (or even worse, philosophers'!) hunches. Fortunately Inglis and Aberdein are on board with the idea of testing my hypotheses, so there might be some more concrete results in the near future.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-13595089514551976242015-11-02T21:48:57.213+00:002015-11-02T21:48:57.213+00:00I've tried to think about how your empirical p...I've tried to think about how your empirical predictions match up with my own impressions of the world I move about in. For some of them it isn't easy, and I think there is nothing for it but to do serious experiments along the lines you suggest. One of the predictions -- that mathematicians disagree in their aesthetic judgments -- is an interesting one, because it seems to me, as you suggest at one point, that there are certain points on which there is almost universal agreement, but there does still seem to be room for disagreement. While I don't have a good concrete example to hand, I do at least have a class of examples. There are some mathematical statements that have proofs that are very short and straightforward once you are fully versed in some powerful machinery that may take a lot of effort to learn, before then becoming thoroughly internalized. To a mathematician who has internalized it, such proofs will seem highly explanatory -- the statement has a clear place in a well-established theoretical framework. But a mathematician who prefers elementary arguments to big-machinery arguments will feel the weight of all the theory that lies behind the "simple" proof and may well be very happy to find an argument that is more complicated but that has far fewer prerequisites. I think there are genuinely situations where there are two proofs with these characteristics, and mathematicians will have strong but different views about which one tells them what is "really going on".gowershttps://www.blogger.com/profile/11312457281302462824noreply@blogger.com