{"id":536,"date":"2009-03-28T19:48:10","date_gmt":"2009-03-29T02:48:10","guid":{"rendered":"http:\/\/palblog.fxpal.com\/?p=536"},"modified":"2009-10-30T16:20:39","modified_gmt":"2009-10-30T23:20:39","slug":"advice-for-researchers","status":"publish","type":"post","link":"https:\/\/blog.fxpal.net\/?p=536","title":{"rendered":"Advice for researchers"},"content":{"rendered":"

The Princeton Companion to Mathematics<\/a>, which came out just a few month ago, contains a wonderful short section entitled “Advice to a Young Mathematician”<\/a> with advice from five eminent mathematicians. I was in the need of inspiration this weekend, and found some in these personal statements. Below the fold you will find a few excerpts applicable to any researcher of any age.<\/p>\n

Readers: Please help me and other readers of this blog by posting in the comments section pointers to your favorite sources of research advice.<\/p>\n

<\/p>\n

Sir Michael Atiyah:\u00a0 “My own approach has been to try to avoid the direct onslaught and look for indirect approaches. … it can lead to a beautiful and simple proof, which also \u201cexplains\u201d why something is true. In fact, I believe\u00a0 the search for an explanation, for understanding, is what we should really be aiming for.”<\/p>\n

B\u00e9la Bollob\u00e1s:\u00a0 “Keep your ability to be surprised.”<\/p>\n

Alain Connes:\u00a0 “Once a mathematician truly gets to know, in an original and \u201cpersonal\u201d manner, some small part of the mathematical world, however esoteric it may look at first, the journey can properly start.”<\/p>\n

Dusa McDuff:\u00a0 “often one sees further by starting with the simplest questions and examples, because that makes it easier to understand the basic problem and then perhaps to find a new approach to it.”<\/p>\n

Peter Sarnak:\u00a0 “Not to learn the tools is like trying to demolish a building with just a chisel. Even if you are very adept at using the chisel, somebody with a bulldozer will have a huge advantage and will not need to be nearly as skillful as you.”<\/p>\n

I also loved this quote from Alain Connes: “Mathematicians usually have a hard time explaining to their partner that the times when they work with most intensity are when they are lying down in the dark on a sofa.” For me instead of “lying down in the dark,” it is “staring absently across the room.”<\/p>\n

I’ll end with one final quote from Alain Connes that greatly amused me, but also struck me as largely true, at least with respect to certain areas of physics: “in general mathematicians tend to behave like \u201cfermions,\u201d i.e., they avoid working in areas that are too trendy, whereas physicists behave a lot more like \u201cbosons,\u201d which coalesce in large packs.”<\/p>\n

There are other gems to be found in these short accounts; I may blog on some others in future posts. In the meantime, you can find the entire “Advice to a Young Mathematician”<\/a> online, and please add comments with your sources of advice and inspiration.<\/p>\n","protected":false},"excerpt":{"rendered":"

The Princeton Companion of Mathematics, which came out just few month ago, contains a wonderful short section entitled “Advice to a Young Mathematician” with advice from five eminent mathematicians. I was in the need of inspiration this weekend, and found some in these personal statements. Below the fold you will find a few excerpts appplicable to any researcher of any age.<\/p>\n

Readers: Please help me and other readers of this blog by posting in the comments section pointers to your favorite sources of research advice.<\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[49,109,7,47],"tags":[45],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/posts\/536"}],"collection":[{"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=536"}],"version-history":[{"count":13,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/posts\/536\/revisions"}],"predecessor-version":[{"id":546,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=\/wp\/v2\/posts\/536\/revisions\/546"}],"wp:attachment":[{"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.fxpal.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}