{"id":28795,"date":"2016-05-04T11:45:38","date_gmt":"2016-05-04T16:45:38","guid":{"rendered":"http:\/\/blogs.ams.org\/mathgradblog\/?p=28795"},"modified":"2016-05-01T23:37:15","modified_gmt":"2016-05-02T04:37:15","slug":"hey-there-grad-student-youre-good-company","status":"publish","type":"post","link":"https:\/\/blogs.ams.org\/mathgradblog\/2016\/05\/04\/hey-there-grad-student-youre-good-company\/","title":{"rendered":"Hey There, Grad Student, You\u2019re in Good Company – Part 1"},"content":{"rendered":"
\"Math3ma\"

Guest post by Tai-Danae Bradley, a second year PhD student at the CUNY Graduate Center and founder of Math3ma.com.<\/p><\/div>\n

By Tai-Danae Bradley<\/i><\/p>\n

A while ago at my blog Math3ma<\/span><\/a>, I wrote\u00a0a post<\/span><\/a>\u00a0in response to a great\u00a0Slate article<\/span><\/a>\u00a0reminding us that math – like writing – isn’t something that anyone is good at without (at least a little!) effort.\u00a0As the article’s author put it, “no one is born knowing the axiom of completeness.”<\/i>\u00a0Since then, I’ve come across a few other snippets of mathematical candor that I found both helpful and encouraging. And since final\/qualifying exam season is right around the corner, I thought it\u2019d be great to share them here for a little\u00a0morale-boosting.
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The first comes from a\u00a0fantastic post<\/span><\/a><\/span>\u00a0<\/span>written by University of Illinois at Chicago’s recent PhD Jeremy Kun (also blogger at the excellent\u00a0Math \u2229 Programming<\/span><\/a>) in which he answers the question What is it ‘really’ like for a mathematician to learn math?\u00a0<\/i>In short, his answer is contained in the post’s title:\u00a0\u00a0“Mathematicians are chronically lost and confused (and that’s how it’s supposed to be).”<\/span><\/p>\n

Of course, he means this in a\u00a0good<\/i>\u00a0way and elaborates by sharing this colorful metaphor of mathematical research by Andrew Wiles:<\/span><\/p>\n

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You enter the first room of the mansion and it’s completely dark. \u00a0You stumble around bumping into the furniture but gradually you learn where each piece of furniture is. \u00a0Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. \u00a0You can see exactly where you were. \u00a0Then you move into the next room and spend another six months in the dark. \u00a0So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are a culmination of, and couldn’t exist without, the many months of stumbling around in the dark that precede them.<\/p>\n<\/blockquote>\n

I definitely feel like I’m stumbling in the dark whenever I tackle a new subject.\u00a0(I believe the technical term for this is learning.<\/i>) And I’m not even at the research stage yet!\u00a0<\/i>In response to this occasional feeling of lostness that we students tend to feel, Kun says:<\/span><\/p>\n

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Sometimes the answer is to pinpoint one very basic question I don’t understand and try to tackle that first. Other times it’s to learn what I can and move on.<\/span><\/p>\n<\/blockquote>\n

This is great advice for graduate students. Personally,\u00a0I find that there’s just not enough time to learn it all, so often I have to be okay with not being able to understand a topic as well as I’d like. But occasionally I end up “wasting”\u00a0an entire day just grappling with a\u00a0single<\/i>\u00a0problem\/idea. Although those days are frustratingly slow, they actually end up being the most productive and satisfying and not a waste at all! So I was encouraged when Kun mentioned that one of his colleagues has similar sentiments:<\/span><\/p>\n

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If I spend an entire day and all I do is understand this one feature of this one object that I didn’t understand before, then\u00a0that’s<\/i>\u00a0a great day.<\/span><\/p>\n<\/blockquote>\n

A great day, indeed. In fact, I find that math often comes with an initial \u201cshock factor\u201d that (usually!) goes away once I make a conscious decision to focus and, well, do the work<\/i><\/span><\/a>. It\u2019s sort of like going for an early-summer swim at the ocean or pool. The water looks inviting, but as soon as you jump in, its unexpectedly frigid temperature takes your breath away, and your only thought is Agh! What am I doing here?!<\/i> But after wading around a bit, your body adjusts and the cold doesn\u2019t feel so bad anymore. And that\u2019s when the real fun begins.<\/span><\/p>\n

Case in point: I was recently working through some of my school\u2019s old topology qualifying exams and came across a question which I initially<\/i> had no idea how to solve. In fact, here\u2019s the problem (You don\u2019t actually have to read it!):<\/span><\/p>\n

\"Exercise\"But here\u2019s what my brain saw:<\/i><\/p>\n

\"WhatBrainSaw\"<\/i><\/span><\/p>\n

Yep. You see, my first thought was, Is this even English?!<\/i> But after a few minutes of pondering, I realized just how simple both the question and <\/i>its solution were! Of course, in other instances, minutes turn into hours, days, or even semesters, and the end result doesn\u2019t always<\/i> turn out to be simple. But in general, I find that once I put in the work, the math isn\u2019t as terrifying as it seems at first.\u00a0And as Wiles observed, it\u2019s okay \u2013 necessary,<\/em> even! \u2013 to stumble around in the dark before finding the light switch.<\/p>\n

Pretty encouraging, right? Well it doesn\u2019t end there! I\u2019ve got more quotes from great mathematicians that I\u2019d love to share with you. So be sure to stay tuned for part 2! In the meantime, I\u2019ll leave you with a few links that touch on some of the things we\u2019ve talked about today:<\/p>\n