Once again, apologies for the lack of updates. In my defense, I am taking almost entirely graduation requirements so that I can graduate from MIT this semester, and then I plan on taking a gap semester in the spring. I have some incomplete plans for next semester, but I thought I’d throw out the following question anyway: what should I do with all of that time?
My current plans involve going through my backlog of books and papers I haven’t had time to read and writing posts about them, but I’m sure there are plenty of other ways I could mathematically enrich my life before graduate school and I’d be very interested to hear your suggestions.
From my point of view, the obvious answer is that you should instead do something to enrich your life NON-mathematically. Many graduate students have been devoting themselves very intensely and monogamously to mathematics since the age of 18, or even earlier. This makes it easy to burn out. Spend a semester or a year doing something you really care about other than math, and one of two things will happen: 1) (less likely) you’ll find you like that thing more than math, and you’ll follow that path; or 2) (more likely) you’ll find you miss math a lot, and this knowledge will give you strength to persevere when you hit a tough patch in grad school, as most of us do at one point or another.
Good idea! I already did that to some extent this summer (took an internship instead of taking a counselor position at PROMYS) and 2) happened as expected. I haven’t been doing a lot of math this semester and I don’t think I could handle not doing math next semester, but I’ll certainly keep this in mind.
JSE’s response is a good one. I certainly appreciated having a “gap semester” with little math — I ended staying as an ambiguous student/nonstudent at my college co-op, doing work around the place (building shelves, painting, organizing events, …). More mathematically, there are probably labs in the physics or chem departments looking to hire people like you.
In case you decide to do something in pure math, something to think about is applying to hang out for the semester at Simons Center (this spring the theme is Algebraic Topology And Physics, or something to that effect) or MSRI (“Random Spatial Processes”) or another such place.
Incidentally, I assume you have/are written/writing applications to all the top graduate schools. When you come for your Berkeley visit, let me know.
Well, “all” sounded like a bit too much effort to me, but I am applying to Berkeley and I’m also interested in working with Reshetikhin, so I’ll definitely let you know.
Definitely let me know when you visit Harvard! Don’t know what you plan on specializing in (or if you’ve decided already), but I can tell you a little about the department and in particular the algebraists and topologists here. Of course I can’t tell you what a graduate student can.
If I were you, I would probably spend the semester brushing up on overall mathematics culture and try to become better rounded — for instance, by trying to read all the papers mentioned here.
袁翘楚，我对您的生活作息很感兴趣。我不知道对于我们这个年龄段的人来说，睡几个小时才合适，几点钟休息，几点钟起床，我老怀疑自己睡的过多了以至于浪费时间。还有一个问题是，您一天平均看多少页数学书啊，我觉得自己看得太慢了。：）
Do some traveling. Try new things, yes, non-mathematical things — or better yet, non-technical things, non-scientific things…
Qiaochu, I am in a similar position to you. I have just finished my undergraduate degree at the University of Sydney in Australia and I am hoping to undertake a PhD in mathematics in America. Between now and fall 2012, here are some of the things I am planning to do:
- Do some traveling: Despite living in the Asia pacific, I have not visited many Asian countries. I am going to spend 2 months traveling in Vietnam/Laos
- Learn Haskell: I know a bit of C, but I want to learn a more “useable” programing language.
- Do some photography: I really like photography but I havent had much free time to shoot. I am planning on spending a bit of time taking pictures
- Brush up on some “life-skills”: Currently I am a pretty horrible cook. I want to reach a point where cooking for myself is not a chore.
- Do some mathematics! During my undergraduate degree, there were a few subjects which I didn’t learn as well as I would like. I am planning on filling in some of the gaps in my knowledge
I really hope that this post gets a few more replies!!
I’m not qualified to give such advice, but I will still throw out a suggestion that might intrigue you. I hope you don’t mind.
Often I wonder what would people good at pure math (such as you) think of The Art of Computer Programming. I’d be interested in reading some posts by you with stuff inspired by this textbook. It would provide an extra incentive for me to grab the book more often.
I believe there are definitely parts you would like. Problems that involve mathematics in non-trivial ways are clearly marked. For example I scanned only a couple of minutes to find one you might enjoy: “Suppose graph G has girth 5, minimum degree d and d^2+1 vertices. Show that if sqrt(4d-3) is irrational, then d=2.” (I shortened it—the original contains additional hints.)
I believe there are also parts you won’t like, such as the presentation of an assembly language.
Rather than reading even more papers, why not write a paper of your own? Remember that to do mathematical research, nothing is necessary or sufficient. I find that writing original research makes me learn at a far faster rate than I could ever learn reading other peoples’ research.
I just started Part III at Cambridge after a six-month ‘gap summer’ (I graduated from undergrad in late April), and during that time I tried to do approximately what Daniel Barter suggests. I would second Daniel’s suggestions to travel (if you can) and to “brush up on some life skills” (cooking, in particular, is a useful skill).
I don’t really have any suggestions different from those you’ve already received, but I offer you the following reassurance, for what it’s worth: I worried that a six-month trough between intense math-doing at the end of my undergrad and the intense math-doing I’m now doing at Cambridge would cause my all my math-synapses to atrophy, but that turned out not to be the case. I certainly did some math over the summer, but mostly of the bedtime-reading sort (not challenging research papers). I worked through the exercises of a book I hadn’t had the time to go through properly, read some expository articles, etc. The transition from this relaxed schedule to my school schedule wasn’t so bad, and I’m sure the transition would be just as manageable for you.
I don’t think it’s incumbent on you to do something other or significant. You are gifted and generous with mathematics, and I would guess that you handle the rest of your life with the same skill. So I would not establish some reference point of doing or not doing math. Every day you can do, and in fact, do exactly what you want. This time will be no different. And you don’t owe anyone an explanation of “how I spent my not-semester.” The best advice I give my kids is: you know what to do.
Every day I get up looking to undertake two personal endeavors – study math (a self-studier as you know) and work out. With regards to the latter, I have never missed a day in over 40 years. And while I have been trained by great athletes, I never competed. My math skills are decidedly lacking, but I’m in there for the love of the game. I never look for a day off or a break – this is what I came for.
In accordance with the above, the one thing I would suggest to anyone in any circumstance (and maybe you are there already) is get into top physical shape. The benefits are undeniable – excellent health, more energy, clearer thinking, and better looking (maybe).
This may be be way too localized but can you please comment on this issue as a mathematician?Here’s the URL: http://mathematicalexcursion.wordpress.com/2011/11/17/indias-education-system/
I apologise for the inconvenience.
This isn’t actually during the spring, but it might be intersting to you: Mathew Crawford has started a website devoted to free online math education, and is looking for interns for the summer. (I’ll be working there this summer.)
See http://www.gliyanet.com/#!/home and https://docs.google.com/document/d/1dmlu9K_r3wogeQ-hbpY6HcvuaYM06qMz2zoKRGW3Zbg/edit#
Interesting. Thanks for letting me know!
i can recommend:
reading agota kristof’s one-volume trilogy about life in rural hungary
read viriconium by m. john harrison, a novel about the extreme far future
read 1q84 by haruki murakami, a novel about a parallel earth just *slightly* different
i can anti-recommend:
reading moby dick; there are no characters and no plot in it
reading tristram shandy; same, no characters and no plot
reading the wind up bird chronicle by haruki murakami
staying where you are
backpacking in tanzania
for stuff to do:
1) learn to develop photos in a darkroom with different sets of chemicals to achieve different visual effects
2) learn to make some of the stuff in the tiangong kaiwu
3) learn to remember your dreams in clear detail
4) go to egypt and set yourself up as a freelance journalist reporting on what’s going on now. i guarantee you will meet some very interesting people, and probably a beautiful woman.
thanks for your recent answer.