This is, as far as I can tell, a great way to succeed in math academia. But I’m only partway through the process and I’m not married to the idea of being in mathademia (I’m married to my spouse!). Side story: some years back a professor was surprisingly denied tenure at a university where his wife’s family lived nearby. He and his wife (and kids) then moved to a different country so he could be a tenured math professor there [it’s a good job]. I do not identify with this story. I do identify with this: when I was a kid my mom would annually schlep us three kids to California from Minnesota for all two weeks of her allotted vacation time.
Outline of mathademia [I did not know all this til grad school]: you spend 4 years in undergrad somewhere that you want to go/live, then 5-6 years getting a Ph.D. somewhere you learn to enjoy going to/living (though no one cares how long you spend in grad school; I know one professor who took a six year break before going on), then 1-3 years doing a postdoc somewhere you often don’t want to live/go to, then possibly more of those postdocs until you get a tenure-track job somewhere that you better want to live. After 6-7 years in your tenure track job, you either get tenure and will live there forever, or not and will have to go find somewhere else. It’s all fairly civilized and organized. Also, it gets more and more selective the further you go: I regularly hear about people applying to 80 jobs and getting 2-3 interviews and one offer. Also, if you are romantically involved with someone else in academia, good luck with the two-body problem; almost every academic couple I know has had years of long-distance dating or marriage.
- Go to college. While there (4 year liberal arts school or a university that offers PhDs both seem fine), major in math and take as many math courses as you can. If possible, take graduate courses in math as an undergraduate. If none are available, ask to take a reading course with a professor or a graduate student [for instance, several schools have grad-undergrad student reading programs like UT, UMD, UCHicago, Rutgers, UConn, Berkeley, MIT, Yale, and more all the time]. For studying abroad, consider Budapest. I did it and it was great! I’m still in touch with friends from BSM and there are several in my field.
- While in college, do research. Ask a professor for advice on doing a senior thesis project. During your junior and/or sophomore summer, DO AN REU and get a little money to go to math research camp for a few weeks and hopefully get a peek into the publishing world.
- GO TO OFFICE HOURS.
- Also, study for the Math GRE during that same summer if not earlier. Even if you’re a math hotshot it’s a hard test and you should study for it. It’s only offered three times a year. Note: some grad programs don’t require this. Take the regular GRE too but there’s probably no need to study for it.
- Take the Putnam. Do any extracurricular math activities you can.
- If you followed steps 1 and 2 you should be able to get some strong letters of recommendation for applying to grad school. So, apply to grad school. There’s lots of advice out there about this. Also, while you’re applying to grad school, APPLY TO THE NSF GRFP and possibly NDSEG as well. Note: this step is a lot of work!
- Maybe you took some time between undergrad and grad school. In that case, you’d better brush up on your math! Some people have success in looking at their old notes/books/homework. You could also check out these books: All the Math You Missed, Mathematician’s Survival Guide.
- If you’re a woman, consider doing this incredible summer brush up program that I did. It’s great.
- Take 15 minutes and do this exercise. First, quickly write down a list of five things that you value (for me: food, family, learning, math, creativity/writing). Then choose one of the things and take five full minutes (time yourself) to write about why you value that thing. Do so for two other things too. I did this my first semester of graduate school with my roommate based on an article I can’t find anymore, but roughly was this one. The point is that affirming your values and sense of identity can help you cope with graduate school.
- Figure out a physical exercise that you enjoy doing enough to actually do it. If you’re already a gym rat or sports person, great. If not, may I suggest Couch 2 5K. Other things I’ve seen grad students do: rock climbing, cross country skiing, ballroom dancing, triathlons, marathons, swimming, yoga. Physical activity really helps with the mental strain of first year of grad school.
- Swim in your own lane. First and second year it’s easy to compare to other students who are in your same classes/have better or worse preparation than you. After that it gets a lot harder and a lot more tempting to compare with your cohort. Try to avoid this.
- Finish prelims/qualifying exams as quickly as possible, so you can focus on research = primary goal of graduate school. This is how I studied for prelims: took the courses if applicable, downloaded all the previous exams (generally available on the department website), did one or two exams a week and checked answers with a study group once a week. Study group = invaluable for problems that you aren’t sure how to solve. Made a binder of all exams and all solutions (neatly written up) to reread at my leisure before exam.
- Talk to other graduate students, especially older ones. Many programs have a big sib/little sib program for first years. Exploit this. Grad students know so many things that aren’t on the internet (which professors are good to TA for, shortcuts between classroom buildings, who wants what for exams or reading courses, what seminars to attend, who to ask for help).
- Publish if possible. Find collaborators and publish results. This is far easier said than done.
- Read read read. Trawl arxiv every day (takes a few minutes) just to prime some words into your head/see who’s who in your field. Read. Reading math is HARD. You need to do a lot of it in mathademia so you should try to learn how you do it best. I take extensive notes while reading, others don’t.
- Give talks. Every program has somewhere you can give a talk (1st/2nd year seminar, grad student colloquium, junior topic seminars) and you should give at least one before you start doing job talks. It’s terrifying and then gets better the more you do.
- Go to seminars! Every professor who has given me advice has said this to me. I am not great about it but I think I have sleep apnea/mild narcolepsy. My advisor is always falling asleep in talks too, which makes me feel better, but then he wakes up and asks intelligent questions which makes me feel worse.
- Take care of yourself. Mental health days are legit. Get physical exercise. Eat well. DO YOUR LAUNDRY, for all of our sakes.
- Go to at least one conference so people know you. Follow your advisor around and have her introduce you to people in your field. Try to give some talks at conferences.
- Applying to jobs is pretty much a full-time extremely stressful job. So that fall semester of your last year of grad school, don’t expect to get a lot of math done.
- Write for the future version of yourself who doesn’t understand past you’s cryptic notation. Write write write. This is the ultimate goal of graduate school, to write a thesis.
- Write write write. Publish publish publish. Collaborate.
- Make sure people care about your work, somehow (attend conferences, give talks???)
Tenure track job
- Write write write. Publish publish publish.
- From my perspective, be superhumanly amazing and incredible.
- Profit from your hard work! Keep working hard because if you made it this far, you really love math and your work. I’ve heard many professors say “why would I retire?” but I also know that teaching is draining.
ALTERNATE TRACK, STARTING IN GRAD SCHOOL
- Become a really good TA, and try to instruct your own courses. Become conversant in things like flipped classrooms, IBL, clickers, and various pedagogy. Consider doing math circle, DRP mentorship, tutoring.
- Write an incredible teaching statement, and personalize your cover letter to each teaching school you’re applying to. Convince them that you love teaching. Teach the letter reader something they didn’t know/think about before. See notes I took from a talk by the president of the MAA:
- Be an awesome teacher, and continue to do research on the side (depending on your position).
Note that I had a lot more advice for undergraduates than I did for after where I am now (I didn’t follow all that undergraduate advice either). I also have no metrics really of “success” besides getting tenure, which is not for everyone. I feel very successful life-wise with my family and blog and triathlons, but as to professional success I am pretty emo. This blog post is about professional success==tenure. Or you could be a badass and become a freelance mathematician or a mathematical writer or anything else you want to be! You’re getting a Ph.D. in math; the world is your oyster!
Also! Writing this blog has been very fun and rewarding and one of the best parts is when undergraduates or beginning grad students or other people write to me to ask for advice or just say hey. I love hearing from you! I’m on email (yenergy), twitter (yenergy), and instagram (yenergyyy) so hit me up!