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.
Undergraduate
- 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!
Pre-graduate school
- 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.
Graduate 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.
Post doc
- 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.
Tenure
- 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!
Baking and Math 
Great Read! Thanks for sharing your words of wisdom. I’m a first semester grad student and just trying to figure it all out!
Thanks for stopping by, Alexia! I recommend checking out math3ma and the AMS Grad Student blog too. Also your site is beautiful; seems like you’ve got the physical activity/non math hobby part down!
On Wed, Jan 27, 2016 at 8:56 AM, Baking and Math wrote:
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lol – that’s how I found you – through math3ma! 🙂 But I’ll check out the AMS Grad student blog. Thanks!
And thank you! I started the running/photography blog before I started grad school so at this point I’m just trying to keep up the hobby – and stay sane! 😉
Great summary. I would add “Be prepared to move out of your country/your language” but perhaps this is more appropriate for non-US-citizens/non-native English speakers. Would it be okay if I shared this post on the European Women in Mathematics Facebook page?
I would be totally flattered if you did so; thank you. You’re absolutely right this was very US-centric: I know some Americans who did postdocs in other countries but could still get by with just English and a smattering of the home language. In any case, be prepared to move somewhere you never expected you would is definitely sound advice.
On Wed, Jan 27, 2016 at 8:57 AM, Baking and Math wrote:
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Thanks! PS We have a graduate student from the US – he can easily get by with English but he’s so nice he is taking Italian all the same.
I can fill in some of the later steps. I’m currently a tenured associate prof.
Grad school
Teaching lots of classes in grad school (i.e. teaching classes of students as the primary instructor) is a huge time sink, but teaching one or two classes gives you about 10 times more speaking experience than even the most prolific research talk schedule can achieve. You don’t need to commit to the alternate track; even a single course taught traditionally provides valuable benefits when it comes to job talks, which are largely where jobs are won and lost.
Post-doc
Transition to independent research. In grad school, your advisor sets your research program. As an assistant prof, you run your own research. In between, post-docs let you learn the ropes while having a safety net. Aim for about a 50/50 split between papers co-authored with and without your supervisor.
Learn how to absorb math from conferences and talks. In grad school, you read papers because you have no other choice — few grad schools have the resources to send their students to lots of conferences and grad students don’t have time anyway in between classes, TAs, and theses. Post-docs do have the time and resources to attend. A general rule (I forgot the source) is that 15 minutes of one-on-one conversation, 1 hour of seminar, and 2 weeks of reading are about equivalent in learning benefit. Each person is different and you’ll have to find out what works best for you. For me, the key revelation was that not taking notes during the talk allowed me to concentrate exclusively on mental understanding and vastly improved my retention of material.
Seminars are good but conferences are great. You need to specialize. My entire current research program formed as an offshoot of one minor question asked at one obscure conference.
Serendipity is your friend. I’ve gotten top-tier publications from collaborations that started out via the most tenuous connections and beginnings.
At the same time, there’s no need to try to maximize your opportunities. Don’t attend every talk at conferences. It’s more important to maintain peak alertness, so that you can seize the opportunities fully when you encounter them. That means getting rest and exercise.
Grant funding. As a grad student, you don’t have to do it (other than fellowship applications). As an assistant prof, it makes or breaks your career. You can either sink or swim after you get the tenure-track job, or start learning now as a post-doc. Some people are lucky and get a head start with a successful NSF post-doc application. For everyone else, ask to see your supervisor’s grant applications and think very carefully about the future prospects of your research area. Remember that fashions can change quickly. Be prepared to pivot while you are a post-doc; it will be easier than as an assistant prof. I changed research areas completely to another (AMS) MSC during my post-doc.
There are two alternative tracks to getting that tenure-track research position: publish in quantity, or publish in quality. If you look at one school you may think that there is only one path, but in reality there are lots of schools and they place varying amounts of emphasis on each category. Luckily, at a given school the same standards apply to hiring and tenure decisions, so if they’re a good match for you at the hiring stage then you’ll be OK for tenure.
Dealing with rejection. If your paper or grant gets rejected, the referees are theoretically required to give you reasons. While complaints about referees abound, most of the time, you will get valid reasons, and they will be things that you can address. Address them and apply again. The second time, there will be no more valid negative reasons (and often the same people will again be referees). A paper should take no more than two such cycles to get accepted, since there is no shortage of supply of journals that will publish your paper (unless you insist on a top-tier journal, in which case — don’t). A grant may take many more cycles, because there is a shortage of supply of money that funds grants, but the same principles apply.
Job applications. The key is to find an institution which is compatible with your preferences, e.g. if you publish in quality rather than quantity, find a place that values quality. This may seem impossible (“beggars can’t be choosers”), but in the long run you have no choice. Being stuck in the wrong place will make your life horrible and you will quit. I found that having a safety net (“if this job search fails, I’ve already got a job lined up at XXX multinational company”) really helped to cut through the stress. Interviewers and hiring committees can smell stress and desperation. Use this to your advantage by projecting the opposite.
Tenure-track
Read “The survival of a mathematician: from tenure-track to emeritus” which is the follow-up book to Krantz’s first book.
Basically the same advice for post-docs above applies here. In fact: http://blogs.scientificamerican.com/guest-blog/the-awesomest-7-year-postdoc-or-how-i-learned-to-stop-worrying-and-love-the-tenure-track-faculty-life/
Only at the most elite institutions is superhuman performance required for tenure. Everywhere else, if you can make friends, or even simply manage not to alienate everyone completely, the department will take care of you. Remember that they’ve invested a precious hiring slot in you, and have every incentive to make sure you keep it. In addition, your colleagues are mathematicians. They are used to things that normal people would consider antisocial. So it’s really hard to screw up.
In grad school and post docs, we emphasize mental and physical health. These are still necessary for peak performance at the tenure-track level. To this list we must now add one more item: family work-life balance. For most people starting families, you’ll likely need to take advantage of family leave at this stage to produce at your best. Use it.
This last part sounds very 1984, but it is true. The tenure track is mainly designed to filter out people who would abuse the privileges of tenure. It’s not perfect, but it does approximate this goal. If you take your teaching and research seriously, you’ll be fine. If you try to game the system, you’ll probably fail. Tenure is not decided by an objective count of a person’s research publications, teaching scores, or even grant funding. Tenure is decided by the following question: Are you an asset to the university? Always focus on that question. Get into that mind-set and use that approach in your work. Good luck!
Wow thank you SO MUCH for this thoughtful and well-written reply. I and hopefully other readers really appreciate it!