What does a mathematician do all day?

January 24, 2013 6:52 PM

I'm wondering, after breakfast, and a shower, and a commute, and coffee - what is next?

I'm working on an article that will detail the work of a famous mathematician, and it occurred to me that I have no idea what mathematicians do all day. I'd like to add that to the article.

What is the typical day like for a mathematician? I'm not talking about a job description, but the humdrum, daily grind sort of stuff you won't learn about from a typical Google search.

I'm sure there are many variations on the typical work week, and I would like some insight into that. Please, no assumptions and speculation, I'd rather hear real, first-person accounts or get pointed in the right direction.

Thanks!

posted by Lownotes to Science & Nature (23 answers total)

A lot of them are college professors, and do the same kind of thing that other professors do.
posted by Chocolate Pickle at 6:54 PM on January 24, 2013

Chocolate Pickle is correct. mrs_goldfish adds: "Reading papers. Probably doing some sort of computation -- either checking a computation from the paper or trying to use the paper to do something I wanna do." Trying-to-do-stuff occupies a lot of time, and at least 90% of the ideas one tries don't work; hence "the best asset one can have as a mathematician is sheer pigheadedness."

From my personal observation, math can also involve borrowing and stringing together various-colored index cards, embroidery thread, and bug stamps. Sometimes calculations are run on computers. Sometimes they just involve a lot of scribbling and staring into space, and the answer turns out to be: 2.
posted by feral_goldfish at 7:06 PM on January 24, 2013

Wife's uncle is a non-famous mathematician. He works for a defense contractor, most of his day-to-day is designing and running fluid dynamics simulations of IED-like explosions to improve vehicle armor. The hum-drum aspects of this are mostly around IT issues on the systems he uses for the simulations and the usual corporate bullshit that comes along with a job at a big company: expense reports and office politics. A few times a year he travels to meet with military folks or other teams for his employer - the humdrum here is all the bullshit associated with business travel.
posted by These Premises Are Alarmed at 7:08 PM on January 24, 2013

I work with mathematicians who design algorithms for our NLP software.
posted by L'Estrange Fruit at 7:10 PM on January 24, 2013

If a university professor, they will do some combination of:

read math papers/journal articles for their own research,
work on proofs/run computations or whatever their research is,
write up their research to send to journals,
correspond with collaborators about research,
referee journal articles (read them and write comments),
prepare to teach,
actually teach,
grade homework or exams,
write letters of reference for students,
hold office hours/meet with students,
meet with departmental colleagues (about eg what the schedule will be for next semester),
do committee work with other university faculty members (meetings about matters that affect the whole school, like the honor code, or tenure standards, or curriculum decisions),
eat lunch with colleagues,
chitchat with colleagues and students in the department (often there's a lounge down the hall with a coffee machine, microwave, and some chairs),
go to the library,
run extracurricular math activities like math honors societies, tutoring hours, etc,
travel to conferences or to give talks.

The balance of these activities varies quite a bit at different kinds of institutions - for example, more undergrad-teaching-focused vs more research-focused. And it's different if you're talking about a famous mathematician, who will likely spend more of their time attending conferences and doing their own research than even working with advanced grad students, and forget undergrad teaching.

Are you wondering what it looks like when someone does math research specifically? This depends on what area of math. For my household mathematician, it involves sitting at the computer typing, or sitting in a coffeeshop working through a sheaf of papers, maybe writing in pen on paper while trying to figure out a proof, looking things up in books, etc. For some it would involve computer stuff like running computations, but there are many areas that don't rely on computation at all.

Also one big thing that's changed over time is the availability of material online. Math has very good open access to eg the arXiv.

Is your mathematician doing their research now, or some years ago?
What kind of institution were they at?
What's the area of their research?
posted by LobsterMitten at 7:31 PM on January 24, 2013

I used to work at a robotics company which hired a Ph.D. in mathematics. His job was to develop motion control algorithms to allow us to move our robot arms smoothly and to stop where they needed to stop, without exceeding certain force limits at the end effector. And he did it; he was amazing. But his job looked like that of a software engineer, because he was developing code for the DSP inside the robot that controlled the motion. (It was a nontrivial problem because the arm was much too big to control with PID algorithms.)
posted by Chocolate Pickle at 7:36 PM on January 24, 2013

My husband is a theoretical physicist, which is maybe close enough to be helpful.

Here's his day yesterday (as far as I know):

Got up around 8am. Usual morning stuff.
Gets in to work around 9am. Reads random internet stuff while drinking coffee.
Around 9:30 checks to see whether the simulations he was running on a super-computer overnight finished and what happened with them. Spends until 10:30 trouble-shooting, and setting up another attempt at the same simulation.
From 10:30-11:30 he stares very hard at a piece of paper with an equation on it he wrote yesterday. Thinking. Thinking. Finally changes something to a minus sign.
11:30-12:30 goes to the gym. Lifts weights.
12:30-1 Eats lunch.
1-2 Meets with someone senior in the dept to talk about whether they might possibly be able to scrape money together to keep employing him.
2-3 Meets with someone else to talk about his draft of a grant proposal to see if they have useful feedback
3-4 Rewriting grant proposal section about how awesome he is. This mainly requires him to come up with bullshit about how his work fits into the department and university's "Stategic Research Plan" for the future
4-4:30 Stares some more at the equation. Emails it to a PhD student who he thinks is smarter than he is, to see if they can figure out the problem.
4:30-5:30 Brainstorming a new online interactive teaching thingo he's developing together with a colleague.
5:30-6:30 Checks his simulation from this morning. Cannot figure out why it is not even close to the results people are getting experimentally. Decides to simulate the system in zero dimensions instead. Or something. I think that's what he said.
6:30-7 Cycling home
7-8 Dinner
8-9 Panicking about his (lack of) job security. We brainstorm what we will do if we are both unemployed next year.
9-11 Watching a bunch of geeky tv shows to try to calm down (Big Bang Theory, Community, Warehouse 13).
posted by lollusc at 7:41 PM on January 24, 2013

Oh yeah, and at some point during the day (maybe while eating lunch) he had a back and forth exchange with a journal editor about some paper that he'd got a referee's report on. Basically arguing about which revisions were reasonable requests and which were insane.
posted by lollusc at 7:43 PM on January 24, 2013

When you find out, tell me, because I've been a professional mathematician for 6 years, and I'm still not exactly sure what I'm supposed to be doing. *g*

No, actually, a lot of time ends up taken up with class prep, grading, reading papers for literature review for one's own projects, reading papers for Mathematical Reviews or refereeing, attending committees, colloquia, or seminars, editing papers that have been recently refereed, poking collaborators to do their parts of the projects, and trying to turn ideas which are currently inside one's head into lucid presentations in papers.

A fair bit of time is spent squinting at a whiteboard and drawing cryptic examples, equations, and lines of argumentation to actually create mathematics, but that's spread among an awful lot of mundane day-to-day business.
posted by jackbishop at 8:00 PM on January 24, 2013

Wall Street employs a lot of math PhDs.
posted by dfriedman at 8:13 PM on January 24, 2013

So here's an approximated day from someone at a small liberal arts college with a focus on undergraduate teaching. (This person is also a night owl, and gets to set their own schedule.) Notice they spend tons of time on teaching/prep/grading/contact with students, and little time on research on an average day. Research mostly gets shoved into the one day a week they don't teach, and into semester breaks. Something that's similar to a research place is that they spend most of their non-teaching hours in the department, so even if they're not actively doing research they are within chitchat distance of other who are thinking about math; math-related talk and trying things out on a chalkboard are very much the everyday chitchat subjects. Lunch with mathematicians means talking about math projects, math teaching, etc. Also spend most of their "off-work" hours (at home) working. It is very much a job that comes home with you.

10:00 AM - get up, go for a run, shower, breakfast
11:00 - walk to campus
11:15 - office hour, meet with students (If no students: reply to emails, catch up with colleagues in the department common area, grade. But there are almost always students.)
12:30 - teach
2:00 - quick lunch in office, grading
2:30 - teach
4:00 - office hour (again, email and grading)
5:00 - committee meeting for faculty search, going over job applications with a committee of 6 other faculty from around the school
6:30 - back in office, check on students who are still hanging around the department common area, email, grade, prep, drop by library if needed
7:00 - walk home
[dinner, domestic stuff]
8:30 - back to campus for study/tutoring session or math club event (this is not always, but often)
10:00 - back home, grading, answer student emails, prep classes for next day
2:00 - work a bit on own research, correspond with collaborators, referee papers, respond to referee comments on their own papers
3:00- bed
posted by LobsterMitten at 8:24 PM on January 24, 2013

As you can see from all the above administrative **** listed; there's quite a few reasons that mathematicians and physicists famously are very unlikely to make any contributions to the field after the age of 30.
posted by hobo gitano de queretaro at 8:37 PM on January 24, 2013

Chocolate Pickle: "A lot of them are college professors, and do the same kind of thing that other professors do."

I was talking with a grad student the other day in mathematics, and I was surprised to learn that professors pay other people to read papers, and call them "research assistants." As a (former) CS grad students, this idea of reading papers all day sounds like fun, but I have no idea how this translates into collaboration on a new paper. I suppose it's easier if you focus on developing new fields of math rather than the Big Unsolved Problems. Like how Claude Shannon was a pretty smart guy and all, but another factor into his seemingly incredible string of algorithms and theorems is that he was the only person mining those veins at the start.
posted by pwnguin at 9:31 PM on January 24, 2013

I'm a professional pure mathematician, and I'd first say that the average day of a pure mathematician will be somewhat different from the average day of an applied mathematician; I don't know if the distinction is important to you. For me, an average day will involve some teaching work (class prep, actual teaching of the class, office hours, grading) but most of the day is spent doing research.

I first always read the arXiv submissions for the day in my field and categorize papers into 3 groups: 1) not relevant to me; 2) interesting but not something I need to read now; and 3) something I'd like to know about sooner rather than now. If a paper falls into class 3 I'll probably read the introduction and then set it aside for further reading later. Next I'll often spend a few minutes on mathoverflow. This daily process is not just mathematically interesting but also an important ritual, to put myself in the right mindset. After this comes the work of research; I generally start by reading papers and books relevant to the research I'm working on and then after that I get down to the actual research, which involves some combination of scribbling on paper and staring at walls. If I realize things that seem useful for posterity, I'll LaTeX them immediately. (I've learned through experience that it's much better to TeX things right as you think of them rather than to wait until later.) Often I'm also in the process of writing or revising a paper, so that's part of the process too. (The important thing I've realized about the way I do mathematical research is that a lot of it happens in the subconscious, so a good part of the work involves setting the table for my subconscious to chew on various things [that is a weird mixed metaphor!].)
posted by Frobenius Twist at 9:46 PM on January 24, 2013

Today:
--get to campus at 8:45.
--9:30-10:30 meet with colleague to work on research project (talk about old paper, discuss next steps)
--10:30-11:30 office hours. Teach calculus students basic algebra.
--11:30-12 meet with student about undergraduate research project
12-1 try to write a quiz
1-2 department meeting about our graduate program
2-3 teach (business calculus, in this case)
3-430 deal with more students, try to finish the quiz
Evening: should be revising the quiz, grading, writing lecture notes. Forgot about the grading. Damn.

Tomorrow: much the same, except I teach two classes instead of one, and have an early morning committee meeting instead of the department meeting. Probably won't get any math done.

Currently, I have three active research projects (local collaborations, so an hour a week meeting for each), plus a paper I'm finishing with an ex-student, plus another paper I need to write (but the research is mostly done), plus two papers I just received referees reports on that need mild revision, plus a talk for a conference in February that I haven't started preparing yet. Plus two new class preps.

And two young kids.
posted by leahwrenn at 9:49 PM on January 24, 2013

pwnguin, it sounds like you're asking why reading papers is part of the process for writing new papers?

The way to make progress is sometimes to find a method or result that someone else developed, and apply it to a problem you've been working on. You find those methods and results by reading papers (which you find by searching, or seeing their titles/abstracts in the arXiv, or through word of mouth within the network of people who are working on the same problems). If you're working on a bunch of problems and you're training grad students to do math research, you might assign them to read a bunch of papers and report back if they find anything useful that could turn into a publication/dissertation for them, or be applied to your problem(s).

Another reason to read papers is to find out what results are already settled, and which ones are still unsolved, so you know where to direct your energy.
posted by LobsterMitten at 9:50 PM on January 24, 2013

This NOVA documentary might be helpful, The Proof: For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem—the idea that a certain simple equation had no solutions. Now hear from the man who spent seven years of his life cracking the problem.
posted by TWinbrook8 at 11:58 PM on January 24, 2013

My grandfather was a mathematician. While he shaved, he would mentally factor telephone numbers.

I have no idea if that is typical.
posted by BWA at 5:14 AM on January 25, 2013

A lot of the above is what I do so I won't repeat it.
I rarely use a computer as a theoretical mathematician, outside of teaching students how to use it for their own work. I stare off into space a *lot*, to the point that my wife tells me that she knows I'm working when I'm not talking. I'm usually juggling a few problems in my head at any given time and hoping to be inspired by something that leads me to a solution. That usually happens when I'm in the shower, and hopefully doesn't happen when I'm driving (from personal experience I can tell you that doing math while driving is dangerous business).

I also draw lots of examples and do calculations on the board, then stand as far back from it as I can across the room or even in the hall and turn my head a little like when my dog hears a whistle on tv. It rarely helps as much as I hope it will.
posted by monkeymadness at 6:01 AM on January 25, 2013

I am a pure mathematician and a tenured professor. Today we have a bunch of visitors, so I'll attend three hour-long seminar talks by profs from other places (two from U. Sydney, one from U. Illinois. Chicago) and in the morning I'm meeting with another visitor from U. Illinois Urbana-Champaign to talk about some problems at the interface with topology and number theory we're both interested in. The actual way this meeting will look is that we'll sit in a coffeeshop and drink coffee and probably at some point take out pieces of paper and write on them, and it might be that one of us will open a laptop or tablet and we'll look at other people's papers, or it might be that my colleague will show me some data he's generated because he's 1000x as good a programmer as I am (mathematicians vary widely on how much code they write; some might spent a serious chunk of their time developing software for studying mathematical entries, others (like me) write occasional short sage or python or maple programs casually, some never program at all.)

I'll also read twenty or thirty Ph.D. applications and make my recommendations about whether we should admit them; continue reading a paper one of my graduate students has written and scribbling comments all over it and then try to read my comments and write him e-mail asking him to clarify certain points so that I can convince myself he's proved what he says he has proved; compile the scores our grad students got on the various parts of their algebra qualifying exam and submit to the department the list of who passed and who failed.

What almost all of this will look like, from the outside, is either:

* I'm sitting in a room listening to someone talk at the blackboard and asking quetsions;
* I'm drinking coffee with someone and talking with them and maybe writing in paper;
* I'm sitting at my laptop writing e-mail.

This is the great trichotomy of math. OK, there's staring-into-space time, too, but I don't think I have that much of that blocked out today. Actually, I'm not really much of a starer into space. Every mathematician has their own physical correlative of deep thought; some stare, some rock, some go for long walks. Me, I'm a pacer. Small circles, counterclockwise.
posted by escabeche at 6:24 AM on January 25, 2013

Yes, escabeche! I can only turn towards the board counter-clockwise and away from it the opposite way. If I do a full turn the room looks odd to me and I get flustered.

I also take what my wife calls "old man walks" around town for 2-3 hours a week to get a new perspective on problems. You'll find much of mathematics is getting stuck on something, then seeking "fresh eyes" for it. That includes talking to others (collaboration is really important), turning your head slightly, or changing your environment.
posted by monkeymadness at 6:31 AM on January 25, 2013

Wow. Thank you all so much. This is fascinating stuff and very, very helpful. I'm writing about Abraham Wald for those who were curious, and I have a mountain of information about how mathematicians helped the U.S. government and the military during World War II, which is the other focus of what I am working on.

Again, this is immensely helpful, thank you for letting me peek into your lives.
posted by Lownotes at 4:36 PM on January 25, 2013

PS: My husband asked me to come back and clarify something about what I wrote above. He said that the bit of his day that, as a physicist, looks different from a mathematician's is the bit where he lifts weights at the gym. He claims physicists are all big and buff and mathematicians are pale and weedy.
posted by lollusc at 4:57 PM on January 26, 2013