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Aunt Pythia’s advice

November 8, 2014

Holy crap! Aunt Pythia is in love with a new knitting pattern and has just completed her first reversible “flaming hat”:

The orange is cashmere. I got it on sale.

The orange is cashmere. I got it on sale. Ridiculously scrumptious.

The green is leftover from a sweater Aunt Pythia knitted for her husband years ago, a wool/silk blend.

The green is leftover from a sweater Aunt Pythia knitted for her husband years ago, a wool/silk blend. Also scrumptious.

And that’s all I got today, folks.

Just kidding! I’m here for you guys, of course! Let’s dig in. But before I forget,

please think of something

titillating, reversible, and scrumptious 

to ask Aunt Pythia

at the bottom of the page!

By the way, if you don’t know what the hell Aunt Pythia is talking about, go here for past advice columns and here for an explanation of the name Pythia.


Dear Aunt Pythia,

This may be too broad a generalization, but I feel that current practices of teaching math were developed in an era when computers were not available. In an age where powerful, open-source tools are readily available and it’s even possible to do symbolic math using a computer, is it still useful to teach traditional pen-and-paper math to students who have no interest in becoming professional mathematicians? Does one really need to know that a trigonometric substitution would convert a tricky integral to a familiar one? As teachers, should we just focus on “big picture” concepts and use computers to explore problems on a larger scale than are feasible by hand (e.g. 1000 X 1000 matrices instead of 3 X 3)? Or, will lack of rigor in teaching have long term consequences (dubious application of math in real world)? Are there examples of the use of computers in mathematical education that you would recommend?

Obsessive Correlator

Dear OC,

I kind of agree. I never saw the point of cosines and sines until Taylor Series, even though they theoretically help ships navigate in the ocean. I mean, maybe, but that connection was never made clear to us.

If I had my way, we’d spend a lot more time doing simple data analysis, trying to understand what “statistical evidence” means, so we train people to read the newspaper and scientific research papers and not be cowed by the math, which is usually pretty simple.

Also, there are new tools like this one (hat tip Josh Vekhter) which are taking care of the rote arithmetic already:

The good news is, there are efforts underway to modernize the mathematics curriculum. The bad news is they’ve gotten caught in a web of politics. But I do expect this stuff to get sorted out over time.

Aunt Pythia


Dear Aunt Pythia,

I’m an undergrad freshman studying physics and math. I absolutely adore physics and it’s what I want to be doing for the rest of my life. I’d really, really love to become a physicist but I fear I’m just not smart enough. Reading your sample question has worried me. I had always thought if I work hard enough I could do it, but it’s always in the back of my mind that I’m not creative/intelligent enough. When (if ever) will I know if I have what it takes?

Unsure and Insecure

Dear U&I,

Short answer: never.

The long answer has four parts.

First, I have actually never met anyone who thinks they are smart enough to be a physicist or a mathematician at the level they want to be. Just get used to it and enjoy the love for the subject anyway. Also, knowing that nobody ever feels smart enough might be comforting.

Second, in general the more time you spend with something, the better you get at it, and the more you love something the more time you want to spend with it. Sometimes insecurity can be debilitating, but if you remember you love it aside from your ability, you can try to keep things cool.

Third, when your teachers and others encourage you, believe them. If you don’t get into a grad school for math or physics, take it as a sign – probably – that it might not be for you, but if you do get into a grad school, just trust that other people see something in you that you can’t see yourself, yet.

Finally, I am not sure what you mean by my “sample question”, did I ask something that made a bunch of people feel not smart enough for physics and math? If so, I apologize. I never mean to do that. I really don’t think any one question could possibly be sufficient to size someone up in this kind of deep way.

Good luck!

Aunt Pythia


Dear Aunt Pythia,

Lately I’ve been a bit of a hermit. I do go out sometimes, but I often don’t really talk to anyone because of the well-documented awkwardness involved in starting conversations with strangers (which somehow seems to not bother some people).

I have a work friend in a similar predicament, and we came up with the idea for a “woman scavenger hunt” (we’re both single straight men) designed to help us get over our discomfort with talking to strangers (specifically, women). The scavenger hunt would be a race to meet women with particular characteristics such as:

  • wearing a bandanna
  • reading a book in a bar at night
  • has a driver’s license from Hawaii or Alaska
  • knows sign language

We would have to talk to the person in question and secure some sort of evidence, such as a photograph (consensually, of course!)

My questions are:

  1. Does this sound creepy? For some reason it feels like we’re plotting to invade other people’s privacy, and it’s hard to decide if this is real or if I’m just antisocial.
  2. If you endorse the idea, can you add to our list? It has to be something for which one can collect evidence; we ruled out “met Elizabeth Warren”, for example.

Tired Introvert Mulling Interpersonal Development


First of all, I think it’s a goodish idea. I would like to suggest that you enlarge the goal to “meeting a person with the following characteristic” rather than a woman specifically, because the truth is you’re probably awkward meeting men and women, and this will give you practice, and although you are theoretically more interested in the women, meeting men is a good idea too. Plus, men have friends who are girls. If you give a good impression to the men you meet, the women will be like, “who’s this guy?”.

By the way, one of my good friends had a habit when she was single of hanging out with her girlfriends (wingwomen actually) and coming up with slightly artificial arguments at their table, which they would turn into “polls” for the entire bar. In other words, they’d argue aimlessly until they came up with something jicy enough to bring to every other group of men, women, and mixed groups at the bar and poll them. They might do this all night, gradually getting to know people at the bar, and they might have actually been interested romantically or sexually in only a few of the people they interacted with, but their friendliness and interactivity was a hit with everyone, assuming their polls questions were funny and smart, which they were.

In other words, it’s a good idea, and it’s quirky, and if you can play with it and have fun with it, and get other people to be into it and have fun with it, then it’s all good. You might not get laid, but in the worst case scenario you make friends.

Just to be clear, you gotta make sure the “characteristics” you’re looking for don’t get creepy or sexual. Don’t, for example, go up to women and say you’re looking for a woman with such-and-such sexual experience or physical attributes. Gross.

And never, ever, ever do anything this guy suggests.

Good luck!

Aunt Pythia


Dear Aunt Pythia,

I’m applying for (academic) math jobs at the moment. I’m also female (obvious from my name) and a lesbian (unsurprising once you meet me).

Occasionally, as part of the job application, I’m asked to comment on how I might contribute to diversity in mathematics. This is obviously a broad question, but part of my answer inevitably involves a discussion of women in mathematics. The way I talk about this issue is naturally colored by the fact that I’m a woman.

One of the prompts explicitly mentions the GLBT axis of diversity. It is not as clear to me how or whether to address this in my statement. My personal experience is that anti-gay biases in mathematics aren’t as pernicious as racial or gender biases, so I tend not to raise this issue on my own.

If I come out while saying that I’m supportive of GLBT students, then it sounds like I’m looking for extra credit for being a minority. I don’t need brownie points for being queer. But on the other hand, I’m out in my personal life and so it seems weird to be closeted in a discussion touching on GLBT diversity. But then again it seems weird to be discussing sexuality at all in the context of a job application.

In summary: would you come out in a “statement of diversity”?

Closeted Around Diversity

Dear CAD,

Things have changed since I applied for jobs! We didn’t have diversity statements back then. And it’s weird to think they’d be prompting you to disclose stuff like your sexuality – in fact it sounds downright illegal.

After some thought and a minimal amount of googling, I think maybe you should interpret this as prompting your experience in promoting diversity in mathematics. This idea is backed up by the advice on this webpage, although I don’t know if that makes it a universal truth.

In other words, have you mentored women? Have minorities of one type or another felt comfortable enough around you to come ask you questions? Did you organize or give a talk at a Sonia Kovalesky Day somewhere? Were you the faculty advisor for some other group that was diverse? That kind of thing.

I guess I think there’s no reason to talk directly about your sexuality when you talk about your experience promoting diversity, even though it might be inferred, rightly or wrongly.

To sum up, I would not come out in a “statement of diversity.”

Auntie P


Please submit your well-specified, fun-loving, cleverly-abbreviated question to Aunt Pythia!

Click here for a form.

Categories: Aunt Pythia
  1. e
    November 8, 2014 at 1:21 pm

    This is for U&I. I’m a mathematician, 30, nearing the end of my first postdoc. Here’s one thing I didn’t know as an undergraduate: if you keep on in physics and keep loving it, you are going to get so much “smarter”. It’s astonishing. And really exciting.

    The thing about the “genius” trope is that it suggests intelligence is fixed, innate. But as I get older this seems further and further from my experience. I’m a much better mathematician today than I was two years ago and two years before that and two years before that.

    The people who you meet who blow you away, who make you think “wow (s)he’s really good,” are invariably those who work the hardest (usually because they love math/physics the most). And I know a number of people who are really impressive now who didn’t particularly stand out ten years ago. I have a friend who is my age who I met when we were freshmen. He was fine then, obviously not stupid, but neither was he one of the stars of our class. Now he’s the big thing in his field, with whole conferences devoted to understanding his work, prestigious invited lecture series, etc. This transformation happened really quickly during grad school. Maybe he would have predicted it, but I think few others would. Except that stories like this are surprisingly common.

    I also notice signs of progress with myself. There are books I tried reading right after undergrad without much luck, that I was able to breeze through a few years later. Now I can flip open a random page and figure out immediately what’s going on.

    I’m much faster too, not just at reading mathematics, but in thinking about new ideas, coming up with simple proofs. When I teach, I often figure out how to prove the lemmas I present on the fly. I could have never done this when I was an undergraduate, or even a few years later. It’s as if my thinking has been streamlined as I absorb more proof techniques. It’s not just that I know more, but I’m also much “quicker”, which often passes as a first approximation of intelligence.

    This isn’t to say that math (or physics) isn’t hard. It absolutely is. That’s part of why it feels so good when you do figure something out. And coming back to the same ideas day after day when you’re not making any headway can be super discouraging. I’ve had periods of months where all I manage to do is figure out that something I’d understood was wrong. But then there’s a few magic weeks when progress happens really quickly. And all the time I’m getting better.

    So that’s my main takeaway. If you really love physics, you will get so much better at it. I really believe that your potential is unlimited. And if you stop loving physics, then there’s really no harm done. One of the great things about grad school in the sciences is that you typically don’t have to go into debt. If at any time you’re sick of it, you can just walk away. So why not give yourself the chance to love it?


  2. alex
    November 8, 2014 at 10:37 pm

    I didn’t know what U&I’s “sample question” referred to either, and so I typed it into the search bar at the top and found your sample question (copied below) for readers to submit to Aunt Pythia, perhaps that could be what U&I was referring to?

    “Dear Aunt Pythia,

    I’m a physics professor, and an undergrad student has asked me for a letter of recommendation to get into grad school. Although he’s worked extremely hard, and he has some talent, I’m pretty sure he’d struggle to be a successful physicist. What do I do? — Professor X”

    This was in the Nov. 3, 2012 post announcing the conception of Aunt Pythia. The weekly bundle of joy that is Aunt Pythia first arrived a week later on Nov. 10, 2012. In other words, we are two days away from Aunt Pythia’s second birthday! Happy Birthday!!!!!

    I heard Aunt Pythia will be celebrating by going to Haiti. Enjoy the trip. But I was wondering, why is she going to Haiti?


    • C
      November 9, 2014 at 5:18 pm

      Yes, that is the question I was talking about! It made me feel as though even if I have some talent and work very hard I could still be unsuccessful for reasons beyond my control, which scares me.
      Happy Birthday, Auntie P!


      • quasihumanist
        November 9, 2014 at 8:30 pm

        The math job market is terrible, and the physics job market by and large even worse. Lots of talented, brilliant people who are capable of doing math or physics research find themselves unable to get a job that involves math or physics research, or even any academic job at all.

        The rational, [i]homo economicus[/i], move is to learn to code and go get a job with Microsoft, Amazon, Google, or some cool startup. You can always spend a decade or two making a million or two, and come back to research if you’re interested, though maybe by then you won’t be quite as brilliant.

        I’m glad many people, myself included, aren’t rational [i]homo economics[/i] (or whatever the correct Latin plural is).


    • November 9, 2014 at 6:38 pm

      Thank you so much for the birthday wishes!


  3. November 9, 2014 at 10:29 am

    I know I always say some variation on the same thing regarding technology and math education, but here it is again: after (almost) 20 years in this business and dealing with at least 1000 undergraduates in math service courses, I find that, by far, the most important aspect in student success in mathematics is “engagement”: engagement with (a) other students, (b) my university’s (free) tutoring office, (c) the teaching assistants for the course, and (d) the instructors, especially during office hours. I find it tiresome to keep reading “technology changes everything”, especially when the results of experiments (such as San Jose State’s MOOC experiment) show otherwise. Instead of something so grandiose, wouldn’t it make more sense for enthusiasts to focus on something specific: computer graded tutorial exercises give better feedback than one TA can hope to give for each of the 600 solutions (60 students x 10 solutions) that he or she needs to grade in one week?


    • alex
      November 9, 2014 at 11:43 pm

      Jason, great comment and I don’t disagree. I was wondering if you (or other readers) have ever gotten frustrated with students getting too much help, and if so how do you deal with it? I have too many students who go to the math help center with good intentions, but basically end up getting their homework done by the staff there, or intend to “work together” with other students, but end up essentially copying once one person finds out the solution…mathematicians do this too so I understand. I know you were talking about most in math service course, but in your experience do find engagement also correlates with success in upper level undergraduate courses (e.g. abstract algebra)? I am not opposed to students working together – and in fact I encourage it – but I can not spend the effort policing between an honest effort of working together and then writing things up in your own, vs blindly copying without understanding. But then during tests, I am disappointed but not too surprised when some students with perfect homework scores don’t do well. So I have stopped collecting as much homework (I still assign a bunch) and instead rely on in class quizzes. My point is, I have a bunch of engaged students that aren’t being very successful and I’m trying to figure out how they can be successful. Some of them get C’s in the prerequisite course (on proof techniques), so I can’t see how they can get a better grade in say abstract algebra or real analysis.


      • November 10, 2014 at 12:00 pm

        There is definitely confirmation bias in the following: I find that struggling students improve by visiting my university’s tutoring center and by meeting with me in office hours. Absolutely students press tutors to solve their homework, rather than just getting tips to help the student solve the problem. Although that is not optimal, it is often not a bad first step. First, these students are often very confused. So even if we are just showing them how to solve problems, rather than engaging them in the process, that is still relative progress. Even if I solve a problem for a student (a homework problem with some numbers changed), I don’t let the student leave until they repeat back to me what we discussed. Second, usually several students show up at my office hours simultaneously. By working through some problems as a group, sometimes these students bond and form a study group. At any rate, they become more engaged with each other, and not just with me. Of course one of those students may be a “source”, but students tend to learn from each other faster (not necessarily better) than they learn from “us”.


  4. November 11, 2014 at 4:01 am

    I wrote up some observations on hand-calculation vs computer-based math on my family blog (link below) based on something one of my children was doing.

    For you tl;dr folks, the key point I realized is that many current students are so comfortable with technology that the split hand-calculation vs automated as a bright line may not exist for them. Without even realizing what they are doing, they can easily play with small or simple examples by hand to get the feel for what is going on and use machines to do larger, more, or more complex examples. In a single sitting, maybe they will go back and forth several times.

    And yes, for those inequality/social justice folks, this is a point that can perpetuate inequality. There will be some houses where the kids see excel (and desmos, and geogebra, and etc etc) as a matter of course and other houses where they don’t even possess a calculator.

    The link, as promised:


  5. Irene
    November 11, 2014 at 9:28 am

    The problem about needing to know the hard stuff in maths is – how can you know that you’ll want to be a mathematician or physicist early on? Was I unusual in that the head teacher of my primary school told my mother when I was 5 that I was a mathematician or that my daughter (now 22 and studying engineering at Cambridge) said when she was 6 “I want to be a supermodel and then do maths or physics at university” (she managed the modelling too but not the dizzy heights). I’m now a statistician – I struggle with some of the theory but good on new ideas and application of mathematical modelling.


  6. Quentin
    November 13, 2014 at 10:28 am

    I grew up being the best at math and science in my class. Then I got a PhD in engineering and gradually came to feel very average. I feel like I’ve been able to make a meaningful contribution once in a while, but it’s also become clear to me that there are people much more capable than I out there. I once had a very enlightening conversation with a colleague in which we both admitted to feeling a sense of insecurity about what others expected of us due to having a PhD. I’ve worked in companies where I’m surrounded by other PhDs and in others where I’m the only one. Both situations bring out those insecurities in different ways.

    I recall once hearing the very talented Tina Fey say in an interview that she goes through life worrying that any day she’ll be exposed as a fraud. I think that is the reality for nearly all of us. So, don’t let your insecurities stop you from trying to go as far as you’re able.


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