We've all heard it. I even got it in Norwegian recently. It's number 1 on the list of responses to the statement "I'm a mathematician.". Does anyone have any good comebacks? What other responses have you heard?
Standard community wiki rules (not that anyone seems to take any notice of them): one answer per post please. Also, no snide comebacks, please - keep it nice. Extra kudos for answers that would actually educate the other person.
The tricky thing about that response is that there's often some pride in not being good at math, perhaps because they've gotten so far with out having to know any math (so they must be pretty good, right?). More often than not, what the person is getting at is that they were right when they said to themselves in grade school "I'm never going to need this."
I size the person up, and if I think the answer will be an emphatic "YES", I respond with something like, "but you can read, right?" Then I try to draw a parallel between math and reading. Neither of them (in much quantity) is strictly necessary for getting by, or even to be successful, but if you read (or think mathematically) often, it enriches your life. At this point, their curiosity is usually piqued, so I'll try to steer the discussion to how your understanding of the world might be improved by thinking about probability, symmetry, or abstraction (depending on what I think will best engage the person). I try to get across that doing mathematics can be for pure enjoyment or curiosity with examples of interesting or counterintuitive elementary results.
It's hard to see this question as something specifically relevant to mathematics. That is, it sounds pretty much the same as asking `What are good ways of carrying on a conversation?' Of course there's no simple answer to that either. To the extent that I'm able to give anyone advice, I would simply call for general sympathy. If you've already established a reasonable dialogue, I don't see that the response you mention would have to carry any problematic connotations. For example, asking plenty of sincere questions about the other person's interests would be one easy way of eventually having a serious discussion about your own.
I would like to remark that the prevalence of a negative reaction to the mathematical profession appears to me greatly exaggerated. I can very honestly say I've never encountered it myself in any social situation. Unfavorable and unrealisic comparison to the arts appears with surprising frequency, as in Lockhart's Lament. But I wonder if such commentators have ever compared the income or employability of an average mathematician with that of an average artist, musician, or writer. My feeling is we are often misled by the fact that the stars in art, music, or literature are so much more prominent than their mathematical counterparts. I'd rather not do it now, but I believe it's rather easy to establish that mathematicians do very well on the average, and this is generally a good thing about the profession. Average status is alright, and we give our stars due respect without overinflating them. The absence of publically recognizable gloss keeps us humble enough to be suitably happy. One could say the same for academic apitutude in general, brought up in one of the answers above, which again is quite well-rewarded on the average. Muddled thinking surrounding 'creativity' has been detrimental to education in many ways, but it's really quite sad if the rhetoric keeps even my fellow mathematicians from recognizing their overall good fortune! (Incidentally, I won't go into them here, but I also have reasons to consider mathematicians especially fortunate even among academics.)
By the way, I really don't like the answers that suggest blaming former teachers. This is an unfortunately common and irresponsible response to a complex question. I don't want to express this in too harsh a manner, but I might ask Qiaochu if he'd heard the teachers' side of the story before reaching his conclusions. Most primary and secondary school teachers I know of are dedicated people working under frequently difficult circumstances, doing what they can to teach basic and necessary skills. Perhaps their own skills are not optimal, but neither are mine.
Maybe I should nevertheless conclude this ramble with a brief answer to the original question: With genuine sympathy, say `Oh, I'm sorry to hear that,' and proceed with good humor.
P.S. I apologize for the moralistic tone of this reply. My impression is many users of this site are quite young, and I'm still a Confucian at heart.
Added, 18 November:
I feel compelled to add a few comments given the seriousness of the topic. That is, I would like people to consider the possibility that many perceived problems arise simply because of the overwhelming importance of mathematics.
Jonah Sinick made a number of thoughtful comments in a separate email, and one point he brought up was that the math he learned prior to the university looks nothing like the kind he knows and loves now. This is probably true. But since the comparison with music or sports is made frequently, consider how much a beginner at the violin practicing the scales resembles a professional performing Beethoven. And then how about running around the field for hours to build up stamina vs. the antics of NBA players? Obviously, there are many things whose mastery requires patient tolerance of the basic skills. Why then so much more perceived difficulty with regard to mathematics? This is because the entire population must learn it to a certain level, much higher, for example, than typical violin skills. Society in general at present considers mathematics that important, and much of the dysfunction flows out of this situation. I leave it to you to imagine a scenario where every child had to perform basic violin pieces as well as basic arithmetic operations, regardless of their inclination or talent. And then imagine we needed as many violin teachers as teachers of mathematics.
I hope none of you wish to argue then that mathematics is in fact not so important as to require such massive social investment. This is not because it runs against our interest, but because that's a really difficult case to make in our modern age, and probably too long to fit into the margins of this webpage. In short, don't blame teachers, don't blame the children, don't blame mathematicians. Blame industrial civilization, if you're so inclined.
The main thing I find surprising in many such discussions is that everyone realizes playing the violin or basketball well requires many hours of boring practice that lead up to the joy that comes with the different levels of mastery. But mathematics, and perhaps some other academic subjects, are supposed to be constantly concerned with being 'fun'. And then, I don't see the violinists themselves viewing the lack of inspiration in scales as a fundamental problem.
Of course I hope as many teachers as possible are able to convey some real sense of joy in regard to the mathematics they teach, and various notions of creativity can be occasionally useful and inspiring. But given the sheer scale of the task at hand, I wouldn't hope for methodological ingenuity to bring about overall improvement at any easily measurable pace.
Yet another addition.
I realize as I reread my own paragraphs that I've been explaining mostly one side of the story. So I'm adding a link to a short article that attempts to present a more balanced perspective.
"Neither was I." True story. In fact, I'm still not very good at math; but I can trust it.
"Mathematics is a very different subject if you learn interesting topics from someone who really likes it. Then you don't have it be all that good at it to like it too."
That may get to the heart of the matter in many cases. When someone says, "I was never much good at math in school," the typical implication is, "and that's why I don't like it." Yes, most people who say that aren't trying to be rude. Regardless, it is a little rude to imply that you're bored with someone else's profession, before he or she even says anything about it. Still, it's a mistake to be rude in response. The best I can do discuss math in the same terms as music (or even point out the analogy). I have never been much good at music, but of course I still like to listen to it.
I understand Minhyong Kim's point that it's always easy and often wrong to blame past teachers. I maintain that many grade school teachers don't like mathematics, however hard they may work and however much they might like children or teaching. They can't help but teach their feelings along with the material. (A suspect version of the material.) I don't mean to blame all of them. I know grade-school teachers who really do like mathematics. Yet there are others who openly tell their students that they didn't like math. It also doesn't help to have debased calculus classes with huge enrollments at universities — not all blame is at the grade school level.
Anyway, this opening sometimes buys me time to also say something about what I study.
"I'm not much good at it either; I'm just much worse at everything else."
(or anything else in good humor). I don't think an admission from someone that she wasn't good at math in school, by itself, should be taken as an invitation to pedagogy, but if she shows genuine interest in what I do, then that's another matter.
There is at least one category of people who always respond nicely to the statement that I am a mathematician. I live in the UK but don't have a UK passport, so every time I come back here it is necessary to fill a security form on the border. In particular you need to write your profession and I write that I am a mathematician. Security officers are always very curious when they read this and usually quite happy. Some of them would ask you to solve a problem, for example to prove that exp(i*pi)=-1. Others would give a mathematical puzzle trying to cheat you. I advise you to try this once :)
Despite my being a student, I still do receive responses similar to the response cited in the op. My response is usually, "Yes, but have you ever taken a real math class?" This usually results in some sort of explanation that mathematicians (most?) don't sit around doing calculus problems all day. Although, on at least one occasion, the person with whom I was speaking became very hostile at the suggestion that he did not know what real math was.
I tend to respond with something along the lines of, "Well, that's a shame. I hope you found something you were good at?" I've found it's easier to interface with non-mathematicians if you're willing and able to talk about whatever it is they do, rather than hope that they'll be interested in what you do...
It seems to me that frequently people will say this because they find mathematics intimidating. I don't think they're trying to be rude.
I try to get the idea across that mathematics is not always as complicated as it seems. For instance, the average adult may not know the term "integration", but a child can easily count the number of squares underneath a curve.
Yes, I understand your shame. I was never very good at [pick a topic at which you struggle], and it seems a pity to me to be so inept.
What other responses have you heard?
"Oh, I used to be good at math. (often followed by) I never made it to Calculus, though"
In some sense, this response is more annoying given that the individual saying this is often more certain that their (false) understanding of what "mathematics is" is in fact what "mathematics is." And there is somehow an implication that mathematics is nothing more than a college Calculus class.
"Why Nerds are Unpopular" by Paul Graham has some interesting points if someone wants to discuss how someone can be good at technical subjects.
Generally, I just take it in stride that a lot of people in the world think Math is this horrible horrible thing that they had to endure in a way that was almost like torture. I don't agree with that but I can understand how for some Math is an extremely hard subject as I had difficulties with various Arts classes for many years. My struggle is that while the teacher would say, "Oh just write what you want," or "Just draw what you want," this often had some ulterior point that wasn't communicated and when I'd get back the grade that was a 6/10 or 12/20 and I'd want to know what I did wrong, the teacher couldn't really offer specific points that I could use. Luckily I had a high school English teacher give me the algorithm for an essay that finally fixed a lot of my issues so I would start getting As in English as opposed to the C- or D I had been getting previously.
If the situation is where one can have a serious deep discussion, it can be interesting to hear the various horror or war stories that people have in Math classes. I find Math to be that rare subject where it is mostly Application and not knowledge or comprehension like other elementary school subjects.
For a final thought on this subject, I tend to find those that pursue academics to be the social outcasts in school. If most adults think good grades are something that is worthwhile and a good thing, how about rewarding that to the same degree that artistic and athletic abilities get rewarded in modern times? Artistic abilities would include the child actors or singers that can become rather famous for how this can be packaged and marketed. Child athletes are common in some sports like Gymnastics but there are also various team sports where one can become famous or popular for having some talent and combined it with a skill that has been worked. I will admit that even after being out of school for a number of years this still brings up bitter memories and confusing thoughts about what is the point of our education system in North America at times. Anyway, I think that I've rambled enough to have given some thoughts on this subject here.
I think Papert's analysis is in order here. He makes a distinction between school mathematics, which he refers to as "math" (with a somewhat negative tone) and mathematics proper, which he refers to as "mathematics".
School mathematics is often robbed of intuition. Lakoff and Nunez in their book "Where Mathematics Comes From" makes the conjecture that all mathematics is embodied. I think this is quite the case, and as "math" is often taught with no intuition involved, it cannot be embodied in the true sense.
So I suppose I would say
I don't do math. I do mathematics. There's a difference.
And go from there.
Pete Casazza discusses this briefly at the beginning of his article A Mathematician's Survival Guide, available here.
You were in school? How is it?
Here's one that I've been willing to try out: Although I hear a lot of people say that, I don't think I have met many people who were truly not cut out for mathematics. The problem is more that most people haven't gotten the chance -- or given themselves the chance -- to get to know mathematics. If you can think logically, you can do mathematics.
I really believe this is true. So instead of taking their remark as an insult, try to do something constructive with it. Maybe apply the Socratic Method to make them solve a small problem. This might take part of the cause of their disrespect/lack of interest away.
Like Scott Carter, I sometimes say something like: "I was never any good at [e.g.] writing essays..."
"I was never any good at math(s)" always makes me feel funny because usually the speaker is angling for some kind of commiseration which I simply cannot provide. So I try to change the subject as quickly as possible.
I find a far more common response to "I'm a mathematician" is "So you deal with really big numbers, right?"
MLevi's answer suggested a lot of people believe mathematics ends at calculus. In my experience more people don't realise mathematics extends beyond some notion of complicated sequences of arithmetic.
To a few people who replied with this or similar I asked them what they really thought I did with my day:
"I suppose you wake up and do some sums, maybe?"
I hear this pretty often from my freshman. It is one of the reasons why I allow my students to write extra credit papers about famous mathematicians, as a lot of inspiration comes from stories passed down. Maybe when a student reads about Conway, they will see the recreational side of mathematics, or I can use the story of Hypatia to inspire a nobler side of studying mathematics.
Even if a student makes it through Calculus, they have essentially been doing calculations and evaluations their entire mathematical career. A little history can go a long way in giving meaning behind the computations.