I work as a researcher in a very abstract field of Mathematics (this kind of thing) It is very pure Mathematics, without any concrete applications. When I meet somebody for the first time, they often ask me about my job and they want to know the details: What are you working right now? OK, you just wrote a paper, but about what? What theorem did you prove?

Since the abstractness of my field, and since those people usually have at most a vague memory of High School math, the only sincere answer would be: I cannot explain it to you because you would have to know a bunch of stuff you do not know, and I cannot teach you those stuff either, because it would takes years.

Of course such an answer would be rude. So my question is: How could I deal politely in such situations?


  1. It seems to me that many users have interpreted the question as: "How can I explain my job as a mathematician to the average person?". I appreciate the efforts, however, that is not my intended question. The question is how can I politely deal in those situation since I cannot explain my job. Note also that my question is about when people ask details about my job. Of course if they just want a short answer, that is not a problem.

  2. Many answers are of the kind "you should be able to give a vague explanation…", and some even say "if you cannot explain to everyone then you do not understand it..." I kindly invite those who think so to try to explain the material that I linked to the average Joe.


14 Answers 14


If someone who truly does not have the background to understand your work is asking you to talk about it, chances are they are just being polite: They want to show interest in you and your endeavors and to learn more about you. In other words, they're trying to connect with you. The best way to respond is to reciprocate.

Look for common ground. The situation you describe is talking with someone who would literally need years of training to be able to understand your research topic enough to engage with you on that, so don't start there (I disagree with the advice to substitute a simpler explanation of some other mathematical phenomenon or example that isn't actually relevant to your research --- if you do that, you're moving the conversation away from both of you).

You can talk about your work without jumping right into explaining your research. The goal is to provide some concrete details that your conversation partner can connect with. For example:

  • Where (physically) do you work (on campus, at an institute, in coffee shops, etc.)?
  • How do you spend your working time (teaching, writing, programming, fighting with LaTex, mentoring students, traveling for conferences, etc.)?
  • Any notable events in your work lately (just submitted a paper, heading off to a conference next week, faculty at your institution are talking about a strike, one of your former students just started a job at X, you've been trying out a new laptop and you really like the touch screen for graphical notes, etc.)?

Of course, you can and should tailor the types of things you bring up towards things you think your conversation partner might be interested in. For example, if you're speaking to someone who is also an academic, bring up the article review you just got back with ridiculous suggestions from Reviewer #2. If you know they live/work in the same part of the city as you, mention your favorite coffee shop to work at, or the fact that you want to start biking to work. If you know they have some computing expertise, talk about the fact that you're thinking of running some simulations and ask if they know anything about high performance computing. You get the idea.

It sounds like you've run into problems with conversation partners following up on your vague explanations by asking about the specifics of your research:

When I meet somebody for the first time, they often ask me about my job and they want to know the details: What are you working right now? OK, you just wrote a paper, but about what? What theorem did you prove?

It's likely that they're just doing the best they can to keep the conversation going with what you gave them. For example, you may be experiencing something like this:

Them: So, what do you do?

You: I'm a maths professor at University of X.

Them: Oh, that's neat! What are you working on at the moment then?

You: Well, I just submitted a paper this morning, so that's nice to have that done.

Them: Cool. What's the paper about?

You're doing your best to keep the conversation light, but you're also not really providing any invitations topics to connect on. The only real pathway available to your interlocutor is to ask for more detail about whatever you just said, which will inevitably lead into the dreaded discussion of research details. Instead, try to use your answer to introduce details about your work that they might actually be able to talk with you about. Consider something like this:

Them: Oh, that's neat! What are you working on at the moment then?

You: Well, I usually do a mixture of teaching and research. But I have a course release this term, actually, so I'm trying to decide now whether to just spend that time writing or to use it to visit a colleague in Sweden and launch a collaboration we've been talking about the last couple years.

Or this:

Them: Oh, that's neat! What are you working on at the moment then?

You: Well, I do research in theoretical maths, but spend most of my time writing actually! I wish I could go back in time and be less of a smart alec with my high school English teacher --- being able to write about complex stuff in an engaging, approachable way is such a valuable skill, no matter what field you work in.

Or even something like this:

Them: Oh, that's neat! What are you working on at the moment then?

You: Well, I didn't get much at all done today, actually, since the guy in the office next to me had a bird fly in through his window, and we spent the whole afternoon chasing this poor sparrow around the department, trying to get it out.

To use tennis as an analogy, think about their question as a serve, and your goal is to return something that they'll also be able to hit.

If they really persist in asking about the details of your research, you can use something like anongoodnurse's approach to check that they really do want to you talk about it, and then give them periodic opportunities to change the subject if they want to back out.

  • 7
    +1 I think this answer (in contrast with the other - good! - answers) shows exactly what this SE is about. Interpersonal skills. Not telling ways of explaining something to someone, but stepping one step back, and see why would you want to. See if it's neccessary. Teaching something about communication, that is useful for everyone. I wish I could add a bounty.
    – Neinstein
    Commented Oct 15, 2017 at 17:37
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    What I don't really like about this answer is, that it suggests not replying to the question, but give an answer to a question that was never asked.
    – WayneEra
    Commented Nov 7, 2017 at 10:11
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    @WayneEra sometimes answering a question that wasn't asked in relation to the context is a much better approach. Hence why it's an accepted paradigm of conversation. As well as being an interesting way to apply game theory to a conversation.
    – JoeTomks
    Commented Nov 7, 2017 at 10:22

I'm a mathematician too. I think there are two important things to keep in mind: the first is that asking what someone does is just a polite question. The second is that they are probably very aware that they lack knowledge about higher mathematics. You don't need to tell them current exact research interest to answer the question.

What I do is tell them my general area: random graphs, and then a few very simplified sentences about that area. In my case, I say something like:

Graphs are objects that consist of dots, that we call vertices, and edges that connect two dots. To create a random graph, for every two vertices I flip a coin and if it shows heads, I add an edge, tails I don't add an edge. My job is to study properties of these random graphs.

If your area is abstract algebra, you could say something like:

Integers have the property that we can add them, subtract them, and there is a zero that doesn't change the number we add it to. I study the properties of other objects that you also can add, subtract, and have a zero.

If your area is topology, you could say:

It is a little bit like very stretchy geometry. Imagine that all objects are made of some really stretchy material, so you can deform them however you like, as long as you don't cut and new holes or glue any pieces together. I look at what properties remain the same when you deform these objects.

All of these explanations are highly simplified: an undergrad taking their first course in the subject would have more understanding than I give in those short explanations. But, they give the asker some buzzwords and the ability to think "Tzason studies stretchy geometry", in the same way they think "Lisa teaches high school biology".

After this, most people are perfectly satisfied. There might be a follow-up question, like "what kind of properties", which you can answer by taking a simple property, like connectedness in graph theory, or commutativity in abstract algebra, or number of holes in topology. They want a simplified explanation of your job, kind of like I know that an accountant works with an organization's budget, and a corporate lawyer advises a company on business law, and a translator translates things. There are a ton of details and complexities to all those jobs that I don't understand, and that I wouldn't expect them to tell me during a social chat.

If we keep talking about work, I tend to steer it towards the teaching part of my job which is easier to discuss, and maybe throw in some comments about bureaucracy. Everyone can relate to the complaint about having to fill in 50-page forms to get reimbursed for a trip, or that time when you spilled tea down your shirt right before teaching the first class of the semester.

  • 44
    As a (now-ex) mathematician in logic, this is always what I did. Explain (kind of!) what logic is, rather than why my research was. If they "get it" and ask for specifics, keep narrowing in until they lose interest or I lose the ability to say simple words about it. People really do appreciate these little summaries, even if it is an oversimplification. Commented Sep 3, 2017 at 18:41
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    I was talking once with a man who did a PhD in physics. This is all way beyond me, so I asked: "In layman's terms, what was your PhD about?" He started talking, and his wife then immediately corrected "Layman's terms..." "Oh!" He thought for a moment, then said: "We were doing research about observing subatomic particles, and increasing the accuracy of those observations." That I could appreciate. I very much approve of technical people being able to explain their work in plain English. That in itself is a skill!
    – user1923
    Commented Sep 4, 2017 at 9:31
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    I would never ask a mathematician what they specifically did; the fact that they are mathematicians already means I don't understand their work at all. This is a very nice answer; it's very respectful of people and kind. As a doctor, people pretty much assume they know what I do. Your "job" sounds much more challenging. Commented Sep 4, 2017 at 15:53
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    @anongoodnurse Ah, yes... almost everyone have no idea how a doctor really works. "Is it <insert disease>?" "Yes". I have GP doctor friends and that's their answer for the patient, but the true answer is "I don't know. I gave you drugs for all the non-critical diseases and you got better, so it was one of those. If you came back and was just as sick, then I look at the symptoms, move on to the next set of diseases, and give you more drugs."
    – Nelson
    Commented Sep 4, 2017 at 20:04
  • 5
    And you say that no one knows what a Hilbert space is. Well, sure. But for a conversation with a layperson with some high school math background, Google’s definition does nicely: “an infinite-dimensional analog of Euclidean space” (you’ll probably need to remind them that Euclidean space is basically just the space they’re used to). Maybe you can say that it’s a system that lets you look at length and angles for systems more general than ordinary space.
    – Obie 2.0
    Commented Sep 6, 2017 at 6:45

Why are you trying to protect them from not understanding? Why are other people suggesting all kinds of patronizing pre-screening questions? I would never ask something as specific as "what theorem did you prove?" if I wasn't prepared for you to reply with a mathematical theorem.

Perhaps they're asking because they find titles in fields they don't know funny. Perhaps they know more than you think. Just answer them the same way you would a colleague who knows as much as you do. It would be nice if you had a nontechnical sentence that explains why this is something to be proud of, such as

  • this settles a dispute that's been open since a paper by [someone they may have heard of] in 1954
  • this neatly ties together two famous theorems by explaining how they're related
  • this is the final detail in a long string of explorations and means I am likely to have my research fully funded for another 10 years
  • it's a sufficiently important result that I am sure to get tenure next year
  • I am mostly excited to have proven my arch enemy wrong

If you give your technical answer and the person exclaims that they can't understand a word of it, you can laugh and ask them something about their work instead. You're under no obligation to offer to explain or try to get someone up to a graduate-level understanding of your field over the course of a single party. But refusing to say words because you're sure the person you're talking to wouldn't understand them is a terrible way to manage a conversation.

Just this morning I asked someone working on a PhD in quantum physics about the presentation he's scheduled to give. He told me it was on Doppler-free spectroscopy models, to which I said "oh yeah, I hate when my spectroscopy models get all Doppler-y." He then gave me a two-sentence explanation which made perfect sense - though he was able to draw on his background knowledge: that I knew what the Doppler effect was, that room temperature atoms are moving a lot faster than the cold atoms used in a lot of quantum stuff, and what spectroscopy is. Still, having to add those explanations wouldn't have been super difficult. Perhaps you think your work is harder than that, and perhaps it is. But that's why I suggest you focus on the reasons your work matters more than the technical details of how it works. Everyone can relate to that.

  • 10
    I would never ask something as specific as "what theorem did you prove?" if I wasn't prepared for you to reply with a mathematical theorem How many theorems do non-scientists encounter in their lives? Pythagoras's theorem, maybe? It's entirely possible that you (or someone who asks for a theorem) doesn't even understand what they're asking for. In any case almost everyone on Earth would be disappointed by an answer that starts with "Let X be a Calabi-Yau manifold of dimension 12 and let D be a flat connection on X. Then [...]" and yet that is what you would be asking for.
    – user4965
    Commented Sep 4, 2017 at 15:21
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    I guess I would find it infinitely more snobby to reply with a highly technical, incomprehensible explanation and then ask smugly my interlocutor if they feel "educated" about what a theorem really is and if they got what they were looking for... It's not snobby, IMO, to realize that my field of work is very narrow and truly interests very few people. Whenever a non-mathematician has asked me for a theorem I proved or what I work on, I've vaguely explained what algebraic topology is about, and everyone has been (or seemed) satisfied so far.
    – user4965
    Commented Sep 4, 2017 at 15:35
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    "Why are you trying to protect them from not understanding?" If I ask a question, I want an answer that I will understand. Deliberately giving an answer that you think the other person will not understand seems terribly rude. Giving an answer that they don't understand, and then laughing when they don't understand, sounds horribly rude. Am I misunderstanding something? Commented Sep 4, 2017 at 17:17
  • 3
    You don't know this person. They've asked you a question. You think you know better than them, need to protect them. Why? As for the laughing, it's not laughing at them for not understanding, it's taking their potentially rude "your title is utter nonsense and gibberish" as though it was a lighthearted joke. Why is it weird if someone says "what theorem did you prove?" you tell them "that a 12-dimensional manifold and a flat connection can [] if []"? They can then say "wow, that sounds complicated" or ask you probing questions. Assuming you can tell who couldn't possibly understand is WRONG. Commented Sep 4, 2017 at 17:22
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    It's not about "protecting them from not understanding", it's about respecting them. Giving a layperson an expert-level answer is disrespectful. Granted, giving an expert a layperson-level answer is also disrespectful. I think the most respectful thing to do is not to assume that they're an expert; it's to take your best guess at their level of knowledge and answer accordingly. Commented Sep 4, 2017 at 21:52

One way you can answer truthfully and respectfully is to simplify it to the point where anyone can understand it:

I work at X (university?) in the math department, (teaching? and) doing research.

When people ask "what do you do," it's usually just a social query. They can then make the appropriate social response:

  • That sounds interesting. How long have you been doing that?
  • Do you enjoy the teaching or the research more?
  • Other.

You can change the subject at this point if you wish.

If they press further (I wouldn't!), you can give them an "out":

It's very theoretical, and there aren't many of us in my field. Are you sure you want me to continue (with a sincere smile)?

If they insist, I'd start explaining what I did. I'd stop from time to time to let them change the subject.

  • 7
    I'd stop from time to time to let them change the subject. + 10 for that. "No really, I want to hear about what you do" is almost always followed by "So did you catch the latest episode of soft core with a plot on HBO?"
    – coteyr
    Commented Sep 4, 2017 at 23:59
  • 3
    @coteyr - HBO: "...soft core with a plot" Lol! I love it! Commented Sep 5, 2017 at 1:29
  • 2
    Instead of a sincere smile, I like to give the smile of a cat that's about to eat the canary. It usually frightens off unwanted interest, and those people who take me up on the challenge anyways have a curious tendency to be rather interesting people to talk to!
    – Cort Ammon
    Commented Sep 5, 2017 at 18:12

In Randal Munroe's book The Thing Explainer (xkcd.com) he uses only the most common 1000 (English) words to explain things like what a cell is and what a Nuclear Power plant is.

I believe that if you can't explain yourself to "the everyman" that you either don't have a very good handle on it yourself or aren't trying hard enough. It is good that by posting here, you have recognized that that communication is difficult. There is an enormous gulf between the concepts and terminology you use and the everyman's. But, on the other hand, there's a multitude of ways to go about it.

I used to have a book on Pascal (CS language) and inside the front cover were words describing some transformations that characterize thought. (Things like (iirc) categorize, reduce, generalize, analogize, negate, invert, ...) There were dozens and dozens of them (and I added some to them that the author(s) had missed). I think it's ironic that math is ALL about transformations (I mean, if an abstraction isn't a transformation, then what is it?) and yet many find it so difficult to transform a description of what they are working on to something the "everyman" can understand.

I suggest that the major reason is that they're not able to see the forest through the trees. Suggestions:

  1. If at first you don't succeed (paying attention to the feedback) don't repeat the same experiment, and keep trying.

  2. It is virtually certain that similarly abstract mathematical problems have been 'explained' to the everyman. There are books. Learn from others but note that the art of communication can be as difficult as dealing with mathematical structures.

  3. Don't be too timid to do violence to some deeply cherished truths (fundamental theorems), what's key and core to one is irrelevant and unnecessary trivia to another.

  • Comments are not for extended discussion; this conversation has been moved to chat.
    – Catija
    Commented Dec 14, 2017 at 0:59

Turn the conversation into a 2-way learning experience.

Explaining what you do to people without the background is a great learning curve which I recommend to everyone. (Not least because you never know when a conversation with someone in an utterly unrelated field will spark the idea for your next breakthrough).

Usually I deflect or pre-empt the question away from what I'm specifically working on, to some more general point of contact with non-technicalities. The history of the subject is often the easiest thing for non-specialists to engage with. Not surprisingly, this involved me first learning some history of mathematics. (Lakatos, Proofs & Refutations was an excellent eye-opener).

But I also practise explaining one, or two, technical things. In the case of mathematical logic I've tried explaining Cantor's diagonal argument to people; and I've practised using, "This sentence is false" to explain Gödel's incompleteness proof. Last year (studying machine learning) I practised a 90-second explanation of deep learning.

Adopting the role of a learner in these conversations can turn them into real conversations for both of you: "Actually I find it really difficult to explain what I'm working on, but if you don't mind being a guinea pig can I try explaining ... to you"?

Finally, I apologise that I cannot resist the Feynmann pseudo-quote: If you can't explain it to a first year, you haven't understood it.

  • +1 for turning the difficulty around. "... I find it really difficult to explain..." vs. "You wouldn't have the background to understand."
    – Mr.Mindor
    Commented Sep 6, 2017 at 15:27
  • 1
    I get your good intentions, but it is somehow absurd that you turned the table as I am the one who should improve his ability to explain. I have absolutely no difficult in giving a nice explanation of things like Cantor's diagonal argument, indeed I did so a lot of times. But I explained them to students or very interested people, with a blackboard or a paper, and taking several minutes. Doing that after an introduction to someone is a totally different setting, do you think it would be appropriate saying (essentially): "now sit down and listen to my lesson..." ?
    – Tzason
    Commented Sep 6, 2017 at 17:24

Read the obituary of Maryam Mirzakhani in The Economist. (Mirzakhani was the first woman to win the Fields Medal, in mathematics, the equivalent of the Nobel Prize.)

The obituary included a description of her work, in layman's terms. A description at the level in The Economist's article may still be too abstruse for a conversation, but not by much.

Thus, my advice is for you to write the mathematical part of your obituary now, using the obituary in The Economist as a model, and keep it up to date. Have several practice conversations with a non-mathematician friend, so you can talk about your work in a natural fashion -- not as a monologue. The Economist ended the mathematical part of its obituary with:

Such work might seem abstruse to outsiders, but uses abound, from cosmology to cryptography.

  • Nice article. Does well by its subject. Commented Sep 5, 2017 at 15:10

I think that you have two problems. One is that your work can really only be understood by a small set of people that you will never meet by accident. There are probably a lot of such groups.

Where your problem is unique may be in that, as you said, it is very pure mathematics, without any concrete applications. The question that I have, and I suspect a lot of others would have, is "what's the point?"

I mean that as a question, not to dismiss you. I'd be interested in why you are doing what you are doing, and why those who gave you the grants and/or pay your salary are doing so. I think there are very good reasons for these things (or else abstract math would be financially bankrupt and you'd have to do something else to earn a living), but I don't know them.

The question "what do you do for a living" isn't necessarily a quest for facts (what does it really matter at that stage of meeting someone), but a search for a conversation hook. Sure, you may not be able to describe your specialty to a layman, but you could say something like "I'm an abstract mathemetician. Real abstract; I work on the sort of stuff that makes you able to read Alice in Wonderland and understand it." You're not insulting their intelligence, but warning them a little bit that following that line might take a turn for the bizarre. If they press on, they may be willing to wade through some explanations to get their answer.

If the next question is "If it's so abstract, then why do it?" If your reason is along the lines of "math is beauty", wax poetic about it. If it's because somebody it taking a long shot about it being practical at some point, mention some math that was abstract at the time and show how it became useful. How much work was done on the computability of prime factors of large numbers before somebody picked it up and said "hey, this is a great way to keep secrets!"

If you honestly can say that nobody really cares about what you're doing, that you aren't impacting anything or anyone, then I'm really confused as to why you're so interested, and why people are willing to pay for that sort of stuff. If you can show some impact, even if it's way down the line, you have a connection with the other person. If you can't show any impact, any explanation as to why you still do it is likely to be an interesting story.

  • I have the same question about the really abstract stuff. It's very much in line with this question, because that's what I would want to know: who pays for this? Why? (I suspect the answers may be "government/university grants" and "because they have a certain research budget and this seemed like a defensible financial choice," but I think that's possibly too cynical. But hey, if the mathematicians have fun and get paid....) ;)
    – Wildcard
    Commented Sep 6, 2017 at 5:25

My five-year-old son and my non-technical friends have a similar understanding of my career.

The general job title:

Software Engineer

What I do it for:

Aerospace and defense

My son understands that I tell computers how to fly spaceships. It's not true, but he does seem to grasp that what I do is in support of efforts like that--and that there are a lot of people and jobs in between.

Similarly, my friends joke that I am a "rocket scientist". They know it's not true, but it is a simple way of saying that I work on something complex in support of a larger aim which they understand.

As a mathematician, you work in support of mathematics as a whole. The framework of mathematics has loads of practical applications--arguably, all of human development hinges on mathematics. You can tell people that as a mathematician, you support the ongoing effort to deepen the understanding of this framework that has done so much for us, so that it can continue to do more.

The tough part is when they ask for more details. For me, if asked what exactly I'm doing, the answer might be:

I'm producing upgrades to the health monitoring suite of the common runtime environment for our laboratories.

That might be a bunch of nonsense to most people, so I start with "I support the common software for simulation labs."

For you, maybe you start with "I study the rules of math itself, independent of practical applications." You can reiterate that this is in support of the whole framework of mathematics.

If they press for more still, I just might tell them about that health monitoring suite, at which point the conversation might stop. It's not rude--they just realize they've hit the bounds of what they can relate to.

In summary:

  1. Start broad
  2. Tell them why the whole enterprise that you support is important
  3. Go deeper if asked until they stop
  4. Be ok with them having a knowingly flawed understanding of what you do

In my experience, they will understand that what you do is important, even if they don't understand why. Isn't that all you need?

  • This seems something like "Lies to children" - en.wikipedia.org/wiki/Lie-to-children Commented Sep 7, 2017 at 13:18
  • @GuySchalnat From that article, I like this quote: ""Any description suitable for human minds to grasp must be some type of lie-to-children — real reality is always much too complicated for our limited minds." Also, I think it is unfortunate that the name of the concept implies deceit, as I think no deceit is necessary for lie-to-children to work. People can be taught an imperfect model and still be aware that it is imperfect. As I said in my post, my friends know their understanding is flawed, and I believe my son knows this as well. Commented Sep 7, 2017 at 13:22
  • I think the point of the word "lie" is that it is ok to tell a lie if it points in the right direction of the truth to those who would not otherwise understand anything. For example, we know that Newton's laws of physics are wrong (Einstein changed them), but we are willing to lie to children and teach them anyway because they point approximately to the truth (for speeds nowhere near the speed of light, at least). Commented Sep 7, 2017 at 15:32
  • @GuySchalnat I know, but I think the connotation of deceit is unfortunate. It is a catchy name, but makes it difficult to talk productively about the concept with the uninitiated. Commented Sep 7, 2017 at 15:36

I feel your pain.

I work from home, and it seems that no matter how I try to explain it, I get the same things over and over. They either think:

  • I have no job
  • I do some work but not, like, full time <- my favorite
  • I deal drugs and that's where the money comes from

It never fails. Doesn't matter who it is or how close they are. Aside from my wife (and others that work from home) they all do it. They just don't comprehend that I can work a 9-5 job from a room in my house.

The solution

Use an analog. I tell people that I "own my own business." And if they pry more then I go with "Well, just like you, I go to the office, I punch in at 10, and I punch out at 10, it's just that my commute is shorter." Then comes "What do you do?" Tricky one for me to answer to many people so I go with "I work! Of course. I run my business. That's what owning a business means" Finally I am asked what does the business do? That gets a vague answer; "It does things with computers and websites."

You should use the same tactic. What do you do should be answered with a very abstract concept. "I work for the University, doing research. " What kind of research? "Math stuff"

I can't tell you waht to say, but I leave my story as an example. They don't care what theory or proof your working on, hell I don't even really know what that means. What I do know is that you said "Math Stuff" so guess what are dinner conversation is not going to be?

  • 1
    But "I work, just like you" is such a boring answer. If I ask a question like that, I hope to be told about the difficulties (or fun) of managing people (employees, suppliers, customers) and bureaucracy (taxes, grants, patents). All of these can be interesting and ground for further questions for someone whose line of work doesn't include something similar.
    – Llewellyn
    Commented Sep 4, 2017 at 19:03
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    The problem is that math is "boring". Every field is boring to most people, otherwise they would all be in that field.
    – coteyr
    Commented Sep 4, 2017 at 23:57
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    There is really not a comparison here at all. Instead, compare: "I work from home" to "I work in my office." It's not an answer at all. What do you do is the point. Not related to the question—but you probably could edit it so it is.
    – Wildcard
    Commented Sep 6, 2017 at 5:22

I have read the other answers here, and I think they all offer very useful insights. I'll adopt some of them myself, thank-you all! I'd like to offer one more, if I may...

Whilst my own approach will be very culturally dependent and will not work everywhere, I can say that it works perfectly well in Australia:

I use humour. Self-deprecating humour more often than not. (It's a personal favourite).

I am an organization theorist. Practically, that means I study management and organizations. Academically, 'management' covers a range of sub-fields from soft 'people' things like organization behaviour (which is, in effect, psychology) to hard things like the ways that organizations are structured (and structure themselves), and strategy and such, and a range of other things in between those two extremes along a kind of soft-to-hard continuum.

I have just submitted a doctoral thesis about organization theory. In it I examine the organization structures and power relationships among a group of people who make up a large Open Source Software project. The nature of 'employment' in such an organization means that power relationships are largely inverted as compared to those in a conventional organization, and so I examine those relationships, along with psycho-social and organization-theoretical notions of 'motive' and 'self' and power and resistance and such in the hope of informing management practice in the 'real' world.

That's a hell of a mouthful to explain, and I've already vastly simplified it for this answer. There's a real risk in rendering the conversation at a dead-end from the outset if I start like that. It wasn't until a month or so after I completed that I realized that what I had done was:

"I wrote a book about people fighting among themselves on the Internet".

and that makes me

"An expert in fighting with strangers on the Internet".

This approach works pretty well for me. If a person really wants to make polite untechnical conversation, this tells them what I'm up to, and lets them off-the-hook insofar as being dragged into incomprehensible technicalities goes. If I've dumbed it down TOO much, and my audience (of one) actually does have the capacity to understand more, my flippant approach is self-deprecating, so I'm insulting myself, not them. Again, this is very culturally dependent...

In Australia we have the notion of the "tall poppy syndrome". Analogically, it visualises a field of poppies in which one flower grows taller than the rest, and because it's "head is sticking up", it is at greater risk of being cut down than others. Socially, Australians are uncomfortable with self-promotion and will seek to 'cut down' any 'poppies' that stick their heads up. It is similar to the Filipino notion of "crabs in a bucket" wherein if you put a single crab in a bucket you must put a lid on top to keep the crab inside, but if you have two or more crabs, you don't need a lid because they'll continually pull each other down.

There is another idea, one that I suspect extends further than my own national culture, and that is the broad perception that much funded academic research is meaningless, trivial and wasteful of public funding. Layfolks don't understand the notion of "standing on the shoulders of giants" as the means of building reliability and veracity as we do, so explaining that I spent ten government-funded years watching people argue on the Internet will likely be met with a kind of unspoken derision. I think that folks recognize that research is valuable and useful, but they don't see the long-term connections between individual studies and societal benefit. By describing my work in humourous terms, I allude to that social concern in a way that makes no attempt to defend against it and keeps me firmly in the socially-requisite 'bucket' until my audience chooses to life the lid.

So, explaining my work as "fighting on the Internet" is culturally appropriate here. It's simple, it's self-deprecating (a precise opposite for self-promotion) and, believe it or not, it's accurate. So if my audience DOES want to know more, I can develop the facetious explanation into a more technical explanation about how studying people fighting on the Internet genuinely informs those other theories that I raised above, and how my research will directly inform management practice so as to make managers more successful, staff happier and companies more profitable.

It works for me.

I adopted the approach, in part, after observing an evolutionary biologist whom I admire, Prof. Rob Brooks of the University of New South Wales in Sydney, Australia, regularly introduce himself - often in quite solemn situations and in senior, important and elite company - by saying "it is my job to spend a lot of time thinking about sex". It always makes the more 'proper' individuals ever-so-slightly uncomfortable, but it amuses everyone, and it is accurate.

In both cases, if the inquirer is happy with that answer, they'll leave it there. If they want more, if they want to talk about sex or about fighting strangers, then these flippant and slightly facetious responses are genuine, accurate and valid, and can be developed into more properly technical explanations of our work.

I'd like to add that I think it is important for all scholars, or anyone who does deeply technical work, to be able to explain what it is that we do to laypeople. As @chris-f-carroll pseudo-attributes to Feynman in his comment elsewhere on this page, though perhaps not for the same reason, it is important to be able to explain oneself to non-technical audiences. At some point, you'll want to explain the value of your work to your Mum or your partner or a senior manager who controls funding that you need. For that reason, we encourage research students at all levels to keep thinking about how to explain their work: we set "explain your 80,000 word thesis thoroughly and accurately in 150 words" tasks, ask them to speak for no more than 10-15 minutes at bi-annual progress reports (and to take questions from their audience), and encourage participation in "Three Minute Thesis" competitions.

A final point I will make is that those of us who work at deeply technical things are well used to being misunderstood - or simply not understood - by laypeople. Very occasionally, we meet individuals who do understand what we're talking about and find ourselves having inadvertently "dumbed it down" too much for a particular audience. It feels a little embarrassing when that occurs, but the situation is easily recovered by a brief and honest apology. The other person always understands.

Thanks for the question and the opportunity to reply. I hope my perspective helps somehow.



“You see, doing maths is about changing one's brain to start thinking more clearly about some ideal things, pure objects of thought. That brain changing work takes a few years before it makes sense to talk of the problem that I wrote a paper about; it's a slow process. When you're done, be welcome to ask again.” That way you don't blame your friends' inability to understand you on them, on their wits etc (or on your own inability to explain something). Obviously they had perfect reasons not to spend those years doing such necessary self-changing work.

That's if they really mean it (willing to know what you're doing right now, and so on). That is, if that's what they're willing to figure out. It may well be they want to figure out something else, like why people might need to do that kind of job, anyway (or pay for it, which is a yet different question; or why getting ideal might ever turn out to be useful, another question too).

I once asked a mathematician (a kind man) whether Wikipedia might help in understanding topics like abstract algebra, without working through text-books. He answered along the lines, “well, unless you think you could learn what ‘War and Peace’ is about from a short description, most certainly no”; obviously I didn't think that I could do so, so, if unclear, that answer certainly was not rude. You might think of other comparisons like this. There are other subjects where one has to learn the real thing before uttering anything at all.

I think sarcastic answers (like starting to talk techno) are worse than what you suggested.

PS: a shorter way to say the same: “that's a thing nobody has yet ever explained to anybody; because it's not for explanation, it's for realisation through getting lots of experience in thinking about such objects”; if they ask why it's useful, “the objects are not useful by themselves, but the thinking sometimes is” (opposite to the usual situation like e. g. a road is useful, but the action of building the road is not, by itself).

To explain is to link what you do with other people's experience. Those objects that mathematicians now study have never appeared in anyone else's experience (unlike roads, laws, or food); that's not just a question of terms, additional technicalities, or a complex lingo. I think the only link is not in the objects of the action, but in the very action itself, which is the thinking. Everyone has done lots of thinking in his life, whether wisely or not; so it's in everyone's experience. So, one needs to change the topic: from “what I am doing right now” to “how mathematics is done”.

While it is perfectly possible to give a sincere polite answer, there is an insincere alternative: to say along the lines “I don't like to discuss maths when I don't need it for my work.”

  • 2
    While the quote at the beginning is not necessarily wrong, telling someone that they need to go through a years-long "brain changing" exercise before you can explain what you do to them doesn't seem like a great way to handle this problem...
    – reirab
    Commented Sep 6, 2017 at 2:41
  • @reirab The real problem is that (minus some problems of wording, possibly) that's the truth. If people insist on being told the truth, all one needs to do is to do it in the nicest manner possible. I think the nicest manner is to point out that the problem is objective: one really needs to train for a few years, that's what everybody else has done too, there's no quick way. Therefore, it's nobody's fault. I don't expect to be a piano player without extensive training. Our brains are like pianos that we play, they're not us.
    – Wanderer
    Commented Sep 6, 2017 at 3:40
  • @reirab Just to add: that was the way that the problem was handled with me. After I got it's really this way, I stopped taking offence that mathematicians do things I don't understand at all. Meaning, I could well have understood all that stuff if I just spent some time I wouldn't want to spend; so, that's not my fault. I am at the other side of the problem, really.
    – Wanderer
    Commented Sep 6, 2017 at 3:44
  • This is not true. It depends on what purpose you have for your study of the information. You can have a conversation without doing years of study.
    – Wildcard
    Commented Sep 6, 2017 at 5:26
  • 1
    You seem to no longer be logged in to your account. Please consider following the contact link to merge this account with another as you seem to be submitting edits anonymously.
    – Catija
    Commented Sep 6, 2017 at 18:58

I deal with this problem all the time. My job is very difficult to explain, even to people that are experienced in STEM subjects. Explaining what I do is tedious, both to me and them, and it doesn't really improve their lives in any way - especially since all they usually learn is how to parrot back my explanation without any real understanding. My wife even gave up trying to understand my job, let alone explain it.

Tell them you cannot give them details because of intellectual property (IP) rights, or a non-disclosure agreement (NDA).

This works for me almost all of the time. In most fields where this problem is applicable, there will be some kind of NDA or other IP protection in place. Use it. If there isn't anything like that, and you feel comfortable fibbing, this is still an effective tactic. The conversation would go something like this:

A: What do you do for a living?

B: I'm a researcher in mathematics.

A: Oh cool! What exactly do you research? Or what do you do all day?

B: Well, the math I research is really abstract, and honestly not super exciting. I mostly write papers and things like that, but I really can't get into the specifics since I have an NDA with the University.


Another possible way is to present something from your field that is accessible to a layman to give the flavour of the thing. For logic, you could tell them about the question whether there is the same "number" of rational and real numbers and Cantor diagonalization. That's something an average person can grasp without much background a in a few minutes.

In other words - tell them a Gardner column :)

  • Comments for the down votes? Commented Sep 10, 2017 at 11:31

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