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Agreed. I'm currently in your same position, only a few years ahead (in my second year of grad school, currently). When I try to explain math research to people

Agreed. I'm currently in your same position, only a few years ahead (in my second year of grad school, currently). When I try to explain math research to people, I too am left with strange looks. I think most people honestly think that mathematicians sit around and multiply larger and larger numbers together. Part of the problem of explaining the true nature of mathematical research is one of language. For example, I study Lie algebras and representations. People ask me "What are Lie algebras?" and pretty much the only definition I can give that is understandable is "Lie Algebras are a kind of algebraic structure that is useful in many fields of science, including quantum physics." This is an answer many people understand (on the surface), but it really doesn't say anything. What's worse, most of the time, when we justify or explain our research, it is by connecting it to fields that the person may be more used to (astronomy, biology, physics, economics, etc.). But for those of us in pure math, we really do not think about these fields in our day-to-day work. That is, I study Lie algebras because of their beautiful structure and the interesting combinatorics behind them, not because they are useful in some other field. So a better answer to the question "What are Lie algebras?" would be something like "Lie algebras are vector spaces with additional algebraic structure that gives rise to beautiful and deep combinatorics. They occur naturally as certain sets of square matrices, and are a kind of generalization of the ideas of symmetry." However, this is mostly unintelligible to most people who haven't taken some mathematics beyond calculus, and I find that it sounds condescending to a lot of people, which turns them off from listening to any more explanation. What I've taken to saying lately in response to a question along the lines of "What do you do in math research?" is something like "Mathematicians create new knowledge from existing knowledge. They take things that the human race already knows, and using only logic, they deduce new things. This allows them to find fascinating relationships all throughout the world." I find this response to be pretty good. It's mostly accurate, it's mildly interesting, and best of all, it's short.

geebee 16y ago
"Lie algebras are vector spaces with additional algebraic structure that gives rise to beautiful and deep combinatorics. They occur naturally as certain sets of square matrices, and are a kind of generalization of the ideas of symmetry." I was math major, and I did an MS in a very math-related Industrial Engineering program (lots of proofs about convexity and stochastic processes). And honestly, I don't really understand this either. And I actually know what "vector space", "combinatorics", and "square matrices" are, and I'm aware that algebra is more than a second year high school subject. I wonder if I'd get it if you spent more time explaining. Unfortunately, your field is extremely abstract and difficult to understand, though it is kind of possible (that PBS special on fermat's last theorem did explain some pretty incredible things to people who don't have a math background).
lacker 16y ago
It is hard to explain the value of higher math, but it's worth it. Perhaps a better answer to "What are Lie algebras?" is to respond in terms that mean something to your audience. Avoid words like "vector" and "combinatorics". Instead use metaphors. Like Rubix cubes. Tell them Lie algebra is a way to solve Rubix cubes faster. And also other similar puzzles that are way harder than Rubix cubes. It's true enough for casual conversation and probably more interesting than a vaguer answer.
- shou4577 16y ago
  I realize that using words like "vector" and "combinatorics" are poor choices. This is part of the problem. It is difficult to come up with a good metaphor that is simultaneously interesting and meaningful. I think the Rubik's cube is a great example. Thanks, I'll be using that in the future.
  - protomyth 16y ago
    "There are a lot of hard problems out there, sometimes they are toys like the Rubik's Cube and sometimes its quantum physics. I work on the math that let's people solve them." Every software developer has had this conversation themselves.
  - sliverstorm 16y ago
    Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated. Make sure it's something they've heard of before, e.g. the Rubik's cube example.
    - pbhjpbhj 16y ago
      >"Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated." Although I'd guess for most researchers in Maths what it can be used for is many years away (if it actually has a "practical use") and what it can do is far too esoteric for the layman.
  - 16y ago
gaurav_v 16y ago
I too am super pumped about Lie algebras, and have come up against the issue of how to explain the topic to my less mathematically inclined friends. You have to start with groups. Group structure is something that's both beautiful and something that can be truly appreciated in a 'cocktail party' setting. And you can't convey anything of substance and true about Lie algebras to someone who doesn't know what a group is. Then, once your listener is happy and feeling smarter about his new group theory knowledge, you can try to motivate the idea of a Lie algebra however best fits with your research. This way, you are able to tell your listener something comprehensible, and also hint at what else is out there. At least, I've found that this explanation keeps people pretty happy.

geebee 16y ago

"Lie algebras are vector spaces with additional algebraic structure that gives rise to beautiful and deep combinatorics. They occur naturally as certain sets of square matrices, and are a kind of generalization of the ideas of symmetry." I was math major, and I did an MS in a very math-related Industrial Engineering program (lots of proofs about convexity and stochastic processes). And honestly, I don't really understand this either. And I actually know what "vector space", "combinatorics", and "square matrices" are, and I'm aware that algebra is more than a second year high school subject. I wonder if I'd get it if you spent more time explaining. Unfortunately, your field is extremely abstract and difficult to understand, though it is kind of possible (that PBS special on fermat's last theorem did explain some pretty incredible things to people who don't have a math background).

lacker 16y ago

It is hard to explain the value of higher math, but it's worth it. Perhaps a better answer to "What are Lie algebras?" is to respond in terms that mean something to your audience. Avoid words like "vector" and "combinatorics". Instead use metaphors. Like Rubix cubes. Tell them Lie algebra is a way to solve Rubix cubes faster. And also other similar puzzles that are way harder than Rubix cubes. It's true enough for casual conversation and probably more interesting than a vaguer answer.

shou4577 16y ago
I realize that using words like "vector" and "combinatorics" are poor choices. This is part of the problem. It is difficult to come up with a good metaphor that is simultaneously interesting and meaningful. I think the Rubik's cube is a great example. Thanks, I'll be using that in the future.
- protomyth 16y ago
  "There are a lot of hard problems out there, sometimes they are toys like the Rubik's Cube and sometimes its quantum physics. I work on the math that let's people solve them." Every software developer has had this conversation themselves.
- sliverstorm 16y ago
  Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated. Make sure it's something they've heard of before, e.g. the Rubik's cube example.
  - pbhjpbhj 16y ago
    >"Telling them what it can do or what it is used for is almost always the best way to talk about something you do with the totally uninitiated." Although I'd guess for most researchers in Maths what it can be used for is many years away (if it actually has a "practical use") and what it can do is far too esoteric for the layman.
- 16y ago

gaurav_v 16y ago

I too am super pumped about Lie algebras, and have come up against the issue of how to explain the topic to my less mathematically inclined friends. You have to start with groups. Group structure is something that's both beautiful and something that can be truly appreciated in a 'cocktail party' setting. And you can't convey anything of substance and true about Lie algebras to someone who doesn't know what a group is. Then, once your listener is happy and feeling smarter about his new group theory knowledge, you can try to motivate the idea of a Lie algebra however best fits with your research. This way, you are able to tell your listener something comprehensible, and also hint at what else is out there. At least, I've found that this explanation keeps people pretty happy.