Comment by hypersoar | Hacker News Reader

Comment by hypersoar | Hacker News Reader

I'm pursuing a career as a math professor (currently an undergrad). I'm not shy about my passion for math, and this has lead to countless conversations like the ones below:

"What do you want to do with your math degree?"

"I want to go to graduate school and eventually become a math professor."

"Oh, so you want to teach!"

"No, I want to do research."

(Here they give some expression of confusion. I've had this particular conversation dozens of times)

Also

"So, what do you do in math research? Do you just sit around and solve equations all day?

I do my best to explain to these people what math is like and why I do it, but I usually don't feel like I'm getting through. I have been told by mathematicians many times, and have experienced myself, that doing mathematics requires lots and lots of frustration (I'm sure many people here, including those who don't do pure math, know what I'm talking about).

But for me the most frustrating and disheartening part of math is the fact that most people don't know what it is. It's not just that they don't understand the details, or what happens at high levels. It's certainly not just that they look at an end product (analogous to, say, a product from a startup) but don't get where it came from. It's that most people fundamentally don't understand what I do. They think of math as the capricious monotony they were put through in grade school and can't fathom why anyone would consider dedicating a life to it. Most aren't even willing to try. My love of math is a very big part of me, and it's a part that very few people understand.

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.

"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).

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.

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.

"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.

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.

>"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.

The problem with toy-based analogies is that people then think the math is a toy. "Who cares if you can solve a Rubik's cube faster?"

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.

I get the same thing as a CS person. Every time someone refers to me as an "IT major" or expects me to be able to fix their printer drivers I die a little inside.

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