Yesterday on a hike someone named Sara, who is not a mathematician nor a scientist, asked me what I do. I said I worked on theoretical computer science, that is, the mathematics of computer science. She asked: "What is it that you people do, exactly? I can understand what a musician, say, does in his work, but I have no idea what mathematicians do."
I started trying to answer her: "You like games. You enjoy puzzles. Consider the Rubik's cube, and think about what your brain does as it is trying to figure it out. That is very similar to what a mathematician does while he or she is working on solving a problem. In addition, instead of working with a physical object, it's as though they had a picture of the Rubik's cube in their head, and they work with their representation of the mathematical world inside their head, so it's a bit more abstract." Omer Tamuz intervened: "yes, abstraction is very important. Here is an example. For every group of six people, if you look at which pairs are friends and which are not, there always exist either three who are all friends or three, none of which are mutual friends." He tried to explain it more clearly, I criticized that choice of an example, he asked me what would be a better example of abstraction, I suggested commutativity of addition and of multiplication, he suggested that removing three apples from eight apples leaves five apples, just in the same way that removing three oranges from eight oranges leaves five oranges, I criticized those examples for not being impressive enough, suggested the probabilistic method, it reminded him of Noga Alon's simple and beautiful first lecture in a course, which, upon my request, he proceeded to tell me about in full detail, and suddenly we came upon the others, including Sara, who had stopped for a break.
Sara had long since left Omer and me to join the others, but we had not even noticed her absence. She commented how amazing it was that after she had asked just one simple question, we took off with it, started discussing math, and an hour later we were still going at it. I was a little embarrassed. That doesn't seem like quite the right way to talk to a non-scientist about what we do, does it?
I am afraid that it reminds me of the 19th century cartoon L'idée fixe du savant Cosinus -- a must-read for all French-speaking mathematicians.
On the contrary. You answered the question "What is it that you people do, exactly?" perfectly!
ReplyDeleteMy go-to example is insertion sort versus bogosort. Everyone knows what insertion sort is from playing cards, and it's intuitively really obvious that it's a far superior algorithm to throwing the cards at the floor and gathering them up until you happen upon a sorted set. It's simplistic, but I think captures the seed idea of theoretical computer science for a layperson.
ReplyDeleteThis is something I still struggle with all the time! I vacillate between describing what I do in grandiose philosophical big-picture terms (I investigate the _fundamental_ limits of what can be done with limited resources; how can Nature be manipulated to solve difficult problems - this is usually accompanied by wild gesticulations), and describing what I do in more plain terms (I sit in a room and think very hard about math problems. No, I don't add up numbers all day.).
ReplyDeleteI guess it depends on who I'm talking to. Some people buy the philosophy spiel, some people just want to get a mental image of a mathematician at work.
I have the hardest time with people who have previously had bad experiences with math, because they come with preconceptions about math (it's just rote memorization! it's just being really good at calculation!). I try to convince them otherwise, that "real" math is more like writing a novel or composing music than accounting, but the analogy only goes so far before I hate myself for being inaccurate.
I like the infinite primes proof as an example of math. It differentiates rote calculation (is 37 a prime?) with larger questions about properties of numbers, and can be expressed at a fairly simple level.
ReplyDeleteThe existence of multiple proofs of the same theorem can sometimes enlighten people as well. There's a common perception that math is algorithmic: a set of rules you apply blindly to get a result. If they understand that there are multiple ways to get to a solution, and multiple paths that lead to dead-ends, and that choosing the right approaches to a problem is critical, it can help them see the creativity of the field. This goes along with cipher3d's statement comparing math to novel writing: there are lots of ways to build up a proof/novel, and some are just better than others, even if there's no easy way of telling a priori which is which.