What is the mission statement of the mathematician?
In the past five years, I’ve been learning a lot about how mathematics is used in the “real world”. It’s fascinating, thought provoking, exciting, and truly scary. Moreover, it’s something I rarely thought about when I was in academics, and, I’d venture to say, something that most mathematicians don’t think about enough.
It’s weird to say that, because I don’t want to paint academic mathematicians as cold, uncaring or stupid. Indeed the average mathematician is quite nice, wants to make the world a better place (at least abstractly), and is quite educated and knowledgeable compared to the average person.
But there are some underlying assumptions that mathematicians make, without even noticing, that are pretty much wrong. Here’s one: mathematicians assume that people in general understand the assumptions that go into an argument (and in particular understand that there always are assumptions). Indeed many people go into math because of the very satisfying way in which mathematical statements are either true or false- this is one of the beautiful things about mathematical argument, and its consistency can give rise to great things: hopefulness about the possibility of people being able to sort out their differences if they would only engage in rational debate.
For a mathematician, nothing is more elevating and beautiful than the idea of a colleague laying out a palette of well-defined assumptions, and building a careful theory on top of that foundation, leading to some new-found clarity. It’s not too crazy, and it’s utterly attractive, to imagine that we could apply this kind of logical process to situations that are not completely axiomatic, that are real-world, and that, as long as people understand the simplifying assumptions that are made, and as long as they understand the estimation error, we could really improve understanding or even prediction of things like the stock market, the education of our children, global warming, or the jobless rate.
Unfortunately, the way mathematical models actually function in the real world is almost the opposite of this. Models are really thought of as nearly magical boxes that are so complicated as to render the results inarguable and incorruptible. Average people are completely intimidated by models, and don’t go anywhere near the assumptions nor do they question the inner workings of the model, the question of robustness, or the question of how many other models could have been made with similar assumptions but vastly different results. Typically people don’t even really understand the idea of errors.
Why? Why are people so trusting of these things that can be responsible for so many important (and sometimes even critical) issues in our lives? I think there are (at least) two major reasons. One touches on things brought up in this article, when it talks about information replacing thought and ideas. People don’t know about how the mortgage models work. So what? They also don’t know how cell phones work or how airplanes really stay up in the air. In some way we are all living in a huge network of trust, where we leave technical issues up to the experts, because after all we can’t be experts in everything.
But there’s another issue altogether, which is why I’m writing this post to mathematicians. Namely, there is a kind of scam going on in the name of mathematics, and I think it’s the responsibility of mathematicians to call it out and refuse to let it continue. Namely, people use the trust that people have of mathematics to endow their models with trust in an artificial and unworthy way. Much in the way that cops flashing their badges can abuse their authority, people flash the mathematics badge to synthesize mathematical virtue.
I think it’s time for mathematicians to start calling on people to stop abusing people’s trust in this way. One goal of this blog is to educate mathematicians about how modeling is used, so they can have a halfway decent understanding of how models are created and used in the name of mathematics, and so mathematicians can start talking about where mathematics actually plays a part and where politics, or greed, or just plain ignorance sometimes takes over.
By the way, I think mathematicians also have another responsibility which they are shirking, or said another way they should be taking on another project, which is to educate people about how mathematics is used. This is very close to the concept of “quantitative literacy” which is explained in this recent article by Sol Garfunkel and David Mumford. I will talk in another post about what mathematicians should be doing to promote quantitative literacy.