Remember Barany’s claim that math isn’t everywhere? The adventure continues!

Barany compiled a response to the criticism his essay received and it was published on mathbabe’s blog.

Summary quotes:

By placing the emphasis on how mathematics isn’t everywhere, I claimed that history gave us a different lesson. Politically, I think that it is better to focus on the areas where mathematics does have a profound effect on people’s lives, at the expense of the kinds of tractable examples that are often used to popularize math. […] Pedagogically, I questioned whether stressing the ubiquity of mathematics was the best motivation. If instead we started by emphasizing that math is and has historically been an alienating and exclusive kind of knowledge (indeed, has often been so by design), then those who have felt alienated or excluded from mathematics need not blame themselves for failing to grasp the mathematics that is supposedly all around them, and mathematics educators (as well as theorists) could prioritize inclusive formulations of their subjects.

I think this response is good, in the sense that it clarifies his main thesis. Not sure what to think about it as a whole, but one detail prompted me to write a comment: I believe Barany’s account misses the reason why large part of math popularization takes the “math is everywhere” angle.

My personal take: the vague collection of ideas and attitudes that is “math-is-everywhere” is prevalent, because it’s a way for us mathematicians (and members of sufficiently adjacent and similarly esoteric fields such as theoretical computer science) to justify to layperson why our work is interesting and useful and wonderful. I’m currently writing my M.Sc. thesis; while it’s nice thing to work on and I’m confident the end result (when it’s finished) will be quite good as far as the category of texts called “Master’s thesis in Finnish universities” go, it will probably never have a profound effect on anyone else’s life. I certainly don’t feel like a master of the universe or a member of secluded power-broking elite. And I work in an applied field that has many immediate engineering applications compared to many other fields of so-called “theoretical” or “pure” mathematical nature!

Academic mathematics studied in the public, government-funded universities is constantly under a pressure to justify its existence and why it deserves continued funding. I believe many people who choose a career in mathematics also often feel inclination to justify that personal choice in a society where the only contact with mathematics the majority of populace have had is “solve for x” kind of maths of middle and high school, and many are keen to declare that a) it’s boring and b) they never needed those skills later in their life. And here is where the “math-is-everywhere” comes in: “Of course math is worthwhile: look, math is everywhere!”