Chris Dixon has written an excellent history of mathematics. When most of us think of math, we go “ugh” and call it boring and turn away, but really, it’s so fundamental that we should be far more excited about it. Most of the major turning points in my education involved math: it was geometry when I was in the 8th grade that sparked my first interest, and learning algebra and logarithms in high school chemistry got me focused on science. When I started teaching myself how to program computers (I was an inadequate teacher, and quickly signed up for courses in the CS department), I had to also teach myself basic Boolean logic, because in those ancient days when your only recourse was to learn assembly language, and ANDs, NANDs, NORs, and ORs were the name of the game. Transistors are just logic implemented in silicon.
I agree when Dixon writes,
Mathematical logic was initially considered a hopelessly abstract subject with no conceivable applications. As one computer scientist commented: “If, in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.” And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.
I would add that in the 1970s public education system, we wouldn’t have imagined that, either. I had teachers who thought math was stuff you only needed to know for business school — you know, accounting. You can still see that attitude when people wonder why they need to learn this algebra stuff, anyway — they’ll never use it. They’re wrong. You’ll just use it in unexpected ways, because what you’re being given is a creative toolbox for thinking about the world.
The historical context in this article is useful, though, for making a case that math isn’t just practical, it’s also a foundation for thought that belongs in the liberal arts canon. And also that it’s a significant part of philosophy, which too many scientific pragmatists also tend to dismiss.