How science and math see each other

Ben does it again! We’re back to Math with Bad Drawings, with another post that resonates deeply with me as a math teacher. It begins with the somewhat startling claim that “mathematicians and scientists don’t share all that much in common.”

How can that be?

Let’s say you walk into Weston High School. At one end of the building you see the Math and Science Departments; we share a conference/lunch room, in which you’ll hear many collegial (but sometimes heated) discussions. At the other end of the building you see the English and History Departments; I suspect they too have many collegial (but sometimes heated) discussions. The land in between houses fuzzier departments like Art and Foreign Languages (a vast oversimplification, but not the issue we’re writing about here). So most people think that science and math people view each other as kindred spirits, as do history and English people. You know, STEM vs. humanities and all that — the two cultures.

But it’s not true, except when you’re painting with the broadest possible brush. Ben shows what’s going on with his “bad drawings.” I suppose I should just shut up and let him speak for himself [draw for himself?], but I can’t resist some commentary:

  • The great cartoon near the top of the post says it all. To a mathematician or math teacher, math is like music. To a scientist or science teacher, math is a tool. Yes, I know that’s oversimplified, but I firmly believe that its far more true than not.
  • In a later paragraph, Ben writes, “Meanwhile, mathematics draws on science the way an artist draws on a muse. Science reveals a real-world phenomenon—and the mathematician asks, how can we make this abstract? How can we generalize?” Math is all about abstraction. That’s why the vast majority of math problems don’t have units. A 3–4–5 triangle is a 3–4–5 triangle, regardless of whether it’s 3 inches or 3 cm or 3 smoots. But in science the units are essential.
  • I loved the last cartoon, with the caption, “Math is about taking your brain for a walk.”

And I also loved the two sentences below that cartoon:

Mathematics and science, then, aren’t like two members of the same species. They’re like two entirely different animals, sharing a lovely symbiosis.

Just ask a math teacher and a science teacher to find the hypotenuse of a 3–4–triangle, and they will agree it’s 5; but then ask them to find the hypotenuse of a 4–4–triangle, and they will disagree. In my honors geometry class, I would mark 5.65685 wrong (though with partial credit), not because the number of significant digits might be wrong (how could we know?) but because it loses the entire pattern. Only 4√2 reveals what’s going on. Math and science teachers may speak the same language, and surely look at the world more similarly than do math and English teachers, but there are still some significant differences.


Categories: Math, Teaching & Learning, Weston