What is Math? (Questions, not answers)

It seems obvious, right? We all know what math is. But let me try to ask some tricky questions.

Numbers/Arithmetic

First, anything with numbers is math, right? Counting? I think so. Adding, subtracting, multiplying, dividing? Good. Exponents. Fractions! What about the theory that describes these numbers? Probably, right?

Geometry? Surveying? Construction? Drafting?

Then there’s geometry. The word comes from roots which mean “earth measuring”. That’s not really counting or adding. But not surveying – that’s something different? Seems like a fine line (haha) to be drawing. And construction of figures with pencil and straightedge counts – but drafting does not? That’s a little arbitrary. Really, why would any of it get grouped with arithmetic? And if some of it, why not all of it?

Algebra

Algebra seems an easier fit. It’s like arithmetic, but with a symbol taking the place of a number. And then there’s the stuff that flows out of and beyond algebra… functions, trigonometry, graphing, even calculus.

Other Stuff

What about logic? Some logic is math? And some is not? But none has numbers or anything like them? And Set Theory? And Graph Theory? And Knot Theory?

I’ve heard that Game Theory is more Economics than Math. I’m not sure.

Programming?

Programming and coding are often taught in math departments. I guess they have numbers in them, but is that enough to make them math? Sometimes math teachers teach them, right? But is that enough?

Physics

Clearly Physics is a science, and not math. But a lot of math and a lot of physics look a lot alike. Math is physics without things? And physics is math with things added? How close do circuits come to the line between them? How is there a field called Mathematical Physics?

Statistics?

Is statistics a branch of mathematics? Or a science that studies data (and makes use of a lot of math)?

I should end by giving credit to a book – Jacqueline Stedall’s The History of Mathematics – A Very Short Introduction which poses and answers some of these questions.

It turns out that there is some logic (no pun) to what we include and what we don’t include in mathematics today.

There’s also a lot of history, and tradition. Stedall discusses topics that USED to be part of mathematics – including artillery and astrology (not a typo). Her book is really worth a read (and just 100 pages)