Common misconceptions about math

YARFMO (Yet another reposting from Mathoverflow) ;-)

The more you know about math the more you find conceptions previously thought correct to be false:

1.) math is not as exact as many believe - in many cases, as Gowers points out in his amazing book "Mathematics. A very short intro", it is mainly about approximations, boundaries or even "only" existence. Example: The Riemann hypothesis.

2.) math is not "true" (whatever that means) in its own right - it is only true within an axiomatic system (deductive approach). Example: The parallel axiom.

3.) closed form solutions are not as closed as many think: "closed-form" is just shorthand for "popular enough to be given a name and notation." Examples: $\pi, e, \mathrm{Si}(x), \mathrm{li}(x)$.

My question

Do you have further common misconceptions about math (ideally also with examples)?

I think that the ones given above only scratch the surface because in the end the picture of math also changes historically the further we proceed on this never-ending endeavor of human mind.

(As should be clear already, I am talking about the "meta'-level, so please don't give examples like $(x+y)^2=x^2+y^2$ - this is already covered here and here.)

Here are a couple of misconceptions that people who don't know about mathematics commonly hold. Firstly, that it's immutable, fixed, unchanging; surely it's all been discovered? It's a belief that even a highly educated non-mathematician might hold.

This point was illustrated to me not long ago when a friend, who speaks at least 10 languages fluently, asked why I found mathematics interesting. She believed that it was cold and lifeless and thus inherently less appealing than language, which she viewed as living and dynamic.

I tried to persuade her that mathematics grows and changes too. Areas such as Group Theory were born from ideas used in Number Theory and Geometry. And old ways of doing things can be surpassed. The history of cryptography is a good example.

The conversation also touched on a second misconception: that mathematicians simply follow set rules. I explained that imagination was very important in doing mathematics. And when I said that there was great beauty in mathematics, I was faced with almost total incomprehension. Surely, mathematics was the very antithesis of beauty?

If you're reading this I don't need to convince you that these are indeed misconceptions, but unfortunately I don't think I convinced my friend!

Perhaps more meta than you wanted since it's not about how you perceive mathematics coming from mathematics, but rather how the rest of the world views it.

There's that whole misconception that if you're good at math you're good at arithmetic. You know... that thing where someone says something like "Hey, you're good at math! Can you do this calculation (typically menial multiplication) for me in your head?" Sure I could, but that's because I can keep a lot of stuff in my head at once and make sure I do it correctly. It's not as if that says anything about mathematical ability.

Following up on Kahen's comment, most people who only take math through High School think math is about calculation. For higher math, description is more correct than calculation, but that still doesn't capture the flavor.

Most people think math is about numbers. Some is, some isn't.