Common False Beliefs in Mathematics

Math people seem a lot more interested in math than programmers are in programming. If you asked the same question on SO, the popular answers would be a list of things like "programmers don't deserve big monitors" or "the client is always right" or other such bullshit. (Nothing actually about <i>programming</i>, only about "the profession").<p>Maybe this is why nobody ever calls mathematicians "number monkeys".

That site is crazy. Every time I open it I feel like a complete idiot. I took a decent amount of math in college but I don't know most of the words they use.

What I like about the thread is that it's a window into another world of geek humor whose countours I'm familiar with (they look a lot like the countours for cs humor) but whose specifics are largely unintelligible to me.<p>Great read.

I laughed (before I started to think that crying might be more appropriate) when I heard about the false belief that 1 plus the product of the first n primes is always a prime number. Ouch!

I took 14 hours of calculus in my EE undergrad. Reading posts like this remind me that I really enjoy studying math outside of school. In school, I had to learn so much, so fast, that I couldn't appreciate the beauty, nor take time to ponder the wider implications of what I was learning.<p>Many times, I have thought about opening my Salas and Hille's Calculus book and just starting over from the beginning. Anyone ever done anything like this? Any opinions on a better starting book for someone in my shoes?

I liked this answer in particular:<p>"These are actually metamathematical (false) beliefs that many intelligent people have while they are learning mathematics, but usually abandon when their mistake is pointed out, and I am almost certain to draw fire for saying it from those who haven't, together with the reasons for them:<p>* The results must be stated in complete and utter generality.<p>* Easy examples are left as an exercise to the reader.<p>* It is more important to be correct than to be understood.<p>(Applicable to talks as well as papers.)"

Can someone explain why this one (the top answer) is false:<p>For vector spaces, dim(U+V)=dimU+dimV−dim(UV), so dim(U+V+W)=dimU+dimV+dimW−dim(UV)−dim(UW)−dim(VW)+dim(UVW)

About half of the ones that I understand what they mean seem perfectly plausible to me. We need a page that explains why they are false.<p>For example can someone explain "Every connected component of a topological space is open and closed."<p>Edit: found it on wikipedia: "The components in general need not be open: the components of the rational numbers, for instance, are the one-point sets."

It never really took off so there isn't much there yet, but for anyone interested in math discussion on a less advanced plane, you might try here <a href="http://wiki.lesswrong.com/wiki/Simple_math_of_everything" rel="nofollow">http://wiki.lesswrong.com/wiki/Simple_math_of_everything</a>

"The circle is the only figure which has the same width in all directions."<p>Can someone explain? What exactly do they mean by width and what else has this property?