Intelligence

What does it mean to be "intelligent"?  I mean, you'd be a fool if you called yourself smart without having some clear definition of intelligence.

Merrian-Webster's dictionary gives this as the first definition of intelligence:

(1) : the ability to learn or understand or to deal with new or trying situations : reason; also : the skilled use of reason (2) : the ability to apply knowledge to manipulate one's environment or to think abstractly as measured by objective criteria (as tests)

 But, even after looking at Wikipedia and online dictionaries, there are still a lot of things that I'm unclear on.  The following questions are asked with the knowledge that there is no set scientific definition of intelligence, so there really probably aren't any right answers.

Is knowledge a part of intelligence?  I don't think it has to be.  If you have an ability to learn, then you'll have that ability no matter how much stuff you actually have learned, right?  Then you could be knowledgable, but not "smart", or "smart", but not knowledgable.  But it is hard to apply knowledge if you don't know that much.  Still, maybe you can have an ability to do it, but just no way to demonstrate that ability.

As a follow up, is memory a part of intelligence?  If you could ace a physics test and do even more when given an equations sheet, but without the sheet you couldn't really remember anything, would you still be very "intelligent?"  Or does an ability to learn require an ability to remember?

How do you test intelligence?  If intelligence is an ability to learn, then wouldn't you have to do repeated tests or tests that have something completely new for the individual taking it?  And for IQ tests, what about multiple answers from different ways of reasoning?  1, 2, 3, 4, ?, what's the next number?  29.  The sequence is x^4-10x^3+35x^2-49x+24.  [You can have any sequence where you want to guess the last number, pick any last number you want and find a formula that would give that result.  Something about n points having a unique interpolating polynomial of degree n-1, and taking the sequence and your last number as the n points and finding any interpolating polynomial (you didn't really have to use the unique one of degree n-1), but this is kind of going off topic.]  Besides, who designed the intelligence tests?  If they weren't good at them, then how would they know what it really is to be intelligent?  If they were good at them, what if they were just making the tests based on what they were good at?  I mean, if I were going to make an intelligence test, I would have it test skill at all different kinds of games, with focus on multitasking and some double screen and double game challenges...

Finally, could you increase your intelligence level?  They say practice makes perfect.  Apparently you can improve math skills, word game skills, memory skills, IQ test taking skills..., all kinds of skills through practice.  What about learning skills?