Because they often are. Anything beyond basic arithmetic requires accepting ideas without logical explanations as to why. That's not intelligence; it's faith. You have four apples and I give you three more, how many do you have? I take away one, how many do you have? If you take that number and have three groups of that size, how many apples do you have? If you divide that number into two groups, how many groups are there? Simple, direct, and logical.
Now suppose you have 14,627 apples and need to make 283.4 equally sized groups. Then comes long division, which has absolutely direct derivation from reality. It's nothing more than a series of arcane and esoteric processes. Does it produce the correct answer? Yes. But it has nothing to do with logic.
A positive number squared gives a positive result. A negative number squared gives a positive result. Logically, no negative number can have a square root. Mathematically, we have the constant "i", the square root of negative one, which logic tells us cannot exist.
There is definitely a strong logical component to math, but the farther you go from the basics, the more you veer away from logic and into the territory of faith. If you question the logic behind it, you'll rarely get anything more than "that's just the way it works".
This is a problem because intelligence is not simply the application of logic, it's also the ability to think critically. If you can't do that, you have no business calling yourself intelligent, REGARDLESS of your mathematical ability.
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Intelligence isn't scaler. I would consider someone who is happy in life more intelligent than someone who is small minded and good at math. Intelligence is how good you are at navigating through life and getting to where you want to go with the least amount of obstacles. I would consider someone that could build a car from scratch more intelligent than someone who could do advance calculus. There are tons of practical life skills that require little understanding of math that would make you more intelligent than someone who can only crunch numbers. You spoke about logic. The statement that you aren't considered intelligent without being good at math is an illogical statement. Some of the best thinkers in history were philosophers. You do not need math for deep philosophical thinking. You need logic and reasoning.
I do agree that being good at math is a large component of being intelligent, but it's not just about math. Some people are incredible at everything else (history, English, Science), but they just can't do math. They're still intelligent people, just intelligent people who aren't good at math. Academics aren't the only thing that makes someone smart. Many people who aren't good in school can think logically, and in a way that can/will get them far in life. In my opinion, to be intelligent is to be capable of making difficult, abstract opinions, thoughts, and connections.
You can be intelligent and not be good at maths. There are different types of intelligence too such as; logical-mathmatical (being good at maths), existential (philosophers), interpersonal (therapists), body-kinestheic (athletes), linguistic (authors), intra-personal, spatial (mechanics), naturalist (biologists), musical (musicians). If you want to take IQ tests to be a determination of intelligence they don't have many mathematical questions and most are pattern and logic based, so going by this maths isn't that important in figuring out how intelligent someone is.
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Good at math only means you are good at math.
I am not sure where you got this idea, but being good at math does not mean one is intelligent, and not being good at it does not indicate a lack of intelligence. Also, what exactly is your definition of intelligence other than being good at math?
The same reason why SOME intelligent people have no common sense.
Your logic is flawed, intelligence is measured through various factors.
Shut up
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