Why are mathematical abilities associated with intelligence?

[Crafter_Man]

When a person is good at math, you always hear comments along the lines, "Gosh, he/she is so smart." It doesn't matter if they know nothing about biology, history, art, medicine, law, English, or economics. To most people, good at math = super smart.

Is there a really a strong correlation between mathematical abilities and intelligence?

[Schnitte]

May other disciplines require more knowledge than intelligence - no matter how intelligent you are, you'll never know when the battle of Hastings was if nobody has ever told you or you have never read it anywhere. You just have to know, or you won't.

Unlike mathematics, where (at least in the theoretical ideal) everything can be derived from a set of axioms.

[Napier]

Mathematics is an intellectual pursuit. Saying somebody is good at math and so is smart is like saying somebody is good at playing piano and so is a good musician. You don't mean to ask why people would say, somebody is good at math and therefore must be good at nonmathematical intellectual pursuits, do you?

[astro]

Very strong math usually means a person has (inherently) powerful abstract reasoning capability. This ability is (relatively) rare and is highly admired. It can also be well compensated in a variety a careers.

Unless they are some emotionally or socially retarded type having strong math skills is often a good predictor that a person can acquire other intellectual skills. Whether they do or not is an entirely different question.

[ultrafilter]

In very many cases, the person making such a statement struggled with math, and so they assume that anyone who's good at math comes by it naturally.

[tim314]

In short, because a lot of people find math difficult. People think you're smart if you can do something they find challenging.

Math is also something that everyone had to do in school, so the people who are bad at it have had the experience of struggling through. Whereas if you're really good at, I don't know, philosophy or something, most people don't really have the experience of trying to do philosophy and may underestimate how hard it is.

[j666]

In addition to astro's point, people who are good at math generally have worked at it. Language and learning by analogy seem to come naturally to most people, but math beyond the four basic operations requires work.

Smart people work at it.

Originally Posted by Schnitte

May other disciplines require more knowledge than intelligence - no matter how intelligent you are, you'll never know when the battle of Hastings was if nobody has ever told you or you have never read it anywhere. You just have to know, or you won't.

Unlike mathematics, where (at least in the theoretical ideal) everything can be derived from a set of axioms.

The only flaw in your theory is that everyone knows when the Battle of Hastings was, and doesn't know why.

[Ace309]

Just to make an argumentum ad culo, I think part of it is that when you're working with words as with literature or arguments as with law or philosophy there's a sense that anyone could do the same thing. People can read literature and understand it, so they assume they could do the same thing if they just put their mind to it. Cite: the people in Starbucks who are all writing novels.

Mathematics is an entirely different language and people know they're in over their heads when they look at a group of symbols they don't understand. Thus, it's evident that it's not something a layperson could dabble in without putting in a significant amount of effort.

[Chronos]

The only flaw in your theory is that everyone knows when the Battle of Hastings was, and doesn't know why.

Sure, it was during the appearance of Haley's Comit twelve orbits ago.

[MOIDALIZE]

Originally Posted by Ace309

Just to make an argumentum ad culo, I think part of it is that when you're working with words as with literature or arguments as with law or philosophy there's a sense that anyone could do the same thing. People can read literature and understand it, so they assume they could do the same thing if they just put their mind to it. Cite: the people in Starbucks who are all writing novels.

Mathematics is an entirely different language and people know they're in over their heads when they look at a group of symbols they don't understand. Thus, it's evident that it's not something a layperson could dabble in without putting in a significant amount of effort.

In my ninth grade algebra class, a whiny classmate asked the teacher why we had to do all these different problems for homework. His response was that it wasn't just about learning math but to learn problem solving skills. Solving a math problem requires the same type of thinking that solving any other type of problem takes, just in a different language and format.

[Beware of Doug]

Originally Posted by astro

Very strong math usually means a person has (inherently) powerful abstract reasoning capability. This ability is (relatively) rare and is highly admired. It can also be well compensated in a variety a careers.

More important than the rarity of abstract reasoning is the fact that it's admired and compensated. This is due no doubt to its being useful in "hard," quantifiable ways to business and science.

Abstract reasoning may also be what social scientists call "privileged," ie, valued for other reasons than usefulness. For one thing, hard and quantifiable thinking impresses powerful people whether or not it produces anything useful.

Feminist scholars go so far as to say abstract reasoning is privileged simply because it's historically a masculine ability, something white male money-crunchers and paper-shufflers identify with deeply.

[Magiver]

Math exists in many forms and disciplines. A person who is considered good in music may not understand the mathematical qualities behind it on the level of a mathematician. Example: the The Fibonacci sequence in Tool's song Lateralus. Or the fractal geometry of nature and art. An idiot savant may be able to make incredible mental calculations or compose music but be completely unaware of the process behind it.

Isaac Newton was a mathematical genius on a level I can't even assign a scale too. It’s not just a function of not knowing his level of math, it’s the understanding that I will NEVER comprehend math on his level.

[Ace309]

Originally Posted by MOIDALIZE

In my ninth grade algebra class, a whiny classmate asked the teacher why we had to do all these different problems for homework. His response was that it wasn't just about learning math but to learn problem solving skills. Solving a math problem requires the same type of thinking that solving any other type of problem takes, just in a different language and format.

To clarify, I agree that problem-solving is problem-solving. I think that when English is the language being used to communicate a problem, people don't always have an intuitive sense that they don't have the skills to solve a particular problem, whereas when mathematics is the medium, they understand that they don't recognize the symbols and subject matter. Because it's possible to understand English words, and because of the ambiguity inherent in English, it's possible to construct a bundle of legal or philosophical reasoning that reads simply in the plain sense but that is much more dense than a person without some experience reading in that subfield might realize.* On the other hand, if a person who doesn't grasp math beyond the eighth-grade level reads a problem involving an integral sign or sigma notation, that person is more likely to recognize that there was preparatory work to be done before he could solve it because he doesn't recognize the symbols or notation.

Anecdotally, I don't know many laypeople who claim to have made major discoveries while dabbling in mathematics, but I do know several who believe they've done so in philosophy. In my estimation, the reasoning requirements are quite high in both cases, but it's easier to recognize that you lack the necessary background in mathematics, because you won't understand the language.

*Balance made an excellent post touching on this line of reasoning here.

[Schnitte]

Originally Posted by j666

The only flaw in your theory is that everyone knows when the Battle of Hastings was, and doesn't know why.

Is that so? Probably in Britain, but less so in the U.S. and definitely not in continental Europe, I'd say.

[Spectre of Pithecanthropus]

My thoughts, for what they are worth:

Mathematics is quintessentially about abstraction, a quality which decreases as one moves through the physical sciences and engineering, then to life sciences and social sciences, and finally to the liberal and fine arts.

Everybody appreciates this about math and closely allied fields, but any scholarly field is more than just knowing facts. A successful scholar in German literature or English history succeeds because he or she conceives a new perspective on a topic, or thinks of viable conceptual associations to pursue that haven't been noticed before. In this way their work can be similar to the work of mathematicians, and shares with it the ability to make constructive associations--which is a hallmark of intelligence. A fact is like a dot on a map. Without understanding where the dot is on the map, and where the other dots are, knowing the first dot is there isn't worth much.

[elfkin477]

Don't they call noticing this sort these sorts of comments confirmation bias, though? I knew plenty of Math and Science majors during college who were awed that paper-writing came easily and naturally to those of us majoring in English because they were sure that writing is hard. Likewise, we were awed that they could figure math out, because we knew beyond a shadow of a doubt that math is hard.

[j666]

Originally Posted by Schnitte

Is that so? Probably in Britain, but less so in the U.S. and definitely not in continental Europe, I'd say.

I'm in the US, and it's one of those little mysteries; everyone remembers that date, even if they don't remember what the Battle of Hastings was.

[Speaker for the Dead]

Originally Posted by elfkin477

Don't they call noticing this sort these sorts of comments confirmation bias, though? I knew plenty of Math and Science majors during college who were awed that paper-writing came easily and naturally to those of us majoring in English because they were sure that writing is hard. Likewise, we were awed that they could figure math out, because we knew beyond a shadow of a doubt that math is hard.

As a History student, I never ran into people who were impressed by writing abilities. At most, I might get a "I hate writing. I don't know how you can enjoy it." The culture of awe regarding engineers, Math students, and physicists was definitely present, though. I wonder if our difference in experiences is a factor of geography or time?

[WordMan]

Competence in Math, at its essence, is a proxy for understanding the physical Universe. Name one scientific innovation that truly matters - I suppose with the possible exception of Darwin's theory of evolution - that isn't reducible to a math equation. Newton, Einstein, Galileo, Faraday, Bernoulli - heck, Moore's Law? All math. When Voyager was sent to the cosmos and NASA wanted to include some evidence that Mankind was intelligent - the language they used to communicate where we existed in the Universe was mathematical - various equations relating our existence to a spot in space related to stars.

In the fundamental push and pull of the Platonic ideal of a priori rationalization vs. the Aristotelian a posteriori experience, math is the ultimate language used to establish an experiencial foundation for our observations. If you can't state it via math, it doesn't count - period.

All of that implies that, at some level, the ability to abstract reality and capture some aspect of it using a math equation is a way to express a deeper understanding of our universe...

- okay, pondering my whole "name one innovation..." - stuff like understanding that washing our hands prevents infection and other biological/medical innovations, let along psychology, etc. aren't nearly as reducible, but I hope my basic point is still recognized as sound...

[Student Driver]

Originally Posted by Speaker for the Dead

As a History student, I never ran into people who were impressed by writing abilities. At most, I might get a "I hate writing. I don't know how you can enjoy it." The culture of awe regarding engineers, Math students, and physicists was definitely present, though. I wonder if our difference in experiences is a factor of geography or time?

I get to see it from both sides. I'm currently a dual math and philosophy major, and math/physics/engineering peers come to me for writing help, while liberal arts peers ask for tutoring help in math and statistics. Each side considers the other to be an arcane art (math guys usually will state discomfort with the "shades of grey" grading that comes into play when papers are judged-- they know their math is right or wrong, but feel like they're aiming for a nebulous, arbitrary standard in prose; liberal arts folks seem to be uncomfortable with the deductive logic of math-- the idea of being 100% WRONG if they mess up a single detail of a proof or solution is a little daunting, while an inductive argument can still be persuasive even if some premises or inferences are suspect).

[Hari Seldon]

Well, I once knew a mathematician who could only be described as stupid (not to mention ignorant). He was not an especially good mathematician, but he did research and published it. But if you engaged him in a conversation on any other topic, you quickly realized that this was a fundamentally stupid person.

On the other hand, I have known some highly cultured mathematicians. One thing about mathematicians, though, none of them will say to me that their worst subject was math, which is a typical response when you say you're a mathematician.

[Chief Pedant]

Originally Posted by Crafter_Man

When a person is good at math, you always hear comments along the lines, "Gosh, he/she is so smart." It doesn't matter if they know nothing about biology, history, art, medicine, law, English, or economics. To most people, good at math = super smart.

Is there a really a strong correlation between mathematical abilities and intelligence?

Excellence at math is difficult to fake and it is easier to establish absolute standards. This lack of subjectivity in evaluation is quite different from deciding whose poem is lovely.

As to your question about whether or not mathematical abilities correlate with intelligence: yes, they do. Take a difficult problem, for example: Land a man on the moon. The folks who did that were highly intelligent--it's a difficult problem to solve. I'd venture to say (and lay off the "cite" crapola, wouldya?) the key figures involved in all of the really difficult problems (not counting "problems" such as managing people) were facile with math.

Intelligence is necessary to grasp math. You can paste an isolated fact into an idiot's brain and sometimes it will even stick. You cannot paste robust mathematical ability onto a person of average intelligence.

This is not to say the ability to regurgitate lots of facts, or display linguistic facility does not also correlate with intelligence. The Pedant's mind is a dadburn attic of never-forgotten useless facts despite a math IQ of 50.

[Capt. Ridley's Shooting Party]

Originally Posted by Student Driver

I get to see it from both sides. I'm currently a dual math and philosophy major, and math/physics/engineering peers come to me for writing help, while liberal arts peers ask for tutoring help in math and statistics. Each side considers the other to be an arcane art (math guys usually will state discomfort with the "shades of grey" grading that comes into play when papers are judged-- they know their math is right or wrong, but feel like they're aiming for a nebulous, arbitrary standard in prose; liberal arts folks seem to be uncomfortable with the deductive logic of math-- the idea of being 100% WRONG if they mess up a single detail of a proof or solution is a little daunting, while an inductive argument can still be persuasive even if some premises or inferences are suspect).

Surely philosophy and mathematics aren't that far apart? Loads of philosophers were mathematicians and visa versa: Russell, Hintikka, Quine, etc.

[Simplicio]

Originally Posted by Schnitte

May other disciplines require more knowledge than intelligence - no matter how intelligent you are, you'll never know when the battle of Hastings was if nobody has ever told you or you have never read it anywhere. You just have to know, or you won't.

Not necessarily true. I've heard Cecil once actually derived history from first principles.

[Flander]

Originally Posted by j666

I'm in the US, and it's one of those little mysteries; everyone remembers that date, even if they don't remember what the Battle of Hastings was.

Another vote for an American (age 27) who knows it was 1066. It seems to be a standard trivia question around these parts.

[CC]

Originally Posted by j666

I'm in the US, and it's one of those little mysteries; everyone remembers that date, even if they don't remember what the Battle of Hastings was.

This, of course, is emblematic of the problems with the way schools work. And the more they rely on mindless memorization and decontextualized teaching (i.e. "reading classes"), the more likely that we will continue to be a nation of people who can (possibly) say when, but will be unlikely to know why.

[nivlac]

For sure, people can be very intelligent without any expressed mathematical ability. OTOH people who can display mathematical ability, especially in abstract or esoteric matters, are generally viewed as "intelligent". As already mentioned this ability to think and communicate using symbols, notation, and language that are foreign to most people, yet seem relevant to the real world, gives off an aura of intelligence. But we all know that intelligence in this sense does not necessarily mean street smart or even having a lot of common sense.

[mr. jp]

What, nobody is going to mention The g factor? Come on, people.

[Capt. Ridley's Shooting Party]

As already mentioned this ability to think and communicate using symbols, notation, and language that are foreign to most people, yet seem relevant to the real world, gives off an aura of intelligence.

I think you're confusing mathematics with the language that people use to communicate that mathematics in. IMHO, mathematicians are seen as smart not because they use esoteric symbols, rather because mathematics itself is so abstract. Being asked to reason about something that couldn't possibly exist, or something you have absolutely no grounding with, etc., is what drives the stereotype, I think.

[nivlac]

Originally Posted by Capt. Ridley's Shooting Party

I think you're confusing mathematics with the language that people use to communicate that mathematics in. IMHO, mathematicians are seen as smart not because they use esoteric symbols, rather because mathematics itself is so abstract. Being asked to reason about something that couldn't possibly exist, or something you have absolutely no grounding with, etc., is what drives the stereotype, I think.

I don't know about that. If a person does not communicate his math (in speech or writing) how can you tell that he has math ability? And once he/she starts communicating that's when the association with intelligence occurs. I do grant that the notion of mathematician = abstract thinker is a key part of the stereotypical association with intelligence.

[yelimS]

Originally Posted by Chief Pedant

Excellence at math is difficult to fake

Reminds me of this.