Mathematics and intellect
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Mathematics and intellect
To me it seems that people who are amazing at mathematics and say, physics, are often perceived as smarter than people equally able in other subjects, such as sociology, or english. I mean, is this actually the case or has maths just got a strange reputation?
Your thoughts please
Your thoughts please
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Re: Mathematics and intellect
Someone who is very good at maths stands out just as much as someone who is very good at, say, literary analysis, but math people have more opportunities to demonstrate their abilities in normal life (for example, calculating a price after discount), while the booky guy is pretty screwed up in the unintentionallyshowingoff department.
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 RogerMurdock
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Re: Mathematics and intellect
I've read a lot of discussion about this, mostly in response to http://xkcd.com/451/.
I think History and English and whatnot are perceived as "less smart" than physics and math because people can, at face value, see what is going on and believe they can do it themselves if they so chose. When I see a piece of literature deconstructed, it's not recognizable that the person who did it is a PhD or is just someone making shit up, and everything just kind of gets tossed together. Plus, even if I don't UNDERSTAND the paper in english or sociology or w/e, I can still read it (it's in english after all) and make a good guess about it. Compare this to mathematics or physics where anything above the High School level looks like complete gibberish to someone not in the field. Calculus is taught to kids that are 16, but to many people it might as well be the launch codes for a mission to mars. Math and Science has this kind of aura about it also that says to people "If you do not understand it now you never will and are probably not smart enough". It's a cultural thing stemming from what I mentioned earlier I think.
Interesting topic though, the stereotypes people associate with various professions.
I think History and English and whatnot are perceived as "less smart" than physics and math because people can, at face value, see what is going on and believe they can do it themselves if they so chose. When I see a piece of literature deconstructed, it's not recognizable that the person who did it is a PhD or is just someone making shit up, and everything just kind of gets tossed together. Plus, even if I don't UNDERSTAND the paper in english or sociology or w/e, I can still read it (it's in english after all) and make a good guess about it. Compare this to mathematics or physics where anything above the High School level looks like complete gibberish to someone not in the field. Calculus is taught to kids that are 16, but to many people it might as well be the launch codes for a mission to mars. Math and Science has this kind of aura about it also that says to people "If you do not understand it now you never will and are probably not smart enough". It's a cultural thing stemming from what I mentioned earlier I think.
Interesting topic though, the stereotypes people associate with various professions.

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Re: Mathematics and intellect
No. People just attribute a higher level of intelligence to math, physics, etc. because "oh dear lord, algebra is really hard, how could you ever study math?" There are a lot of damn smart people studying pretty much any subject you can name.
Re: Mathematics and intellect
Yeah, the way math is seen by a large number of people is really very depressing.
On that note, I still can't quite wrap my mind around what the f*ck people mean when they start talking about intelligence and 'brains'. Maybe THEY don't even know what they mean.
On that note, I still can't quite wrap my mind around what the f*ck people mean when they start talking about intelligence and 'brains'. Maybe THEY don't even know what they mean.
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Re: Mathematics and intellect
This.Shokk wrote:On that note, I still can't quite wrap my mind around what the f*ck people mean when they start talking about intelligence and 'brains'. Maybe THEY don't even know what they mean.
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Re: Mathematics and intellect
RogerMurdock wrote:I think History and English and whatnot are perceived as "less smart" than physics and math because people can, at face value, see what is going on and believe they can do it themselves if they so chose.
At the same time, I think there's a bit of the opposite that's sort of going on as well. As in, they think they can do lit crit so they figure it's not so difficult, and they think this because they really *don't* understand much of anything about how it's actually done well. But they know just enough about math and physics to understand what's difficult about it.
Actually, it's probably comparable to why I'm more impressed by a good pianist than a good race car driver. On the one hand, like your argument, I can drive a car too, so what's so hard about driving it faster? On the other hand, though, like my argument, I have studied the piano, which is why I understand what goes into doing it really well.
Re: Mathematics and intellect
I've been trying to source the statement "x% of Americans believe they could write the next Great American Novel." I can't find an actual survey, but I keep finding numbers around 80%, enough to make it a cultural meme if not an actual data point. We all think we can be great authors! And history? Isn't that just memorizing dates?
Scientists make discoveries! Lexicographers compile lists of words. Which captures the imagination better?
Mathematicians use symbols I don't understand to figure out things like Zorn's Lemma, which I don't understand, that applies to problems I don't understand. Therefore, they must be smarter than sociologists, who study things I [pretend to think I] do understand.
Back in the day, I scored frighteningly high on spatial reasoning and such on standardized tests. I squeaked by on math. Now, people are all impressed when I "calculate" a median or crank out the confidence interval of a proportion. Building a shed with plans and dimensions and joinery all in my head doesn't seem to impress anyone.
Scientists make discoveries! Lexicographers compile lists of words. Which captures the imagination better?
Mathematicians use symbols I don't understand to figure out things like Zorn's Lemma, which I don't understand, that applies to problems I don't understand. Therefore, they must be smarter than sociologists, who study things I [pretend to think I] do understand.
Back in the day, I scored frighteningly high on spatial reasoning and such on standardized tests. I squeaked by on math. Now, people are all impressed when I "calculate" a median or crank out the confidence interval of a proportion. Building a shed with plans and dimensions and joinery all in my head doesn't seem to impress anyone.
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Re: Mathematics and intellect
Mathsy smart might just be a rarer type of smart than booky smart, making it stand out more.
Re: Mathematics and intellect
A basic reason is that it's hard to read formulas, but easy to read words. Mathematicians use a lot of syntax that is unfamiliar, so it looks very impressive. English professors and philosophy professors use a lot of words that are familiar, but with more precise meanings, so it looks much less impressive. A related issue is that it's easy to spout nonsense in an English paper but impossible to do so in a math paper.
Re: Mathematics and intellect
The following is entirely personal opinion and not at all substantiated by any facts or data (but also not contrary to any that I'm aware of)
I don't think people who are good at math are naturally smarter than people who are good at English or whatever else. I do think however, that working on math makes you better at other things at a much higher rate than working on English. To my knowledge, the best way to learn how to solve problems, how to abstract and or generalize, how to connect facts and information from disparate areas, how to see patterns, and so on, is to do lots of math. I'd object to any definition of intellect that would imply it is constant over a person's life, and I'd argue that studying math is a very efficient way of increasing it.
I was told once, and I can't find a source on this one way or the other, so please correct me if you have information otherwise, but I was told that they looked at LSAT/MCAD/GMAT/etc scores grouped by educational background and mathematics was on top. (Admittedly, if this is indeed true, this could be because smarter people are biased towards math to begin with)
I don't think people who are good at math are naturally smarter than people who are good at English or whatever else. I do think however, that working on math makes you better at other things at a much higher rate than working on English. To my knowledge, the best way to learn how to solve problems, how to abstract and or generalize, how to connect facts and information from disparate areas, how to see patterns, and so on, is to do lots of math. I'd object to any definition of intellect that would imply it is constant over a person's life, and I'd argue that studying math is a very efficient way of increasing it.
I was told once, and I can't find a source on this one way or the other, so please correct me if you have information otherwise, but I was told that they looked at LSAT/MCAD/GMAT/etc scores grouped by educational background and mathematics was on top. (Admittedly, if this is indeed true, this could be because smarter people are biased towards math to begin with)
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 RogerMurdock
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Re: Mathematics and intellect
gmalivuk wrote:RogerMurdock wrote:I think History and English and whatnot are perceived as "less smart" than physics and math because people can, at face value, see what is going on and believe they can do it themselves if they so chose.
At the same time, I think there's a bit of the opposite that's sort of going on as well. As in, they think they can do lit crit so they figure it's not so difficult, and they think this because they really *don't* understand much of anything about how it's actually done well. But they know just enough about math and physics to understand what's difficult about it.
Actually, it's probably comparable to why I'm more impressed by a good pianist than a good race car driver. On the one hand, like your argument, I can drive a car too, so what's so hard about driving it faster? On the other hand, though, like my argument, I have studied the piano, which is why I understand what goes into doing it really well.
I know what you mean, and I personally feel this way. I know just enough about math and science to allow me to appreciate the intelligence needed for the upper echelons of it, but I know next to nothing about sociology or w/e, so it's much more difficult for me to appreciate that.
This is probably due to how our educational system works (just guessing). In high school there is a rather large focus on maths and sciences compared to something like literary criticism. There are exactly 2 AP english classes at my school, sociology is a half semester course, there are a few AP histories but nothing really in depth. Meanwhile there are 4 AP Science courses and 4 AP Maths. People usually max out at "regular" physics and precalculus or statistics, if they know they are not going to be doing anything math/sciency. This is JUST to the point to convince them "yep, I'm not smart enough to do this" if they were having doubts already. Meanwhile if they know a friend in AP Physics or Calculus or whatever, they catch a glance of a worksheet now and then and their brain explodes. So they get that "just enough" exposure in high school while they get literally no exposure to most other disciplines.
Re: Mathematics and intellect
Maybe, but on the other hand, most people don't have any idea what real mathematics is about.

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Re: Mathematics and intellect
t0rajir0u wrote:A basic reason is that it's hard to read formulas, but easy to read words. Mathematicians use a lot of syntax that is unfamiliar.
I disagree, and this is testable.
Try, as an exercise, translating an article in a mathematics journal into English. Or even something from an advanced undergraduate math textbook. If you're right, then the English translation should be easier to understand. I claim it'll be *harder* to understand because the formulas are a crutch to make the math *easier*
I think what's difficult about math is the way abstract objects are built out of abstract objects. How many layers down do you have to go, before you get to something "concrete," that children understand, like whole numbers?
Consider how much difficulty people have with even one layer of abstraction, like going from "X is morally wrong" to "A legal system which forbids X is morally inferior to one which permits it."
Re: Mathematics and intellect
mouseposture wrote:Try, as an exercise, translating an article in a mathematics journal into English. Or even something from an advanced undergraduate math textbook. If you're right, then the English translation should be easier to understand. I claim it'll be *harder* to understand because the formulas are a crutch to make the math *easier*
I don't quite understand what you're proposing. Is the article not supposed to be in English?
mouseposture wrote:I think what's difficult about math is the way abstract objects are built out of abstract objects.
I would certainly agree if most people ever got that far. But I think the majority of people have a much shallower appreciation of mathematics than this; for many it is probably almost entirely limited to manipulating numbers.

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Re: Mathematics and intellect
Only for a mathematician. A nonmathematician will find the symbolic version completely incomprehensible, but they may be able to make some sense out of the 'English' version (and will at least be able to read it).mouseposture wrote:I claim it'll be *harder* to understand because the formulas are a crutch to make the math *easier*
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Re: Mathematics and intellect
Ended wrote:Only for a mathematician. A nonmathematician will find the symbolic version completely incomprehensible, but they may be able to make some sense out of the 'English' version (and will at least be able to read it).mouseposture wrote:I claim it'll be *harder* to understand because the formulas are a crutch to make the math *easier*
No, not what I meant. I mean the layman will find it more difficult.
Like I said, it's a testable hypothesis.
In practice, I think what you'll actually find is that the layman finds it no less difficult (i.e. equally incomprehensible).
A realworld case where mathematicians try to explain nontrivial math to laymen is undergraduate math classes. What would a course in calculus, or differential equations be like if it were Englishonly, noformulas. An intriguing idea, but obviously the people who teach these courses don't think that would make the concepts easier for nonmathematicians to understand. They could be wrong, of course.
t0rajir0u wrote:I don't quite understand what you're proposing. Is the article not supposed to be in English?
Sorry, I wasn't clear. I meant translate the formulae (specialized mathematical notation, whatever) into English. The text, if it was in English, stays in English.
 mmmcannibalism
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Re: Mathematics and intellect
I'm going to take a slightly different angle here, I think the design of education plays into this at least to some degree. I think the cause may be a quicker differentiation in skill between math and english. Because writing stays at a very basic level(imo) during elementary school, everyone has to start with a more similair skill set in middle school and beyond then in math where advanced students get a better chance to gain ground(this also applies to the start of algebra being a big divider in class later). So, most of the gain beyond the rest of the class for an english based person will start to occur at a later age. Compared to the math kid who started getting ahead of the class in fourth of fifth grade, an english kid will only start showing that seperation in high school(or at least the larger part of it).
Thats not well written, hopefully someone can word that better then I have
I also agree it has to do with how math defeats more people in high school. Even without much understanding, you can stay pretty high in an english class(memorize plot and the theme teacher discusses is usually sufficient); however, a Calculus class will blow you out of the water unless you have a good understanding of math.
Thats not well written, hopefully someone can word that better then I have
I also agree it has to do with how math defeats more people in high school. Even without much understanding, you can stay pretty high in an english class(memorize plot and the theme teacher discusses is usually sufficient); however, a Calculus class will blow you out of the water unless you have a good understanding of math.
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Re: Mathematics and intellect
I had a somewhat related discussion with one of my professors a couple years ago. He used to run some sort of biotech business, and he told me that he generally preferred to hire math majors rather than biology majors. While the biology majors may have had previous knowledge about the material they were working on, he found that mathematicians could much more reliably learn new material. I've heard similar comments from other people.
Perhaps this is because the way math is taught emphasizes the process of getting from one piece of knowledge to another, whereas many other subjects seem to focus on a body of established knowledge (at least for much longer than math). Now, the only fields I have studied for any meaningful length of time are ecology and math, but my experience with those subjects seems to support my opinion. Undergraduate math (and even some high school math, depending on the school) is very much focused on learning how to prove things and derive new information. In ecology, on the other hand, I didn't encounter very much emphasis on deriving new information from old in undergraduate classes. We were first expected to learn an extensive list of facts, and I really only found mentally stimulating work once I started doing research with professors and graduate students.
In summary, I suspect that being taught how to solve problems (although I hate to use that phrase, because it brings to mind a worksheet of equations with the heading "solve for x") makes you more intelligent (at least for some common definitions of intelligence). In my experience, mathematics education focuses on this sort of problem solving earlier than education in other fields. This would make people who study mathematics smarter (again, for some common definitions of the term). Dear god, though, when I say it like that it sounds horribly politically incorrect. If you're easily offended, try to focus on the indictment of Ecology education practices rather than the summary.
Perhaps this is because the way math is taught emphasizes the process of getting from one piece of knowledge to another, whereas many other subjects seem to focus on a body of established knowledge (at least for much longer than math). Now, the only fields I have studied for any meaningful length of time are ecology and math, but my experience with those subjects seems to support my opinion. Undergraduate math (and even some high school math, depending on the school) is very much focused on learning how to prove things and derive new information. In ecology, on the other hand, I didn't encounter very much emphasis on deriving new information from old in undergraduate classes. We were first expected to learn an extensive list of facts, and I really only found mentally stimulating work once I started doing research with professors and graduate students.
In summary, I suspect that being taught how to solve problems (although I hate to use that phrase, because it brings to mind a worksheet of equations with the heading "solve for x") makes you more intelligent (at least for some common definitions of intelligence). In my experience, mathematics education focuses on this sort of problem solving earlier than education in other fields. This would make people who study mathematics smarter (again, for some common definitions of the term). Dear god, though, when I say it like that it sounds horribly politically incorrect. If you're easily offended, try to focus on the indictment of Ecology education practices rather than the summary.
Re: Mathematics and intellect
I doubt it. Try looking at the old mathematics with words only. The word becomes so long that it isn't even funny. The converse, ie. symbol spam, is also not funny. I had a student handing that in for his assignment before, and I was like......Ended wrote:Only for a mathematician. A nonmathematician will find the symbolic version completely incomprehensible, but they may be able to make some sense out of the 'English' version (and will at least be able to read it).mouseposture wrote:I claim it'll be *harder* to understand because the formulas are a crutch to make the math *easier*
Of course, if you want to do math and stay away from most symbols, do graph theory.
Re: Mathematics and intellect
Screw Basically Decent:
Saying that a mathematician is less intelligent than a sociologist is like saying that a man who has practised martial arts his whole life is less physically apt than a man who has spent his whole life filming kungfu movies. Saying that a mathematician is less intelligent than a biologist is like saying that the martial arts master is less physically capable than a world champion pool player. Saying that math is only perceived as difficult because of its arcane symbols is like saying that martial arts is only considered difficult because of its association with asian philosophy.
Martial arts *is* difficult: you are constantly fighting a life or death battle with your opponent, who wants to win just as desperately as you do. Math *is* difficult: you are constantly trying to find ways to solve problems that no one has found a way to solve before, though they may have been cleverer than you, problems which may not even have solutions. If a mathematician is less capable of solving any problem than a writer is after having spent his whole life honing his mental abilities, he should feel as ashamed as a master of kung fu who has lost a fight to a ballerina.
Man, I've beaten that analogy into the ground.
Saying that a mathematician is less intelligent than a sociologist is like saying that a man who has practised martial arts his whole life is less physically apt than a man who has spent his whole life filming kungfu movies. Saying that a mathematician is less intelligent than a biologist is like saying that the martial arts master is less physically capable than a world champion pool player. Saying that math is only perceived as difficult because of its arcane symbols is like saying that martial arts is only considered difficult because of its association with asian philosophy.
Martial arts *is* difficult: you are constantly fighting a life or death battle with your opponent, who wants to win just as desperately as you do. Math *is* difficult: you are constantly trying to find ways to solve problems that no one has found a way to solve before, though they may have been cleverer than you, problems which may not even have solutions. If a mathematician is less capable of solving any problem than a writer is after having spent his whole life honing his mental abilities, he should feel as ashamed as a master of kung fu who has lost a fight to a ballerina.
Man, I've beaten that analogy into the ground.
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Re: Mathematics and intellect
mouseposture wrote:t0rajir0u wrote:
that children understand, like whole numbers?
Not so. I'm going by what my cousin said, and she is a middle school teacher for math, that a lot of children struggle with even whole numbers.
I think what it comes down to is appreciation for a subject because from my experience, many people don't even learn while they are in school. It is all rote learning that they forget as soon as they can. And it may be harder to remember facts that have more symbols than words might be more difficult which leads them to the view that mathematicians and physicists are more intelligent because of their knowledge of math. And they always fail to see with history that it is not just raw facts, but interpretations of the facts that may just be as imaginative and creative as much of the mathematics that we know.
Re: Mathematics and intellect
Contrary to some of the first replies, in a sense I think you can say we actually are more intelligent. Not in the usual sense, but in our knowledge that the brain as a muscle which can be trained. Most people don't consider that, and thus understanding is a tautology from the outset: If they get it right away great, if they don't get it immediately they probably never will. Or at least they think they won't. That's my impression. It might be more pronounced with a bit older people. Most people in my circle at least try, but none (but the other math students) are presented with more puzzles and challenges, and sometimes it shows.
Re: Mathematics and intellect
mouseposture wrote:Sorry, I wasn't clear. I meant translate the formulae (specialized mathematical notation, whatever) into English. The text, if it was in English, stays in English.
I believe that mathematics is clearer without notation. I have seen this explicitly given as advice for mathematical writing from at least two reputable sources, Knuth and Munkres, who both have been writing mathematics long enough that they should know what they're talking about.
Notation doesn't (necessarily) make math easier; it makes it denser. This is good if you have a lot of math to communicate in a short amount of time, but it's no way to teach.
Re: Mathematics and intellect
t0rajir0u wrote:mouseposture wrote:Sorry, I wasn't clear. I meant translate the formulae (specialized mathematical notation, whatever) into English. The text, if it was in English, stays in English.
I believe that mathematics is clearer without notation. I have seen this explicitly given as advice for mathematical writing from at least two reputable sources, Knuth and Munkres, who both have been writing mathematics long enough that they should know what they're talking about.
Notation doesn't (necessarily) make math easier; it makes it denser. This is good if you have a lot of math to communicate in a short amount of time, but it's no way to teach.
I think a good example of the fact that you can write densely without much notation is Halmos' texts, such as FiniteDimensional Vector Spaces and Naive Set Theory. Excellent examples of how to go about writing mathematics.
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Re: Mathematics and intellect
I think once notation is understood well, it makes reading texts easier. Sure if you wrote 'implies that', 'if and only if', 'for all members of the set labelled A' I would be able to read the text, but I'm fairly certain most of us, once we know and understand the notation, would be able to read faster and probably better understand the material when the symbols '[imath]\Rightarrow[/imath]', '[imath]\iff[/imath]/[imath]iff[/imath]', '[imath]\forall a \in A[/imath]' are used.
A notable corollary of this, unfortunately, is laypeople cannot read the text until they're provide with a 'translation' from notation to plain English. In a lot of cases this is handled through formal definitions but like any scholarly work, some definitions are simply assumed by the author for brevity.
A notable corollary of this, unfortunately, is laypeople cannot read the text until they're provide with a 'translation' from notation to plain English. In a lot of cases this is handled through formal definitions but like any scholarly work, some definitions are simply assumed by the author for brevity.
Re: Mathematics and intellect
Symbols should be reminders and not the entire text.
 isomorpher
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Re: Mathematics and intellect
Whether mathematicians are actually more intelligent than other intellects probably has no definite answer, as the definition of "intelligence" is too ambiguous. Who are we to say that a mathematician is smarter than a great poet or engineer? Certainly we excel at one particular type of thinking, but there is far more to intelligence than being able to work though abstract logic. However I think there is good reason why mathematics is generally perceived as a higher intellect.
From a psychological standpoint, mathematics, being essentially an exercise in pure abstract thinking, only appeals to people who are adept at that way of thinking. I would guess that the vast majority of mathematicians (also physicists and comp scientists) are INTP's or INTJ's, which combined only account for about 2% of the population. Thus our entire way of thinking, including mathematics, is seen by the majority of people as highly intellectual, yet needlessly abstract and somewhat detached from reality. Just think how mathematicians are portrayed in pop culture, especially movies: smart, yet idiosyncratic and often a little insane.
This perception is only further solidified by most people's limited and often tumultuous interaction with math. Most people as children dream of being doctors, astronauts, athletes, etc. yet here they are studying about numbers and weird lines that seem to have nothing to do with anything. Most people come to realize that math can be incredibly useful outside of science, especially for financial and business applications, but they only see it as a tool and are confined to the rather simple and straightforward formulas that they need to get the job done. I think a great many people who use math in their everyday lives really don't understand why these formulas work. They see them as cryptic, yet seemingly magical symbolic statements that make their job a whole lot easier. Naturally then anyone who actually knows why these things work, and better yet people who come up with them in the first place, must therefore be brilliant.
At least this was how I thought of mathematics before I actually got into math.
From a psychological standpoint, mathematics, being essentially an exercise in pure abstract thinking, only appeals to people who are adept at that way of thinking. I would guess that the vast majority of mathematicians (also physicists and comp scientists) are INTP's or INTJ's, which combined only account for about 2% of the population. Thus our entire way of thinking, including mathematics, is seen by the majority of people as highly intellectual, yet needlessly abstract and somewhat detached from reality. Just think how mathematicians are portrayed in pop culture, especially movies: smart, yet idiosyncratic and often a little insane.
This perception is only further solidified by most people's limited and often tumultuous interaction with math. Most people as children dream of being doctors, astronauts, athletes, etc. yet here they are studying about numbers and weird lines that seem to have nothing to do with anything. Most people come to realize that math can be incredibly useful outside of science, especially for financial and business applications, but they only see it as a tool and are confined to the rather simple and straightforward formulas that they need to get the job done. I think a great many people who use math in their everyday lives really don't understand why these formulas work. They see them as cryptic, yet seemingly magical symbolic statements that make their job a whole lot easier. Naturally then anyone who actually knows why these things work, and better yet people who come up with them in the first place, must therefore be brilliant.
At least this was how I thought of mathematics before I actually got into math.
Re: Mathematics and intellect
isomorpher wrote: Just think how mathematicians are portrayed in pop culture, especially movies: smart, yet idiosyncratic and often a little insane.
Yeah I was just thinking about how every math/physics guy in media tends to have 170+ IQ, socially inept or mentally unstable, eidetic memory. Pi, Big Bang Theory, Good Will Hunting, etc.
Re: Mathematics and intellect
Birk wrote:isomorpher wrote: Just think how mathematicians are portrayed in pop culture, especially movies: smart, yet idiosyncratic and often a little insane.
Yeah I was just thinking about how every math/physics guy in media tends to have 170+ IQ, socially inept or mentally unstable, eidetic memory. Pi, Big Bang Theory, Good Will Hunting, etc.
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Re: Mathematics and intellect
t0rajir0u wrote:I believe that mathematics is clearer without notation. I have seen this explicitly given as advice for mathematical writing from at least two reputable sources, Knuth and Munkres, who both have been writing mathematics long enough that they should know what they're talking about.
Notation doesn't (necessarily) make math easier; it makes it denser. This is good if you have a lot of math to communicate in a short amount of time, but it's no way to teach.
An excellent point. I'll have to reconsider. Although I'd still like to push the idea that the question could be answered experimentally. I admire Knuth as much as the next guy, but it's an appeal to authority, nonetheless. I'd think insufficient density would impede understanding.
Re: Mathematics and intellect
Let's try an experiment with expanding Math into English
"A Scheme is a locally ringed space such that every point has an open neighbourhood containing it which is isomorphic as a locally ringed space to the spectrum of some ring."
Becomes...
"A Scheme is a collection of points along with a collection T of collections of those points containing the collection of no points and the collection of all points, with the properties that for any collections of points U, V in the collection T, the collection of all points contained in both U and V is in the collection T, and for any collection of collections that are in the collection T, the collection of points in at least one of these collections is itself a collection T, along with an assignment of a set of things and two operations that we call addition and multiplication on that set that satisfy the distributive, associative, and commutative properties, along with having additive inverses, to each collection of points U in T, so that for any pair of collections U, V in T, U containing every point of V, we have an association of the elements of the set assigned to U to the elements of the set assigned to V respecting the operations of addition and multiplication, and so that...."
Ok, that was an exercise in futility. Maybe I should have picked an easier topic...
But there is a reason that reading a math book typically takes at least ten times the time it would take to read a philosophical paper of the same length.
"A Scheme is a locally ringed space such that every point has an open neighbourhood containing it which is isomorphic as a locally ringed space to the spectrum of some ring."
Becomes...
"A Scheme is a collection of points along with a collection T of collections of those points containing the collection of no points and the collection of all points, with the properties that for any collections of points U, V in the collection T, the collection of all points contained in both U and V is in the collection T, and for any collection of collections that are in the collection T, the collection of points in at least one of these collections is itself a collection T, along with an assignment of a set of things and two operations that we call addition and multiplication on that set that satisfy the distributive, associative, and commutative properties, along with having additive inverses, to each collection of points U in T, so that for any pair of collections U, V in T, U containing every point of V, we have an association of the elements of the set assigned to U to the elements of the set assigned to V respecting the operations of addition and multiplication, and so that...."
Ok, that was an exercise in futility. Maybe I should have picked an easier topic...
But there is a reason that reading a math book typically takes at least ten times the time it would take to read a philosophical paper of the same length.
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Re: Mathematics and intellect
Notation and terminology are two very different things.

 Posts: 42
 Joined: Tue Sep 15, 2009 2:42 am UTC
Re: Mathematics and intellect
t0rajir0u wrote:Notation and terminology are two very different things.
How? Notzeb uses terminology, e.g. strings of Romanalphabet letters like "space," "spectrum," and "is isomorphic as." If he replaced each with a single letter in Greek, or Hebrew, or some obscurer alphabet, would that be notation? Or is the difference between notation and terminology more than that?
Re: Mathematics and intellect
Surely in the argument of mathematician versus say literary critic, we need to clarify the mathematician bit.
There's mathematicians of the calibre of Fermat, who produce new and groundbreaking work during their lifetime. And then there's your average maths postgrad. Who makes a tiny incremental addition to their field.
Fermi is equivalent to say Dostoevsky ie people that add in a significant way to any field that are in.
But most litcrits are equivalent to the average maths postgrad. Someone who has added slightly to their field but nothing significant.
Literary criticism can never compare favourably to a Fermi in the same way as someone who can understand Zorn's Lemma cannot be favourably compared to Dostoevsky.
There's mathematicians of the calibre of Fermat, who produce new and groundbreaking work during their lifetime. And then there's your average maths postgrad. Who makes a tiny incremental addition to their field.
Fermi is equivalent to say Dostoevsky ie people that add in a significant way to any field that are in.
But most litcrits are equivalent to the average maths postgrad. Someone who has added slightly to their field but nothing significant.
Literary criticism can never compare favourably to a Fermi in the same way as someone who can understand Zorn's Lemma cannot be favourably compared to Dostoevsky.
Re: Mathematics and intellect
chilled wrote:Surely in the argument of mathematician versus say literary critic, we need to clarify the mathematician bit.
There's mathematicians of the calibre of Fermat, who produce new and groundbreaking work during their lifetime. And then there's your average maths postgrad. Who makes a tiny incremental addition to their field.
Fermi is equivalent to say Dostoevsky ie people that add in a significant way to any field that are in.
But most litcrits are equivalent to the average maths postgrad. Someone who has added slightly to their field but nothing significant.
Literary criticism can never compare favourably to a Fermi in the same way as someone who can understand Zorn's Lemma cannot be favourably compared to Dostoevsky.
I disagree strongly here. I know many mathematicians, and find them to be on the whole to be erudite, literate, multilingual, talented, and so on. The arts professors I know, and I know quite a few as well, are also all of these. However, there is a big difference: whereas a mathematician will tend to know a reasonable amount about music, literature, art, etc., an arts professor will be completely ignorant of any field remotely scientific or practical. I sometimes play a game with arts people, a general knowledge quiz:
1) What is the second law of thermodynamics?
2) How many electrons in an atom of potassium?
3) How does a refridgerator work, i.e., cool things down?
4) What is a xylem?
5) What does it mean for a company to be highly geared?
6) What is bauxite?
7) What's the difference between mean and median?
8) Where is your filtrum?
Or similar things. Basic questions about various scientific endeavours. I throw 5 in there to show that they know nothing about business either. I'm not saying that all arts professors are ignorant. (Of course, this is a sweeping generalization.) It is just that they seem, on the whole, to have no idea about the natural world. Considering the fact that the arts are useless (I mean useless in any practical sense) you would have thought that a knowledge about the natural world would be  how shall I put it?  naturally gained.
Maybe I'm being a bit harsh, and it is quite difficult to nuance an argument on an Internet forum, especially when you haven't had much sleep.
Re: Mathematics and intellect
mouseposture wrote:If he replaced each with a single letter in Greek, or Hebrew, or some obscurer alphabet, would that be notation? Or is the difference between notation and terminology more than that?
The key is not so much the big words he uses as the small words he uses between them: "is a," "such that every," "has an".... These are all English words that everybody understands, and the rest is just a matter of getting used to specialized terminology (which, I will remind you, is present in every specialized discipline). Mathematical notation, on the other hand, is much more crytic: nobody finds it natural to read long strings of existential or universal quantifiers (that I know of).

 Posts: 309
 Joined: Tue Feb 27, 2007 2:27 am UTC
Re: Mathematics and intellect
DavCrav wrote:I sometimes play a game with arts people, a general knowledge quiz:
1) What is the second law of thermodynamics?
2) How many electrons in an atom of potassium?
3) How does a refridgerator work, i.e., cool things down?
4) What is a xylem?
5) What does it mean for a company to be highly geared?
6) What is bauxite?
7) What's the difference between mean and median?
8 ) Where is your filtrum?
So, I just graduated with a physics BA, and I can only answer 3 of those perfectly without resorting to wikipedia. Maybe I'm an idiot who has no idea about the natural world or anything vaguely practical at all. I'm just good at physics.
Or maybe I just spent my time learning different things than you. Maybe I could come up with an equally embarrassing "common knowledge" quiz. Is it possible that you are just judging arts people harshly because they don't have exactly the same knowledge base as you?
Daylater Edit: Wow, that was way more jackasssounding than I wanting.
Last edited by Shadowfish on Sat Jan 16, 2010 11:09 pm UTC, edited 2 times in total.
I'm mostly a lurker. I lurk. Kind of like a fish, in the shadows.
Re: Mathematics and intellect
I think one key ingredient is measuring quality transparently. Mathematics has this: colleagues can check the proofs are valid (in some cases, even software can), subsequent publications show if the "hunch" leads anywhere, and if applicable the applied scientist who asked the question can say if it solves the problem. Works of literature critique are probably harder to judge.
There is evidence quality of university level music education improved vastly when they started doubleblind testing applicants during admissions, i. e. the board of admission would only listen to someone playing, but didn't know or see who, and could not be subconciously influenced by anything but the actual music.
There is evidence quality of university level music education improved vastly when they started doubleblind testing applicants during admissions, i. e. the board of admission would only listen to someone playing, but didn't know or see who, and could not be subconciously influenced by anything but the actual music.
Re: Mathematics and intellect
DavCrav wrote:1) What is the second law of thermodynamics?
2) How many electrons in an atom of potassium?
3) How does a refridgerator work, i.e., cool things down?
4) What is a xylem?
5) What does it mean for a company to be highly geared?
6) What is bauxite?
7) What's the difference between mean and median?
Where is your filtrum?
Although I think this particular test is a little extreme, C.P. Snow's The Two Cultures is relevant here.
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