NationStates Jolt Archive

I'm doing a lot of math at the moment, including stuff I've never actually done before: not solving equations, but much more pure math type proofs and the like. Set theory for the most part as related to preference relations, budget sets and the construction of utility functions.

At the same time I'm also doing intertemporal optimisation stuff using Hamiltonians to express the behaviour of agents in macroeconomic models mathematically and solve the models.

Oh, and Stats of course. GARCH (General Autoregressive Conditional Heteroskedasticity) models this week.

Weirdly, despite my belief for most of my studies that I merely tolerated math and could never enjoy it, the proofs in particular are actually kinda fun, when you finally work them out.

I'm doing this thread because

a) There'd been a bit of a discussion about the kinds of math used by different discipline, and whether any of them were "harder" than others. Specifically, there'd been people who said that physics- and engineering math is heaps harder than econ math. So, I'm making a poll and asking: what sort of math do you do, why do you do it, and how difficult would you say it is? I'd like to find out what the level actually is for real-world physics or engineering students or practitioners.

b) In another thread there are a few people bickering about whether the ability to do math is a skill one can learn, or just some random talent that comes with your DNA. My mother is absolutely convinced it is the latter, and that she can't do math, so she doesn't even try. So what do you say? How much math can anyone do, if they practise? How important is just being able to "think that way" by nature when it comes to learning this stuff?

EDIT: I just noticed that I didn't put in a "Finance" category. If you happen to be doing financial math, just put it under Economics. Merton, Scholes, Black...they're all economists anyways. Similarly, any other categories I've missed, just pick one that is closest to it.

Anyone can learn to do math. Some people learn much more quickly and effortlessly than others.

Combination of nature and nurture, obviously.

Anyone can learn to do math.

Unfortunately, that's not true.

er...I get a bit hazy in even with multiplication* but I haven't done any "hard math" in maybe 3 years so its left me a bit out of touch

*don't get me wrong I can do it all but it just takes me a while...and angles can go fuck themselves

*runs screaming from this thread*

I fucking loved math and physics, but never felt like I really 'got it'. It was like there was some way of seeing it that was just slightly out of my reach. Drove me nuts. I have forgotten absolutely everything I learned because I haven't had to use it at all, and this is also frustrating, because if I wanted to pursue it again, I'd have to start from scratch. That sucks diseased monkey balls. Fuck math. Or rather, I'll fuck someone who is better at math than me, and can meet all my mathy needs.

Is it just people from the UK who say maths rather than math?
Anyone can learn maths except those with dyscalcula.

It was like there was some way of seeing it that was just slightly out of my reach.

this.

like I could do it all perfectly but I didn't really grasp why so much as I knew how to do it which is a bitch if your doing math coursework (come to think of it I maybe just wasn't confident with it)

Is it just people from the UK who say maths rather than math?
Anyone can learn maths except those with dyscalcula.

We are so bad at math that more than one math makes us nervous, so we keep it singular.

And dyscalculia? omg! *self diagnoses* This is going to be the new Aspergers!

Or rather, I'll fuck someone who is better at math than me, and can meet all my mathy needs.

If that's true, I'll immediately redouble my efforts to learn math. :D

Is it just people from the UK who say maths rather than math?
I have no idea. I find "maths" harder to pronounce, and I just settled on one and went through with it.

To anyone who feels I made the wrong choice, feel free to replace the offending words with better ones in your mind.

Weirdly, despite my belief for most of my studies that I merely tolerated math and could never enjoy it, the proofs in particular are actually kinda fun, when you finally work them out.

Next thing you know you'll be giving up that banking lark and coming to join the mathmos.


a) There'd been a bit of a discussion about the kinds of math used by different discipline, and whether any of them were "harder" than others. Specifically, there'd been people who said that physics- and engineering math is heaps harder than econ math. So, I'm making a poll and asking: what sort of math do you do, why do you do it, and how difficult would you say it is? I'd like to find out what the level actually is for real-world physics or engineering students or practitioners.

It depends. I'm a mathematician (in training) with an interest in the more abstract areas such as group theory. This is where mathematical intuition really starts to come into play (see below). It's not that such subjects are inherently incredibly complex, but that they are very abstract. This makes it harder to comprehend than (relatively simple) differential equations, which can (in some cases) be solved by cookbook methods.


b) In another thread there are a few people bickering about whether the ability to do math is a skill one can learn, or just some random talent that comes with your DNA. My mother is absolutely convinced it is the latter, and that she can't do math, so she doesn't even try. So what do you say? How much math can anyone do, if they practise? How important is just being able to "think that way" by nature when it comes to learning this stuff?

There is such a thing as mathematical intuition, basically a knack for logical and abstract thinking of that sort. This varies between people.

But study and work is still required, in almost all cases (Ramanujan being the exception that proves the rule). A strong knack for maths will make it easier to learn, especially more abstract and advanced areas, and helps guide research mathematics, but isn't needed to be able to do maths, especially when applying it to some other field.

So basically, there is mathematical intuition, which is basically required to follow mathematics to very advanced levels, and makes study at earlier levels much easier. However, discipline, diligence, and a willingness to accept the abstract can get you very far.

To answer the poll: I'm currently finishing up high school, and will then be off to university to pursue a degree in Mathematics, with (as it stands) more of an emphasis on the pure side. Mild interest in the philosophy, but probably won't study that too much.

*runs screaming from this thread*

I fucking loved math and physics, but never felt like I really 'got it'. It was like there was some way of seeing it that was just slightly out of my reach. Drove me nuts. I have forgotten absolutely everything I learned because I haven't had to use it at all, and this is also frustrating, because if I wanted to pursue it again, I'd have to start from scratch. That sucks diseased monkey balls. Fuck math. Or rather, I'll fuck someone who is better at math than me, and can meet all my mathy needs.

So how you doin?

Edit: also, sorry for double post.

.. It was like there was some way of seeing it that was just slightly out of my reach. Drove me nuts....

I remember that feeling - I always put it down to the speed at which we were taught.

If you can do math, you can do it. You might have to have someone show you the path, or you might be able to force your way through when the circumstances require it.

If you can't do math - if your brain just doesn't work that way - it's always going to be somewhere between pain and impossible. (I work with a guy like that - so long as he can pump the numbers into a calculator, he's all good - but when you actually make a shortcut leap through the methodology, he gets that 'deer-caught-in-headlights' look.)

Is it just people from the UK who say maths rather than math?


I'm a UKian, and I say math. They all did, at my school, though - maybe that has something to do with it?

I'm a UKian, and I say math. They all did, at my school, though - maybe that has something to do with it?

Oh God, it's a generation gap thing and I am old :(

If you can't do math - if your brain just doesn't work that way - it's always going to be somewhere between pain and impossible.
Yeah, but how do you separate that from a sort of immediate negative reaction to seeing anything that looks like math that just comes from bad past experiences or something. It's very easy to convince yourself that you can't do something, and that then becomes self-fulfilling.

If that's true, I'll immediately redouble my efforts to learn math. :D



So how you doin?



Sorry, I've already got a penis attached to someone good at math. :p

Sorry, I've already got a penis attached to someone good at math. :p

a calculator with a dildo tied on?

Where's the "Pilot" option? We have to do math too, you know.

Oh God, it's a generation gap thing and I am old :(

UKian here, I say maths, as do most of the people I know my age.

Where's the "Pilot" option? We have to do math too, you know.
Really? What sort?

Really? What sort?

Probably what would be considered Algebra I is as far as I have to go.

EDIT: To expound, the most that we have to do on paper is a weight-shift calculation, which is algebraic in nature. We're moving X amount from A to B position, without exceeding a certain C.G. number.

We also do spotball geometry in the air, but that's more of a time and experience thing rather than mathematical in nature.

Also, I think how good you are at maths is on a spectrum of ability, rather than you simply can do it, or simply can't do it. It's more like, some are amazing at it, some are pretty capable at it, some are just about able to do it, some can barely do it at all etc... Different types of maths take different kinds of abilities. I know people who are fantastic at arithmetic, but are just unable to solve complex algebra, calculus and abstract mathematical logic questions. For me it's the other way round, I'm pretty good at the problem solving stuff etc..., but not great at immediate mental arithmetic.

a calculator with a dildo tied on?

You never know when you're going to need the square root of pi during masturbation.

Oh God, it's a generation gap thing and I am old :(

Maybe, or geographical, or just Grammar schools, or just my school. (This would have been... later 80's and early 90's).

Different types of maths take different kinds of abilities.

the problem with this is once you get left behind on a particular bit your pretty much fucked

You never know when you're going to need the square root of pi during masturbation.

Sin, I'm going to have to correct that last math problem you were doing... pi isn't three point one four oh oh ohhhhh.

Is it just people from the UK who say maths rather than math?
Anyone can learn maths except those with dyscalcula.

I think I possibly have this. Beyond arithmetic, everything takes effort.

I chose IT, because that was my most recent application of maths; 'life' things like going to the shops and getting a ballpark figure of what you bought, I don't count as math, it's sort of instinctual.

Sorry, I've already got a penis attached to someone good at math. :p

Awww. :(

Is it just people from the UK who say maths rather than math?
Anyone can learn maths except those with dyscalcula.

I must admit I was bit surprised to see Leon (an Australian) put down Math instead of Maths. I have always called it Maths and so to do most people in Australia.

I chose IT, because that was my most recent application of maths...
To clarify, I meant more things like this (http://en.wikipedia.org/wiki/Computational_complexity_theory) or this (http://en.wikipedia.org/wiki/Algorithmic_information_theory).

To clarify, I meant more things like this (http://en.wikipedia.org/wiki/Computational_complexity_theory) or this (http://en.wikipedia.org/wiki/Algorithmic_information_theory).

Oh, sorry. I thought you meant anything requiring the processing of arithmetic in programming in general... sorry.

I'm a chemical engineer, so my maths are most closely related to electrical engineering. Or more so than civil/architecture, anyway.

I'm currently taking calculus based physics 1 and engineering calculus 2. So that, I guess. I'm studying to become a chemical engineer.

And I think there is a natural talent element to math in a way, but in that in only goes so far and different people hit the point where it stops coming naturally to them and they have to really work at it at different points. In engineering calculus 1 I got an A+ pretty easily with no more than average effort (I did all of the assigned homework but not really any extra studying). In engineering calculus 2 I tried the same thing at first and got a C on the first test. I realized that I was probably at the point where talent alone wasn't enough anymore and I'd need to start doing more than what was assigned and studying more to make sure I'd do well. I got an A on the next test, so my grade's at an 88 now with another test and a final project still to go. I know for some people in my class it still comes naturally and for others it doesn't seem to but they seem satisfied with C's, or maybe resigned to them.

I know that on the other hand, one of my roommates studied for hours and hours for one of her business calculus tests, only to fail it. After that I helped her study for the next one and I think she ended up with a C in the end, but... yeah...

I'm a civil engineer who is looking to minor in math, and all of my maths have been calculus-based.

I've taken all of my core math classes, and I'm about to take a course on triple integrals and even more vector calculus. Will be... fun?

The ability to do math (especially when one gets into derivatives and integrals) relies on both a natural instict and material learned. You have to be able to transform the equation you're dealing with into one that you can work with so that you can use learned material to process it.

i'm primarily a graphic designer who works in business. i mostly use maths to work out profit, costs, margins, POR and the like. i use some maths in analysing the odd bit of market research, but its not that complicated, and the computer does it... i just have to figure out the equations. its more logic than maths per se. it very rarely stretches beyond simple arithmetic.

we did econometrics at university, but to say i sucked at it would be an understatement. i don't get on well with things that don't have a practical application. of course, it doesn't help that i don't know my times-tables (for starters). the dyslexic institute said i had some mild form of dyscalculia. mental arithmetic is fine as long as i can count to the answer in my own time... using my fingers. in short, i've never liked maths.

edit: that said, i love some of the results of maths, from physics and chemistry to computer programming and data modelling. i just can't do it myself lol

I don't care how many times someone explains it, demonstrates it, and even proves it. I just can't get my head around the Monty Hall paradox.

It's ungodly I tells ye.

I'm a civil engineer who is looking to minor in math, and all of my maths have been calculus-based.

Really? I've found that in homework and class most math done is algebraic or geometric. Of course there are lots of things that have calculus in them but usually theres tables or something with solutions unless the prof. gives you a bit of a different problem (like deflections, that type a shit).

So yea, we do a bit of everything- algebra, geometry, calculus, Diff Eq. For me mostly algebra and Geometry, then calculus, which is only used less because most problems have been solved already.

I wonder how appropriate it is to but architecture in with Civil, but I've never taken architecture before so I can't say... just my innate engineer hatred of architects coming out :)

Maths for physics here (not extremely advanced: no quantum field theory, or general relativity; just up to quantum optics, quantum electronics, statistical mechanics).
Plus some math for the fun of it (theory of numbers).
Occasionally some accountant's thingies, like when I have to peruse into the financial part of laws. I hate accountants.

The best teacher I had at school was my maths teacher who taught me A level maths. He had a real passion for his subject and was an enjoyably grumpy bastard. Yet despite his best explanations I was left with that feeling Neesika describes of understanding it being just out of my reach. I put it down to two things - one they crammed a huge amount into the curriculum - and secondly and most importantly that they taught maths in a very abstract way. In order to understand things I need to be able to visualise how things are used, to mentally take them apart and see how they work. The way it was taught seemed to deliberately not do this - it was even called pure maths and if you were really good at pure maths they encouraged you to do a second A level in applied maths. Now to me this emphasis on pure maths seems to me entirely the wrong way round. Surely it would be easier for people to learn maths if it is taught with concrete examples of how it is used and potentially relevant to them? The maths I use now in my daily life involves analysing statistics and surveys, financial management, and probability for backgammon - yet I was pretty much taught all of the techniques I use but without any real-life examples that were relevant to me. Something must have sunk in as got the top grade and briefly at university managed to cope with spherical trigonometry in an astronomy module. But overall I hope the teaching of maths has changed to suit peoples learning styles more.

You did miss the option of psychology (and related sciences, I know parts of biology, sociology and medicine use similar techniques) maths - a lot of statistical analysis and a lot of statistical modelling (Structural Equation Modelling is the current fun one I'm on). I suspect the maths are somewhat different to that seen with economics.

Edit: and I say Maths too - from the UK.

Edit 2: Forsakia - the Monty Hall paradox only makes sense when you remember that the first option displayed is non-randomly selected - still makes my head hurt too.

The way it was taught seemed to deliberately not do this - it was even called pure maths and if you were really good at pure maths they encouraged you to do a second A level in applied maths. Now to me this emphasis on pure maths seems to me entirely the wrong way round. Surely it would be easier for people to learn maths if it is taught with concrete examples of how it is used and potentially relevant to them?
I actually think that pure maths and applied maths require different ways of thinking. I reckon that someone could be great at solving complicated differential equations or something, but when you ask them to prove some concept on exactly why their differential equations actually work the way they do, they could have trouble. And the other way around.

You did miss the option of psychology (and related sciences, I know parts of biology, sociology and medicine use similar techniques) maths - a lot of statistical analysis and a lot of statistical modelling (Structural Equation Modelling is the current fun one I'm on). I suspect the maths are somewhat different to that seen with economics.
I'm not sure. I've done structural models in econometrics for example. The thing with econ maths is that you have relatively pure stuff, when doing theoretical microeconomics, such as proving the welfare theorems in a GE setting, occasionally somewhat complex applied stuff when solving certain types of models in macroeconomics and then the whole wide world of econometrics as a third option. As far as exposure to different types of stuff is concerned, it's actually pretty good.

At any rate, I suspect that the sort of statistical analysis used to analyse samples of psychology et al is similar to the techniques used to deal with economic data.

I'm not sure. I've done structural models in econometrics for example. The thing with econ maths is that you have relatively pure stuff, when doing theoretical microeconomics, such as proving the welfare theorems in a GE setting, occasionally somewhat complex applied stuff when solving certain types of models in macroeconomics and then the whole wide world of econometrics as a third option. As far as exposure to different types of stuff is concerned, it's actually pretty good.

At any rate, I suspect that the sort of statistical analysis used to analyse samples of psychology et al is similar to the techniques used to deal with economic data.

I suppose I was thinking about economics in the more theoretical sense. I imagine when it comes to analysis of real world data you may be right. The aim is the same after all, to test significant relationships between different, and theoretically related, variables whilst controlling for other possible confounding effects.

Oh Gods...how I hated maths. My enthusiasm for the subject wasn't entirely helped by my teacher from Year 7-8 being a bullying, incompetent piece of shit who was insistent that I was crap at his subject despite test scores repeatedly demonstrating otherwise, and then tried to have me put in the bottom set for Year 9, despite the fact I had the scores to be on the borderline for two sets higher.

Then in Year 9 and Year 10 (I moved up a set, so I got him twice!) we had a teacher who must have been about twenty years over retirement age, who was, rather cruelly, but not entirely inaccurately, nicknamed 'senile' by the students. He couldn't remember any of the students' names, and on several occassions set the same exercises in the textbook for homework for about three weeks in a row.

Then in Year 11 he finally retired, to be replaced with an absolute evil cow of a teacher, who on the basis of the first test of the year set everyone a target grade, and any piece of work that fell even one mark below she'd shout at you for about ten minutes and threaten to write to your parents.

With all this, perhaps its not surprising I hated maths. But I also think its something more...I mean to say that the subject, much like the Sciences, just had no appeal. As a geek, of course, I studied equally hard in these, and indeed got A* in all of them at GCSE, before promptly giving them all up

But when I found what "x" equalled, or plugged a bunch of numbers into a formula successfully, I just thought "what the fuck is the point of this?". History, English Literature etc we found out about events, people, their views, and how they tried to get them across. And to me its just inherently more interesting looking at the subjective social world rather than the objective scientific world. Which is why I despair deeply when I encounter in some of my politics modules people who think you can model every aspect of human life objectively and scientifically using a mathematical formula. Not only do I believe that they are wrong, but it is so terribly dull to study.

I actually think that pure maths and applied maths require different ways of thinking. I reckon that someone could be great at solving complicated differential equations or something, but when you ask them to prove some concept on exactly why their differential equations actually work the way they do, they could have trouble. And the other way around.

I agree, but I think for most people an emphasis on applied maths would be more productive, both in terms of being useful and also being easier to understand.

I don't do any math these days beyond simple arithmetic. Calculating how much my groceries are going to cost, that sort of thing. I do really enjoy math though, and never had any problems with it when I was taking courses in the subject.

As for the amount of math that people are able to do, I think that natural ability does help but I wouldn't go so far as to say that you can't learn to be good at math. I do think that some abstract concepts may come easier to people who have an intuitive grasp of the subject, though.

Nerdy math joke/song. (http://www.youtube.com/watch?v=UTby_e4-Rhg)

I didn't read it all but Maths is enjoyable.. I'm a mathematical fanatic :P

I am not a fan of maths.

Doing a science degree requires me to do some maths. And some mathematical logic, since it's a computer science degree.

Computer sciencey math - set theory, recursion theory, graph theory, proofs, probability & statistics, linear algebra, and other bits of math that we steal from other disciplines.

Infinity times the square root of negative one equals . . . ?

eight

Next thing you know you'll be giving up that banking lark and coming to join the mathmos.



It depends. I'm a mathematician (in training) with an interest in the more abstract areas such as group theory. This is where mathematical intuition really starts to come into play (see below). It's not that such subjects are inherently incredibly complex, but that they are very abstract. This makes it harder to comprehend than (relatively simple) differential equations, which can (in some cases) be solved by cookbook methods.



There is such a thing as mathematical intuition, basically a knack for logical and abstract thinking of that sort. This varies between people.

But study and work is still required, in almost all cases (Ramanujan being the exception that proves the rule). A strong knack for maths will make it easier to learn, especially more abstract and advanced areas, and helps guide research mathematics, but isn't needed to be able to do maths, especially when applying it to some other field.

So basically, there is mathematical intuition, which is basically required to follow mathematics to very advanced levels, and makes study at earlier levels much easier. However, discipline, diligence, and a willingness to accept the abstract can get you very far.
Mathematical intuition, like any intuition, is developed, not inate, and can be trained. It just takes time.

Probably what would be considered Algebra I is as far as I have to go.

EDIT: To expound, the most that we have to do on paper is a weight-shift calculation, which is algebraic in nature. We're moving X amount from A to B position, without exceeding a certain C.G. number.

We also do spotball geometry in the air, but that's more of a time and experience thing rather than mathematical in nature.
Ah, but it is mathematical, just not conciously so. It's that mathematical intuition kicking in ;)

You never know when you're going to need the square root of pi during masturbation. I prefer looking at pictures of pie, but to each thier own :tongue:

the problem with this is once you get left behind on a particular bit your pretty much fucked
Are you talking about school-wise? Have you no outside resources?

Ah, but it is mathematical, just not conciously so. It's that mathematical intuition kicking in ;)

Yeah, it's like doing geometry on the basis of a right triangle most times. It is A distance to the destination at B speed, where X is the target altitude at that point, and how many feet per minute descend/ascent will get us there at that precise point.

It's not an exact, more of a quick estimation.

Infinity times the square root of negative one equals . . . ?
Stop being irrational!



As for me...Don't do maths at the moment, but I have a sneaking suspicion that next year (well, this autumn) I will be doing more maths than I'd care for :tongue:

Mathematical intuition, like any intuition, is developed, not inate, and can be trained. It just takes time.

If mathematical talent is not innate, but is only developed, how do we get mathematical child prodigies?

I was really good at maths, but I hated it. I left school three years ago with Maths and Physics being my highest scored subjects, but I had no inclination to ever touch them again.

Mathematical intuition, like any intuition, is developed, not inate, and can be trained. It just takes time.

Depends. It is trainable - sets of heuristics like Polya and Tao present (How To Solve It and Solving Mathematical Problems, respectively), are useful for teaching you how to approach things, how to look at a problem and turn it around to get a better angle at it. Nearly anyone can improve by working with such a book and a good teacher.

But fundamentally, there's still a problem there - what they are providing is rule sets, but what one really needs to develop is flexibility. You can get very good at applying rule sets, and very good at solving problems from that, but the underlying mental fluidity (for want of a better way to put it) is harder to teach. What training does is improve the capacity someone has for it, give them more ways to think around a problem and explore it.

Mathematical intuition isn't the best phrase for it, maybe. How about "acceptance of abstraction" or something like that? At it's heart, it's about how willing you are to let go of something locked into reality, and step into abstraction - you might come back to reality with the tool later, but the abstract idea at the heart of it is the most important bit. This is (I think) why most people say "I never got algebra" - it's the first piece of real fundamental abstraction that they hit.

(Not the best phrasing for some of this post, do ask for clarification if you need it)

Well the most math I do is when it comes to engines, volumetric efficiency, cfm and the like. I guess that would be high school math?

You missed out the s. Anyway, fucking hate it, don't understand quite a bit of it, and I discount anything that isn't just times/divide/add/subtract with numbers or algebra as being maths. I mean, simultaneous equations, geometry, what the fuck?

man, back in elementary school we had these math speed tests. i never won, but i always got everything right. unlike the people who actually did it fast - most of them had just memorized most of the problems, so they'd miss ones they didn't remember

i actually love math, but the last time i had any formal math was my junior year in high school. now i just play with logic instead.

I am a draftsman, or was before I was laid off, and I use(d) trigonometry and geometry all the time. I haven't needed the quadratic equation or any other advanced algebra since college, and I hardly remember anything from calculus because I never used what I learned after I was done with the class.

You missed out the s. Anyway, fucking hate it, don't understand quite a bit of it, and I discount anything that isn't just times/divide/add/subtract with numbers or algebra as being maths. I mean, simultaneous equations, geometry, what the fuck?

Optimisation, bombing runs, orbital mechanics, etc. All contain applications of at least one of those fields.

If mathematical talent is not innate, but is only developed, how do we get mathematical child prodigies?
I don't know enough of how the brain works to say, but I do know that when I began studying 4-dimensional geomerty, I had to spend a lot of time training myself to think about it before I developed an intuitive feel for it (see Rudy Rucker's work for an excellent example of how to develop an intuitive feel for 4-dimensional geometry ;))

Depends. It is trainable - sets of heuristics like Polya and Tao present (How To Solve It and Solving Mathematical Problems, respectively), are useful for teaching you how to approach things, how to look at a problem and turn it around to get a better angle at it. Nearly anyone can improve by working with such a book and a good teacher.

But fundamentally, there's still a problem there - what they are providing is rule sets, but what one really needs to develop is flexibility. You can get very good at applying rule sets, and very good at solving problems from that, but the underlying mental fluidity (for want of a better way to put it) is harder to teach. What training does is improve the capacity someone has for it, give them more ways to think around a problem and explore it.

Mathematical intuition isn't the best phrase for it, maybe. How about "acceptance of abstraction" or something like that? At it's heart, it's about how willing you are to let go of something locked into reality, and step into abstraction - you might come back to reality with the tool later, but the abstract idea at the heart of it is the most important bit. This is (I think) why most people say "I never got algebra" - it's the first piece of real fundamental abstraction that they hit.

(Not the best phrasing for some of this post, do ask for clarification if you need it) I think "mathematical intuition" is a fine phrase for it. People often confuse intuitive understanding for inate understanding. It is not inate, but is aquired informally, without study, which is what confuses people. Humans are learning machines, especially when young. Formal education is a very recent social invention.
As for having a flexible mind, one can perform a sort of mental yoga, via puzzle solving and lateral thinking exercises. And some people need more time to learn things, sometimes more than they (or others) are willing to take.
As for abstraction vs reality, I often find the reality of the abstract world more real than most people's so-called "reality." :eek2:

Infinity times the square root of negative one equals . . . ?


It's on the unit circumference. Easy.

It's on the unit circumference. Easy.

Uh, the correct answer is in white, underneath the question. I answered the "post a math joke" poll option :(

I hated, and still hate, math. :mad:

The maths I still do ranged from simple arithmetic (calculating drug dosages, body mass indices) to complex equations I still don't really get (that's why I hated pharmacokinetics and clinical epidemiology :mad:).