How can one be naturally good at maths?

[jd12345]

Maths is a tool made by us to understand the nature( or whatever reason). Then how can one be naturally good at it? You have to study the subject, practice it and then become a master of it. But i have heard of prodigies who have done miracles at a very low age.
Is there a part of the brain dealing with maths(which is human-made)?

 

[chiro]

I think like any language, one has to see beyond syntax, structure, and formalism to really understand what mathematics actually is and what it really corresponds to.

Mathematics to me is like the epitomy of language in that it provides a language that regardless of cultural, social, or any other class or division, everyone can agree on. This to me is the real power of mathematics.

The properties about it being consistent, logical, rigorous, and so on are definitely great properties, but they simply re-inforce the characteristics of why math is the best candidate so far for a global language.

But like any language, what representation corresponds to, even with mathematics doesn't always have a clear meaning and that's the real challenge of knowing what something actually corresponds to.

Sure we know how to define numbers, sets, functions, algebra and so on, but these things in a purely symbolic context really have no deep understanding. If you don't believe me, ask many of the people who have constant difficulties in mathematics who struggle because of the primary fact that the symbols and the systems employed do more to confuse people than to enlighten them.

Intuition in any language is built up through time, and commonly when one is introduced to any language what happens is that a kind of bridge is used to take a person from a language of great familiarity to one of no familiarity when they are starting.

Once the intuition has been built up, the concepts become a lot easy to grasp at high levels just like the person is able to craft sentences and even entire reports, novels, essays, and so on with ease.

But to have the real understanding, you have to leave the symbols behind and look for a way to take those symbols, concepts, and so on and put it in your own language.

But language is really the bread and butter of analysis and information is everywhere. Information is present when you look out at the world and isn't just available in the symbols, flow-charts, diagrams, proofs, and definitions and restricting yourself to just one language means you miss out on all the opportunities to create otherwise valuable connections to all the other components that are a lot more natural.

People also like things they can relate to and initially if you teach people mathematics in a way that they can not relate to in a meaningful way, they will lose interest or even end up hating something.

The way mathematics is taught, is done in a way that there is no meaningful relation. Looking at right-angled triangles, corresponding angles, and rules of algebra is not in any way useful if it has no relation to something meaningful. Unfortunately what happens is that when people don't see the meaning and don't get what's going on, some think they are stupid, and others think that if this is what mathematics is about, then it is completely devoid of any kind of meaning, creativity, or any practical use whether purely intellectual, purely technical and applied, or a mix of the two.

The other thing that mathematics does is it meets two very important needs: the first is that it is specific which is something that the best of languages aspire to be, and the second thing is that it is also broad.

These two sound contradictory but they are not, and mathematics shows how this is done. The specificity comes in the attributes associated with unambiguity, consistency, and logic. The broadness comes in with variability.

The variability itself gives the power known as the abstract nature of mathematics. Mathematics is, in a nutshell, the study of variability. The variation occurs in every known sub-topic and thereof of mathematics including analysis, algebra, and topology. Without variation, there would be no need for mathematics whatsoever.

Also to become a master at something, you have to seek true understanding and sometimes that means coming in contact with situations that may not seem what you think they seem. It means that you have to accept always the possibility that what you thought might have something that is not complete, and this means having an open mind. This is a lot harder to do when you are older than it is when you are younger.

The other important thing is to observe and look at what other people are thinking and doing. Just like everything else, communities naturally tend to form when common interests emerge, and like everything else they tend to become a lot more organized with regards to how they operate and how they communicate. This is true of every endeavor and really shows a small glimpse into the amazing capacity of this thing we call reality.

So always listen to what other people are saying, and offer your own viewpoint whether it's right or wrong. Usually, things are a bit of both and it's going to be better in the long run to get a reference point for your own thinking which other sources provide: the more reference points (and the greater the actual diversity of the points regardless of what they are), then the better you have to grow in your own conclusions.

Finally I'll leave you with the thought of considering the circumstances of the different people in all aspects. Think of the upbringing, the people that they came in contact to throughout their lives and what these had in terms of impacting their own visions, philosophies, and directions and also on the activities and the connection of all of these on the work of these mathematicians (or any other master). These are often not mentioned, but they are the most important thing to consider.

For example most people don't know that Gauss had to calculate values of logarithms frequently so the idea of the prime number theorem happening merely without relativeness or context is not true at all, and I think you'll find that this kind of thing without putting it into context is also misleading to say the least.

 

[KiwiKid]

I've always thought that abstraction is a very important quality to have. In order to be good at math, you have to be able to take concrete examples and abstract them into oblivion.

 

[Jimmy Snyder]

Actually, no one is naturally good at maths. But in the land of the blind, the one eyed man is king.

 

[zoobyshoe]

Maths is a tool made by us to understand the nature( or whatever reason). Then how can one be naturally good at it? You have to study the subject, practice it and then become a master of it. But i have heard of prodigies who have done miracles at a very low age.
Is there a part of the brain dealing with maths(which is human-made)?

There are also other prodigies in other activities that can be considered "man made": art and music for example. The fact of prodigies is really what needs to be explained, not just math prodigies.

 

[Boston_Guy]

Maths is a tool made by us to understand the nature( or whatever reason). Then how can one be naturally good at it? You have to study the subject, practice it and then become a master of it. But i have heard of prodigies who have done miracles at a very low age.
Is there a part of the brain dealing with maths(which is human-made)?

In high school I showed no signs at being any good whatsoever in math. However when I got to college I turned out to be special in math. I was a whizz at it so I double majoerd in physics and math, since the former requires a lot of the later. I think that by the time I got to college, which was after a stint in the military, I wanted to become an electrical engineer. I was scared stiff of all the math I had to take. But when it came to learning it I had already had a preview of its applications from life experience so I absolutely loved it, especially since I lovede the topic. I couldn't get enough of it. It was hard socially though to be so good. Other students rejected me because I made the rest of the class look bad. It was a traumatic time in my life. But I do understand this kind of thing to a very small extent.

 

[leroyjenkens]

Why do people around here pluralize math by adding an s? Isn't math the plural of math?

 

[Dembadon]

Why do people around here pluralize math by adding an s? Isn't math the plural of math?

It's a U.K. / Australian thing, I believe. They love adding superfluous letters to words.

 

[StatGuy2000]

Why do people around here pluralize math by adding an s? Isn't math the plural of math?

The people who pluralize math by adding an "s" are applying the British spelling convention (and hence are likely from either the UK or from former British colonies e.g. Australia, New Zealand, South Africa, etc.).

 

[KiwiKid]

Why do people around here pluralize math by adding an s? Isn't math the plural of math?

*shrugs* It appears to be just another way of saying mathemathics

 

[zoobyshoe]

It's a U.K. / Australian thing, I believe. They love adding superfluous letters to words.

I've always assumed they think in terms of each kind of math, arithmetic, algebra, geometry, calculus, etc. being a separate math, and that referring to more than one requires the use of a plural. In other words, these people never evolved to the level of developing the concept of a singular collective noun in the arena of math.

They also say "aluminium", which is a waste of syllables.

 

[DragonPetter]

From my personal experiences, the inaccessibility to math for me has always been notation created by someone else with minimum or no explanation, and assumptions made by teachers or books that either omits critical ideas or information or includes too much unimportant information that hides the concepts. Also, when the information makes leaps from one idea to another, or tries to organize the information that might seem logical from a classification standpoint of someone who already knows the material, but not from a relation based learning perspective, it can really make things more confusing if not impossible since the running dialog in my mind as I'm learning will put up barriers that I don't want to just walk around.

Once I get over what someone else is trying to tell me, and understand it in the way that my brain thinks, I can quickly adapt and understand things and suddenly what seemed so cold and untouchable is very familiar and even easy at times. I have found that real math, involving proofs and facts about relationships, is much more fascinating and interesting than "work math" where you are taught how to do things mechanically with minimum explanation. The real math is almost like learning a story or learning nature, but work math (the kind I was taught almost exclusively) is like learning how to read and spell.

I could go on about textbooks and the way instructors choose to present material, but then I would already get more verbose than I already have been. I think the learn by discovery method has severely crippled math education though; I get severely annoyed when an author leaves an example or proof for the reader to solve alone with no hint or end result to compare to, and portrays great delight at the solution as if to encourage the reader to figure it out.

 

[KiwiKid]

They also say "aluminium", which is a waste of syllables.

Pah, it's not half as bad as all you English-speaking people messing up what should be 'Natrium' and 'Kalium'. I mean, seriously, Na = Sodium? K = Potassium? What kind of irrational being thought that'd be a good idea?

Back on topic: what kind of 'math' are we talking about? Most people would consider arithmetic some form of mathematics, yet the skills required are totally different from those required to do mathematical proofs.

 

[BobG]

Back on topic: what kind of 'math' are we talking about? Most people would consider arithmetic some form of mathematics, yet the skills required are totally different from those required to do mathematical proofs.

You know what they say. Those that can calculate cube roots in their head become engineers, while those that can't add 2 plus 2 become mathematicians.

I guess one can be naturally good at math (or at least with numbers) the same way some people are just naturally good at sprinting. The only real difference is that mental skills are invisible, while you can look at person with certain physical skills and understand why they're better at what they do than anyone else.

 

[KiwiKid]

I guess one can be naturally good at math (or at least with numbers) the same way some people are just naturally good at sprinting. The only real difference is that mental skills are invisible, while you can look at person with certain physical skills and understand why they're better at what they do than anyone else.

I've always thought that IQ tests - while they may not be perfect for testing intelligence per se - may be a good test of this kind of mental power.

 

[AlephZero]

You can be naturally good at math the same way as you can be naturally good at anything else. Just choose your parents very, very carefully

"How can your improve your math ability" is a different question, of course.

 

[Boston_Guy]

I've always thought that IQ tests - while they may not be perfect for testing intelligence per se - may be a good test of this kind of mental power.

I don't hold much value for IQ tests. One has to be very cautious about using them. I am high school they gave us IQ tests but they never told us they were giving tghem to us nor did they tell us the results. My IO tested at 100. A few years later when I was in college I took an IO test which came out to 130. I find it hard to believe that my IQ could change that fast. I probably didn't care about the hs test since they didn't tell us that it affected our grades so I probably didn't do as good as I could have it they'd have told me I was taking it.

 

[KiwiKid]

I don't hold much value for IQ tests. One has to be very cautious about using them. I am high school they gave us IQ tests but they never told us they were giving tghem to us nor did they tell us the results. My IO tested at 100. A few years later when I was in college I took an IO test which came out to 130. I find it hard to believe that my IQ could change that fast. I probably didn't care about the hs test since they didn't tell us that it affected our grades so I probably didn't do as good as I could have it they'd have told me I was taking it.

Were both tests administrated by a qualified psychologist? If so, these results were significant. If not, well, I'm not surprised - there are a lot of bad or incomplete 'IQ' tests. (And, of course, IQ tests don't measure everything, but they're reasonably at measuring mental 'processing power'.)

 

[BobG]

Or, more likely, the test wasn't an IQ test at all, but had some estimated correlation to IQ added on based on the percentile ranking of your results (which would explain why they didn't tell you you were taking an IQ test). If you're in the middle percentile, you probably have an average IQ, if your results were in the top 10% you probably have a higher IQ, if you were in the top 1% an even higher IQ and so on. This is a fairly common thing to do for some tests, while some tests absolutely refuse to correlate their results to IQ (even though they do give you a percentile ranking that someone else could correlate to IQ).

 

[AlephZero]

They also say "aluminium", which is a waste of syllables.

So I guess that's why Americans write and say titanum, magnesum, etc. Not to mention uranum, plutonum ... oops, I forgot, you just say "nucular". But even that has more syllables than "nuclear"

 

[Boston_Guy]

Were both tests administrated by a qualified psychologist? If so, these results were significant. If not, well, I'm not surprised - there are a lot of bad or incomplete 'IQ' tests. (And, of course, IQ tests don't measure everything, but they're reasonably at measuring mental 'processing power'.)

I never even knew I took a test. A few years after I graduated I looked at my record and it stated my IQ. Maybe I misunderstood.

 

[Boston_Guy]

Or, more likely, the test wasn't an IQ test at all, but had some estimated correlation to IQ added on based on the percentile ranking of your results (which would explain why they didn't tell you you were taking an IQ test). If you're in the middle percentile, you probably have an average IQ, if your results were in the top 10% you probably have a higher IQ, if you were in the top 1% an even higher IQ and so on. This is a fairly common thing to do for some tests, while some tests absolutely refuse to correlate their results to IQ (even though they do give you a percentile ranking that someone else could correlate to IQ).

Thank you so much for your reply. I never considered that. Thanks for sharing that with me. I never would have found that out otherwise.

 

[BobG]

So I guess that's why Americans write and say titanum, magnesum, etc. Not to mention uranum, plutonum ... oops, I forgot, you just say "nucular". But even that has more syllables than "nuclear"

It's not 'i' that bothers me, it's 'u'.

Which explains why Americans delete so many extraneous 'u's ... and why we say "yo".

 

[zoobyshoe]

So I guess that's why Americans write and say titanum, magnesum, etc. Not to mention uranum, plutonum ... oops, I forgot, you just say "nucular". But even that has more syllables than "nuclear"

You had a point until you got to nucular/nuclear. They both have three syllables.

 

[AlephZero]

You had a point until you got to nucular/nuclear. They both have three syllables.

Not in British English. "Clear" is only one syllable.

I was looking for other words to compare the pronunciation, but in the 150,000 word list I searched, the only words ending in -clear were "nuclear" plus assorted prefixes, and "unclear". Not a big sample, but "unclear" is also 2 syllables in British English.

Actually I can see the logic behind three syllables for nuclear as a derivative of nucleus, but that's not how Brits pronounce it.

 

[zoobyshoe]

Not in British English. "Clear" is only one syllable.

I was looking for other words to compare the pronunciation, but in the 150,000 word list I searched, the only words ending in -clear were "nuclear" plus assorted prefixes, and "unclear". Not a big sample, but "unclear" is also 2 syllables in British English.

Actually I can see the logic behind three syllables for nuclear as a derivative of nucleus, but that's not how Brits pronounce it.

nu·cle·ar/ˈn(y)o͞oklēər/
Adjective:
Of or relating to the nucleus of an atom.
Denoting, relating to, or powered by the energy released in nuclear fission or fusion.

If you can find a dedicated British dictionary online I'd be interested in seeing it broken into two syllables.

As for unclear, it's two syllables for us as well:

un·clear/ˌənˈkli(ə)r/
Adjective:
Not easy to see, hear, or understand: "the motive for this killing is unclear".
Not obvious or definite; ambiguous.

 

[genericusrnme]

All this talk of Americans spelling things badly reminds me of this;

 

[sophiecentaur]

It HAS to be "Nuclear" because it relates to the Nucle-us. This follows the general rule as in Solar, radial, insular, mandibular. . . . .
"Nucular" must have developed because some hot shot US general misheard it, then mispronounced it and no one dared to contradict him, subsequently.

But the US is such a long way from the centres of culture and learning. You can't really blame them for getting so much of it wrong.

I notice that my spell checker has underlined the word 'centre' too. There really is no hope left for the language. Yet they still call it "English", over there.

 

[leroyjenkens]

"Nucular" must have developed because some hot shot US general misheard it, then mispronounced it and no one dared to contradict him, subsequently.

I've heard that "Nucular" came about due to the way the ending part "ular" is more common in English than the "lear" ending. The same way the first R in the "ruary" part of February is omitted due to that sequence of letters being uncommon in English, therefore harder to pronounce. I suppose if we had more words with that sequence of letters, we wouldn't omit that first R. But getting back to "nuclear", I find it easier to pronounce than "nucular", so who knows.

And here's something completely off topic, but kinda on topic. I like to practice my diction and enunciation so that I speak properly and clearly, and that may be why it really bugs me that it's hard for me to say "particularly" quickly and clearly without it feeling like my tongue is tripping over the R's and L's.
I also have trouble transitioning from one word to the next in certain sequences of words, such as in this sentence "is this the thing?" I can't really say it quickly while pronouncing the "th" sound clearly and separately from the "s" sound.

Anyone else have these problems?

 

[sophiecentaur]

Thing is, there is no u between the c and the l in nucleus / nuicleon etc. so 'nucular' is mangling the spelling up and not just changing the ending to make it an adjective. I always reckon that saying nucular makes one sound like George W. That's enough to make me behave properly! But it's all down to useage, really. 'Foreigners' can't help it, bless em.

People can't even pronounce the word 'boson' right. Poor old SN Bose (pronounced buttons and "BOWS") is over shadowed enough by Einstein, the least we can do is pronounce correctly the particle description which uses his name. He wasn't a boatswain, in any case.

I also find it hard to say some words quickly. The secret is to have the confidence that, when you choose to say something, it is worth taking your time and getting it right. People will wait for the good stuff to emerge. We nearly always tend to speak faster than professional speakers. The really fast speaking celebs are an exception and have a knack of being listened to.

 

[zoobyshoe]

It HAS to be "Nuclear" because it relates to the Nucle-us. This follows the general rule as in Solar, radial, insular, mandibular. . . . .
"Nucular" must have developed because some hot shot US general misheard it, then mispronounced it and no one dared to contradict him, subsequently.

No one is arguing it's "nucular". The question is whether Brits actually pronounce "nuclear" as two syllables or three.

If you can find a dedicated British dictionary online I'd be interested in seeing if it's broken into two syllables.

But the US is such a long way from the centres of culture and learning. You can't really blame them for getting so much of it wrong.

The British are such a long way from where nuclear physics was actually developed you can't blame them for trying to make culture the issue.

I notice that my spell checker has underlined the word 'centre' too. There really is no hope left for the language. Yet they still call it "English", over there.

If you hadn't bequeathed us such an un-spellable language there would be no need for spell check.

 

[genericusrnme]

No one is arguing it's "nucular". The question is whether Brits actually pronounce "nuclear" as two syllables or three.

If you can find a dedicated British dictionary online I'd be interested in seeing if it's broken into two syllables.

It's nu-clear, two syllables.

The British are such a long way from where nuclear physics was actually developed you can't blame them for trying to make culture the issue.

Thomson, Chadwick and Rutherford totally weren't british ;)

 

[KiwiKid]

And here I was thinking this thread was about natural math skills. Silly me.

 

[zoobyshoe]

It's nu-clear, two syllables.

I'd like to see a link, or even a scan of a dedicated British dictionary.

Thomson, Chadwick and Rutherford totally weren't british ;)

Read the section Collaboration with the United Kingdom

http://en.wikipedia.org/wiki/Manhattan_Project

The USA was the hopping place to be. It took the British a while to face that.

 

[zoobyshoe]

And here I was thinking this thread was about natural math skills. Silly me.

Study: Math Skills Rely on Language, Not Just Logic

“Langauge input is important for everybody’s representation of number, and how counting works,” Spaepen said. “This isn’t something you just get for free because you’re human. It depends on the quality and amount of input you get. If you’re not getting it in your language, you’re not going to just come up with it on your own.”

http://www.wired.com/wiredscience/2011/02/homesigning-numbers/

 

[sophiecentaur]

If you hadn't bequeathed us such an un-spellable language there would be no need for spell check.

You can just make up the words up as you go along, I suppoze. (Well - why not a Z?)

You will find that the last bastion of properly used English is probably in India, actually.

 

[zoobyshoe]

You will find that the last bastion of properly used English is probably in India, actually.

One of my favorite writers of English at PF is Gokul90210, who has origins in the Indian Subcontinent, yes.

 

[KiwiKid]

http://www.wired.com/wiredscience/2011/02/homesigning-numbers/

Nice save.

 

[zoobyshoe]

Nice save.

With google you can connect anything with anything.

 

[AnTiFreeze3]

It's nu-clear, two syllables.

I've done your work for you, in order to back up your empty claim.

http://dictionary.cambridge.org/dictionary/british/nuclear_1?q=nuclear. Click on the pronunciations in both American-English and British-English to see the difference.

 

[zoobyshoe]

I've done your work for you, in order to back up your empty claim.

http://dictionary.cambridge.org/dictionary/british/nuclear_1?q=nuclear. Click on the pronunciations in both American-English and British-English to see the difference.

I'm hearing "NEW clee ah" and not "NEW cleer".

 

[AnTiFreeze3]

I'm hearing "NEW clee ah" and not "NEW cleer".

My thoughts as well. They definitely don't just combine the words "new" and "clear" together, it just appears that, in the United States, we emphasize the end of the word more so than the British.

 

[20Tauri]

Well, putting aside the question of whether math is something we invented or discovered, it is possible to have a natural aptitude for something artificial. Painting, for example, is not a "natural" activity, but some people are better at painting than others. Of course, there's also the consideration that in any activity, a lot of what gets praised as talent is actually the result of lots and lots of practice.

 

[chiro]

Absolutely agree about the practice part, but I don't know if painting should be classed as un-natural.

Creativity and expression are pretty natural things IMO of which painting is a mere tiny-subset. Also you should think about things like savants who seem to have a very narrow focus towards forms of expression including painting and music (often the savants are autistic savants or the term (which I don't like one bit) 'idiot' savants).

 

[zoobyshoe]

Well, putting aside the question of whether math is something we invented or discovered, it is possible to have a natural aptitude for something artificial. Painting, for example, is not a "natural" activity, but some people are better at painting than others. Of course, there's also the consideration that in any activity, a lot of what gets praised as talent is actually the result of lots and lots of practice.

I think painting probably is natural. Primitive cultures have always painted as far as we know, though, as with math, the more primitive the culture the less sophisticated the painting. The cave paintings at Lascaux are estimated to be 17,300 years old and they're top notch as primitive art goes. I bet people were drawing with charcoal as soon as we harnessed fire. It probably started out as doodling, exploring the fact you could make marks with the charcoal on a rock or tree. (Kids today make marks everywhere as soon as they realize it can be done.) Little by little the marks became more deliberate and controlled. The next generation copied the more controlled marks and developed more control themselves, and so on, and eventually you had Michelangelo.

 

[20Tauri]

I think painting probably is natural. Primitive cultures have always painted as far as we know, though, as with math, the more primitive the culture the less sophisticated the painting. The cave paintings at Lascaux are estimated to be 17,300 years old and they're top notch as primitive art goes. I bet people were drawing with charcoal as soon as we harnessed fire. It probably started out as doodling, exploring the fact you could make marks with the charcoal on a rock or tree. (Kids today make marks everywhere as soon as they realize it can be done.) Little by little the marks became more deliberate and controlled. The next generation copied the more controlled marks and developed more control themselves, and so on, and eventually you had Michelangelo.

You could make the same argument that math is fundamentally natural because undoubtedly people figured out how to count fairly early in the history of civilization, then they learned arithmetic, etc. But if you don't think painting is an artificial pursuit, then we could talk about playing the piano (certainly someone had to invent such an instrument, whether or not the musical drive is natural) or building model airplanes or driving stick shift or any number of things. I just picked painting as an off-hand example.

 

[zoobyshoe]

You could make the same argument that math is fundamentally natural because undoubtedly people figured out how to count fairly early in the history of civilization, then they learned arithmetic, etc. But if you don't think painting is an artificial pursuit, then we could talk about playing the piano (certainly someone had to invent such an instrument, whether or not the musical drive is natural) or building model airplanes or driving stick shift or any number of things. I just picked painting as an off-hand example.

Now that you mention it, everything people do has to be based on some core activity which is natural. What seems unnatural, artificial, is how far we take it compared to other animals. Euclid, for instance, collected all the then known knowledge of geometry, wrote it down and began to teach it. Compared to animals that seems like an extremely artificial thing to do. But calling it "artificial" really only means we don't observe other animals doing it.

The core activity of collecting information that no one individual alone would have figured out, and passing it on, must actually be quite natural for humans. Adding to it and developing it over generations must also be perfectly natural for humans: we see it happening all over the world in the history of all peoples.