How can one be naturally good at maths?

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Discussion Overview

The discussion revolves around the question of whether individuals can be naturally good at mathematics, exploring the nature of mathematical understanding, the role of practice, and the phenomenon of prodigies. It touches on theoretical and conceptual aspects of mathematics as a language and tool for understanding, as well as personal experiences with learning and mastering math.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants argue that mathematics is a human-made tool for understanding nature, questioning how one can be naturally good at it.
  • Others propose that like any language, mathematics requires a deep understanding beyond symbols and formalism, emphasizing the importance of intuition and meaningful connections.
  • One participant suggests that abstraction is crucial for success in mathematics, highlighting the need to generalize from concrete examples.
  • Another viewpoint states that no one is inherently good at math, using the metaphor of "the one-eyed man in the land of the blind" to illustrate relative skill levels.
  • A participant shares a personal narrative about initially struggling with math in high school but later excelling in college, suggesting that life experiences can influence mathematical understanding and appreciation.
  • There is mention of prodigies in mathematics and other fields, raising questions about the nature of innate talent versus learned skill.

Areas of Agreement / Disagreement

Participants express a range of views on the nature of mathematical ability, with no consensus on whether natural talent exists or how it relates to practice and understanding. The discussion remains unresolved regarding the existence of innate mathematical ability versus the necessity of study and practice.

Contextual Notes

Some claims about the nature of mathematics and learning processes depend on individual experiences and interpretations, which may not be universally applicable. The discussion also reflects varying definitions of what it means to be "good" at mathematics.

  • #31
sophiecentaur said:
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. :biggrin:
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.
 
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  • #32
zoobyshoe said:
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 ;)
 
  • #33
And here I was thinking this thread was about natural math skills. Silly me.
 
  • #34
genericusrnme said:
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.
 
  • #35
KiwiKid said:
And here I was thinking this thread was about natural math skills. Silly me.

Study: Math Skills Rely on Language, Not Just Logic

“language 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/
 
  • #36
zoobyshoe said:
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.
 
  • #37
sophiecentaur said:
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.
 
  • #39
KiwiKid said:
Nice save. :wink:
With google you can connect anything with anything.
 
  • #41
  • #42
zoobyshoe said:
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.
 
  • #43
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.
 
  • #44
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).
 
  • #45
20Tauri said:
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.
 
  • #46
zoobyshoe said:
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.
 
  • #47
20Tauri said:
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.
 

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