Understanding mathematics

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ruveyn
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23 Jun 2009, 3:02 am

pandabear wrote:

A lot of the article reminds me of Sheldon Cooper :lol:

He is the Super Nerd! My hero! Before I learned to adapt thoroughly to the NT world, I was Sheldon Cooper.

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23 Jun 2009, 9:25 pm

Sand wrote:

Applied mathematics is a separate field...

Exactly!

What Lockhart seems to be lamenting is the lack of any teaching of pure mathematcits. According to Wikipedia, this isn't a new concept

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Orwell
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23 Jun 2009, 9:49 pm

NobelCynic wrote:

Sand wrote:

Applied mathematics is a separate field...

Exactly!

What Lockhart seems to be lamenting is the lack of any teaching of pure mathematcits. According to Wikipedia, this isn't a new concept

Even what we do teach of "applied mathematics" in the public schools is crap. People aren't taught the uses of algebra, geometry, or calculus. All the examples given are painfully contrived.

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Sand
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23 Jun 2009, 10:31 pm

Orwell wrote:

NobelCynic wrote:

Sand wrote:

Applied mathematics is a separate field...

Exactly!

What Lockhart seems to be lamenting is the lack of any teaching of pure mathematcits. According to Wikipedia, this isn't a new concept

Even what we do teach of "applied mathematics" in the public schools is crap. People aren't taught the uses of algebra, geometry, or calculus. All the examples given are painfully contrived.

Although it might make teaching applied math more difficult as a concept it seems to me that applied math should be handled as an adjunct to teaching something else such as problems in physics or biology or economics or finance or architecture where the need to solve real problems re-enforces its usefulness.

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23 Jun 2009, 10:41 pm

Sand wrote:

That is where people (at least, non-math geeks) seem to learn and remember math- where they are forced to learn it as a means to an end. Biologists would likely lapse into a coma if you tried to put them through an intensive statistics course, but they're able to do their chi-squared tests just fine whenever you bring up genetics.

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23 Jun 2009, 11:19 pm

Orwell wrote:

Sand wrote:

As indicated by the author in the article one of the intellectual barriers for some minds is the abstract notation which divorces problems from contact with the reality of other types of sense input. It is a commonplace that some minds enjoy the freedom and flexibility of abstract notation which frequently reveals startling relationships of previously unperceived areas but other minds (like my own and, I have heard, Einstein's), are happier with geometric visualizations of concepts where images are involved. It seems possible that even topological problems such as the colored map classic could be made interesting to kindergartners with pieces of colored paper and only later in their development could these be made abstract for further exploration and manipulation.

Last edited by Sand on 24 Jun 2009, 7:13 am, edited 1 time in total.

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24 Jun 2009, 6:46 am

I was passionate about maths till the age of 12. I reluctantly carried on studying it till the age of 21.

I know that as a teenager my interest would have been rekindled if only someone at the time had told me about ... The Hairy Ball Theorem!!

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

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24 Jun 2009, 1:54 pm

skysaw wrote:

I love it!

One of the things I hate most is when I show someone one of my mathematical ideas (generally about Pythagorean ratios or exponentiation), and they say, "So what's the practical application of this?"

Kill. With fire.

Can't they just appreciate the beautiful patterns that seem to exist for no other reason than but to be?

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ruveyn
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24 Jun 2009, 2:57 pm

skysaw wrote:

I was a teaching assistant University of California, Berkeley Campus in 1959. I taught this theorem to a class of freshmen who were not going on to study mathematics any further. I taught this theorem and the proof that the general angle could not be trisected using ruler of compass. If this was to be their last dalliance with mathematics, we made it a good one.

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24 Jun 2009, 9:34 pm

MrLoony wrote:

skysaw wrote:

There is no such thing as beauty in nature . All biological and natural forms and inter-relationships of patterns exist as a function of time and space and the necessities of survival. You cannot require everybody to understand or appreciate this as each of us exists as a dynamic interaction of experience and capability. I do not appreciate baseball or playing cards or surfing or the concerns with ancestry. They are irrelevant to my life. There are enough people in the world with common interests to sustain each of these preoccupations without everybody being absorbed by the same interests. We each miss many things in life because life has more to offer than each of us can contain.

ruveyn
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25 Jun 2009, 3:01 am

MrLoony wrote:

skysaw wrote:

G.H.Hardy the world famous British mathematician used to say the following toast: To pure mathematics, may it never be of use to anyone.

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25 Jun 2009, 3:01 pm

Interesting article. A lot of high school maths is put into a cook book so to speak. There's not a lot of thinking that goes on if it's all reduced to a set of recipes.

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25 Jun 2009, 3:45 pm

ruveyn wrote:

G.H.Hardy the world famous British mathematician used to say the following toast: To pure mathematics, may it never be of use to anyone.

That could support the argument that mathematics is an art form considering Oscar Wilde's quote "All art is quite useless."

Speaking of G.H.Hardy, I just started reading his essay A Mathematician's Apology which I think makes a simular argument.

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25 Jun 2009, 3:48 pm

Sand wrote:

You cannot require everybody to understand or appreciate this as each of us exists as a dynamic interaction of experience and capability. I do not appreciate baseball or playing cards or surfing or the concerns with ancestry. They are irrelevant to my life. There are enough people in the world with common interests to sustain each of these preoccupations without everybody being absorbed by the same interests. We each miss many things in life because life has more to offer than each of us can contain.

But you accept and appreciate the fact that other people find them interesting for reasons beyond practical applications, do you not?

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25 Jun 2009, 6:05 pm

MrLoony wrote:

Sand wrote:

But you accept and appreciate the fact that other people find them interesting for reasons beyond practical applications, do you not?

Mathematics is fascinating because the abstract inter-relationships have firm laws which create universes both applicable to our own universe and applicable to theoretical universes not our own. It is a way of exploring basic creation itself and no doubt is interesting whether or not it is practical. Nevertheless many assumed impractical mathematical explorations have unexpectedly found practical application.

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26 Jun 2009, 5:27 am

ruveyn wrote:

G.H.Hardy the world famous British mathematician used to say the following toast: To pure mathematics, may it never be of use to anyone.

ruveyn

Although I've forgotten almost everything I learnt about maths, I can appreciate Hardy's sentiments. As it turned out, Hardy's speciality - number theory (the purest of the pure! perhaps) - turned out to be very useful in the world of cryptography.

Ruveyn, you mentioned that you worked as a teaching assistant. Did you then go on to get a full-time university position?

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