A Mathematician's Lament

[*T*]

A Mathematician's Lament

...if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-
crushing ideas that constitute contemporary mathematics education. Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.


Mathematics and Culture

The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?

[Diarmuid]

Re: A Mathematician's Lament

A Mathematician's Lament

Math as the greeks understood it had four seperate components but all of the one subject.

Arithmetic - the study of the nature of number

Geometry - the study of number in space

Music - the study of number in time

Astronomy - the study of number in space and time

When studied in this form rather then from just the straight jacket of thereoms, axioms, formuli and algebric equation, maths' beauty and artistry becomes self evident to hear and see imho.

[swgprop]

Re: A Mathematician's Lament

Lockhart's passionate essay somehow reminded me of Zander's delightful presentation at TED:

http://www.ted.com/talks/benjamin_za...d_passion.html

[ThePythonicCow]

Re: A Mathematician's Lament

When studied in this form rather then from just the straight jacket of thereoms, axioms, formuli and algebric equation, maths' beauty and artistry becomes self evident to hear and see imho.

I beg to differ. The beauty of mathematics is in the form of its theorems, axioms and formuli.

You see, that beauty serves an essential purpose. It allows more to be understood. That which is beautiful is that which fits easily within the narrow limitations and varied capacities of the human mind. The best mathematics distills what seemed like a mountain of confusing detail into a few elegant constructs. Having done so, those constructs fit well enough within the momentary grasp of a mathematicians mind that he has some energy and capacity remaining, to build further.

[Diarmuid]

Re: A Mathematician's Lament

Lockhart's passionate essay somehow reminded me of Zander's delightful presentation at TED:

http://www.ted.com/talks/benjamin_za...d_passion.html

Thank you for posting link - really wonderful stuff

[jimmygu3]

Re: A Mathematician's Lament

I beg to differ. The beauty of mathematics is in the form of its theorems, axioms and formuli.

You see, that beauty serves an essential purpose. It allows more to be understood. That which is beautiful is that which fits easily within the narrow limitations and varied capacities of the human mind. The best mathematics distills what seemed like a mountain of confusing detail into a few elegant constructs. Having done so, those constructs fit well enough within the momentary grasp of a mathematicians mind that he has some energy and capacity remaining, to build further.

True, theorems et al crystallize the beauty of mathematics, but a student sees no beauty without first understanding the premises, variables and relationships contained in said formulae. With other types of art, like music, painting, and culinary arts, the finest works can be appreciated on some level by even the most ignorant observers. Math requires you to be in the club before you can see the elegance of its many wonders.

Maybe there is a way to turn kids on to the beauty of math, at least in a small way, before they decide it's just frustrating, confusing and nerdy.

Jimmy

[ThePythonicCow]

Re: A Mathematician's Lament

Maybe there is a way to turn kids on to the beauty of math, at least in a small way, before they decide it's just frustrating, confusing and nerdy.

It depends too much on the inherent talents and energies of the person.

No one made Chittoor Ramamoorthy a mathematician, or Wolfgang Amadeus Mozart a musician.

The endsheets in my middle school english books were filled at the end of each year with equations and solutions, as I entertained myself with inventing and solving problems during the rather boring English class. I was too poor to provide my own paper.

Our talents are many and innate. What makes a rose a rose, and an oak an oak, is inherent in the unplanted nut or seed.

Parents and family and community and schools have a critical role, to provide the soil, the water, the tending, pruning, weeding and nourishment needed to allow a plant to grow. Some hearty plants will grow in damn near any soil. Some are more delicate.

But you can't make an apple seed grow a rose bush, no matter how hard you try.

[marvenger]

Re: A Mathematician's Lament

education is to prepare kids for the working world, and the working world is boring with little beauty, thats the problem. i did an actuarial degree and worked in insurance for a while, hated it.

[Diarmuid]

Re: A Mathematician's Lament

I beg to differ. The beauty of mathematics is in the form of its theorems, axioms and formuli.

You see, that beauty serves an essential purpose. It allows more to be understood. That which is beautiful is that which fits easily within the narrow limitations and varied capacities of the human mind. The best mathematics distills what seemed like a mountain of confusing detail into a few elegant constructs. Having done so, those constructs fit well enough within the momentary grasp of a mathematicians mind that he has some energy and capacity remaining, to build further.

Hi mate

I can agree that theorems, axioms and formuli can and do have an inate beauty in them but I do not believe it encapsulates or in of themselves give rise to the beauty of Math, although, they can and are used to reveal the subjects underlying beauty but not exclusively.
For example Euclids Elements is a work of art imo, however when Math is constrained or straight jacketed by the axioms and postulates it can and does stagnate, it took well over 2000 years to break from Euclidean geometry because of the strict adherence, belief and faith in these axioms and posulates, hyperbolic geometry, spherical geometry, tensors, relativity etc.. only came about because the authors of which, broke from the ridgid structure of axiomatic and postulate based academia. All things in moderation, when one neccessity is given precedence or taken in large quantities to the exclusion or reduction of others, that necessity may become itself posionous.

That being said, I personally find much wisdom in many of your post, so I just wish to express my thank for them.

Peace

[ThePythonicCow]

Re: A Mathematician's Lament

For example Euclids Elements is a work of art imo, however when Math is constrained or straight jacketed by the axioms and postulates it can and does stagnate ...

The axiomatic expression of mathematics (and occassionally philosophy - cf Spinoza) is but a tool, as rivets and welding torches are tools of the building trade. Proper training in use of the tools enables more reliable and predictable results than from the untrained, but invariably frustrates many a student, and emboldens many a pedestrian teacher with claims to authority of which they might not be worth.

Always sufficiently inspired minds, having learned to use the tools for what they are worth, then proceed to invent new constructs and new tools for their construction, going past the limitations of the previous means. That is the way of growth in human understanding.

That being said, I personally find much wisdom in many of your post, so I just wish to express my thank for them.

Thank-you for such kind words.

[ThePythonicCow]

Re: A Mathematician's Lament

the working world is boring with little beauty ...hated it.

Sad. My sympathies. Some of us are fortunate to have found means of employment that we quite enjoy.

[marvenger]

Re: A Mathematician's Lament

yep but i think they are few and far between. you've done extremely well if you're one of the lucky few. i think how we all make a living is inherently corrupt and if we can figure out how to get around that, that would be a harmonious and beautiful world.

[cjppjc]

Re: A Mathematician's Lament

yep but i think they are few and far between. you've done extremely well if you're one of the lucky few. i think how we all make a living is inherently corrupt and if we can figure out how to get around that, that would be a harmonious and beautiful world.

Marvenger:

Read this and think what he is saying. I know you try things.

Why Organize a Universe this Way?
What does not exist looks so handsome.
What does exist, where is it?
An ocean is hidden. All we see is foam,
shapes of dust, spinning, tall as minarets, but I want wind.
Dust can't rise up without wind, I know, but can't I understand this
by some other way than induction?

Invisible ocean, wind. Visible foam and dust: this is speech.
Why can't we hear thought?
These eyes were born asleep.
Why organize a universe this way?

With the merchant close by a magician measures out
five hundred ells of linen moonlight.
It takes all his money, but the merchant buys the lot.
Suddenly there's no linen, and of course there's no money,
which was his life spent wrongly, and yours.
Say, Save me, Thou One, from witches who tie knots
and blow on them. They're tying them again.
Prayers are not enough. You must do something.

Three companions for you: number one,
what you own. He won't even leave the house
for some danger you might be in. He stays inside.
Number two, your good friend. He at least comes to the funeral.
He stands and talks at the gravesite. No further.

The third companion, what you do, your work,
goes down into death to be there with you,
to help. Take deep refuge
with that companion, beforehand.

[marvenger]

Re: A Mathematician's Lament

Hear what he/she is saying and think there's a lot truth to it. However, what I'm saying is that if people really did focus on their work, or let’s just call it daily actions, in this transcendental way then we would be focused on our similarities; our differences would be like the surface foam of the sea: interesting, amusing, with its own beauty; and wholly inappropriate, when compared to the vast common depths of the ocean, to justify some with wealth in the billions while 900 million people suffer malnourishment in a world of abundance. fficeffice" />

I’m actually fairly happy, have managed to lose a lot of my anger, probably appear more messed up than I am. J

[cjppjc]

Re: A Mathematician's Lament

Hear what he/she is saying and think there's a lot truth to it. However, what I'm saying is that if people really did focus on their work, or let’s just call it daily actions, in this transcendental way then we would be focused on our similarities; our differences would be like the surface foam of the sea: interesting, amusing, with its own beauty; and wholly inappropriate, when compared to the vast common depths of the ocean, to justify some with wealth in the billions while 900 million people suffer malnourishment in a world of abundance. fficeffice" />

I’m actually fairly happy, have managed to lose a lot of my anger, probably appear more messed up than I am. J

Marvenger:
You bleed to much. You can only be responsible for your own actions, and your own efforts. By focusing your attention on yourself you can help to create conditions which do benefit others as well. Maybe not in the large way that you wish.

I am glad to hear you have been able to lose some of your anger. It is a useless emotion.