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A Mathematician’s Lament (2002) [pdf]

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Re: A Mathematician’s Lament (2002) [pdf]

#111

Post by saraid216 »

dwc wrote: post #105
john_b wrote: post #40

Earlier quoted context omitted.

I think that language (at least English) fails us here. The word "creative" can be used to mean both "relating to or involving the imagination or original ideas, especially in the production of an artistic work" [1] or "resulting from originality of thought, expression, etc.; imaginative" [2]. It seems that most people identify the word more strongly with the artistic sense of the word, in which creativity is a proxy…

> creativity is a proxy for a kind of self-expression that is not bound by any rules, logic, or structure I do not find this to be the case. Art is full of structure, rules and logic. When artists "break" the rules, it usually means they been able to operate using underlying rules, and understand well the rules they break.

Or they're creating new rules.

Re: A Mathematician’s Lament (2002) [pdf]

#112

Post by stiff »

NoodleIncident wrote: post #103
stiff wrote: post #37

Please read the article with a critical eye, some of it is complete non-sense, for example: CALCULUS: This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-ba…

All of this misses the author's point. How many students make it through calculus without learning that it is the mathematics of motion at all? I'd wager that it's more than half.

Almost any calculus course goes over accelaration being the derivative of speed and so forth. It doesn't make students suddenly understand calculus.

Re: A Mathematician’s Lament (2002) [pdf]

#113

Post by stiff »

kalid wrote: post #102
stiff wrote: post #37

Please read the article with a critical eye, some of it is complete non-sense, for example: CALCULUS: This course will explore the mathematics of motion, and the best ways to bury it under a mountain of unnecessary formalism. Despite being an introduction to both the differential and integral calculus, the simple and profound ideas of Newton and Leibniz will be discarded in favor of the more sophisticated function-ba…

Hi, I hope you take my comment well. This need to avoid some theoretical logical contradiction far down the road is similar to explaining the perils of split infinitives before teaching a child to say "I want food." 99.9% of calculus students are there to expand their mind. They will never design a quantum mechanical reactor and think "Wow, I'm getting all these weird results, my calculus education must have held me…

The author is criticizing calculus courses. The level of formalism in calculus courses is relatively low, and none of it has anything to do with quantum mechanics or contradictions far down. It is only enough formalism to give a definition of derivative and integral that actually makes sense, that's all.

Re: A Mathematician’s Lament (2002) [pdf]

#115

Post by dominotw »

Attempts to present mathematics as relevant to daily life inevitably appear forced and contrived: “You see kids, if you know algebra then you can figure out how old Maria is if we know thatshe istwo years older than twice her age seven years ago!” (Asif anyone would ever have access to that ridiculous kind of information, and not her age.)

I wince every time I see these examples in my niece's textbook. So ridiculous.

Re: A Mathematician’s Lament (2002) [pdf]

#116

Post by dwc »

saraid216 wrote: post #111
dwc wrote: post #105

Earlier quoted context omitted.

> creativity is a proxy for a kind of self-expression that is not bound by any rules, logic, or structure I do not find this to be the case. Art is full of structure, rules and logic. When artists "break" the rules, it usually means they been able to operate using underlying rules, and understand well the rules they break.

Or they're creating new rules.

Yes, indeed. For instance, the creation of bebop in jazz. Of course Bird could only do this by a comprehensive understanding of the existing rules and seeing deeper.

Re: A Mathematician’s Lament (2002) [pdf]

#117

Post by giardini »

stiff wrote: post #89
giardini wrote: post #84

Earlier quoted context omitted.

"... earlier and more general lack of any decent understanding of how calculus works at all that was solved by Cauchy, Weierstrass and others. It is their introduction of what the author considers "unnecessary formalism" that made us finally really understand "mathematics of motion" ..." I don't think so. 99.99% of the mathematics of motion consists of continuous functions with continuous derivatives of all orders. I…

99.99% of the mathematics of motion consists of continuous functions with continuous derivatives of all orders. Infinitesimals are just fine for that. There were logical contradictions even in Newtons and Leibniz works, far before anyone considered continuous functions without derivatives etc., they were basically making decisions about when a given operation or transformation can be applied based on intuition alone…

I took courses in graduate level QM and Newton-style calculus sufficed. The only unusual artifact that stands out in my memory was the Dirac delta function.

Perhaps physicists (e.g., your example of Newton above) somehow intuitively step over the "holes" in the underlying analytical frameworks that mathematicians fall into with regularly. Mathematicians are wont to build "manholes" to cover those holes and physicists have no desire to stop them, seeing that it is honest labour and keeps the mathematicians busy.

Re: A Mathematician’s Lament (2002) [pdf]

#118

Post by kazagistar »

For music, the formal curriculum does involve memorizing songs and scales and whatnot. The problem is that the best way to start a subject is to fuck around with it (playing random songs you like on your guitar, drawing cool shapes and noticing patterns in them, etc), but our schools are ill equipped for such things, and enabling this style is difficult and incredibly expensive.

Re: A Mathematician’s Lament (2002) [pdf]

#119

Post by kazagistar »

A classic issue that mathematicians, philosophers, and even computer "scientists" have is the idea that they can somehow reason their way to the truth. Oh, he makes a good argument. But the greeks made great arguments about how the sun goes around the earth.

I could say that this or that argument is flawed. But really, the only valid arguments are data. His data is severely lacking, and many modern methods of teaching are much more supported by experimentation. Logic is a tool for finding logically consistent imaginary realities. Science is a tool for finding out about this reality.

Re: A Mathematician’s Lament (2002) [pdf]

#120

Post by mathattack »

ef4 wrote: post #46
mathattack wrote: post #13

I hated math until I got to calculus. I never knew why, but I might as well quite this mathematician... They took an exciting topic that interested me as a youth and killed it with rote repetition. The question I struggle with is... How do you really get by without math as a mandatory topic? How can you teach science? How can you teach someone to balance a checkbook? The current system is awful, but do we push the su…

> The question I struggle with is... How do you really get by without math as a mandatory topic? That's the wrong question, because "mandatory learning" is a contradiction in terms. It very clearly doesn't work. Beyond the most primitive pavlovian conditioning, you can't force people to learn if they don't want to. Intrinsic motivation is the dominating factor in how well a person can master an intellectually demandi…

True enough. And that's a tough question too. I waited from 4th grade to calculus to get inspired again. And then I think it was the material more than the teaching method.
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