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A Mathematician’s Lament (2002) [pdf]

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

#41

Post by stiff »

vlasev wrote: post #39
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…

The point he's making is against unnecessary rigorization of introductory calculus and I think you are getting a bit too hung up on the "function-based approach". I repeat - introductory calculus. There's lot of time and space to make things more rigorous in a class like Analysis. When I help students with calculus most of them have no trouble with the ideas but the implementation that they are required to perform. I…

Introductory calculus classes are hardly ever rigorous. The only formalism you see is functions and limits, and that's a very useful one, far from unnecessary, it might just not always be motivated appropriately by poor teachers who themselves have little understanding of its usefulness. Your interpretation is also very far from what he has actually written. I edited my parent comment to make what I mean more clear.

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

#42

Post by ColinWright »

gizmo686 wrote: post #33
rtfeldman wrote: post #32

This is intensely thought-provoking and beautifully well-written. It's not directly about hacking, but it's the type of treasure that hackers love to stumble upon. It's worth noting the times when HN really delivers. I doubt I'd have come across this anywhere else.

>It's worth noting the times when HN really delivers. I doubt I'd have come across this anywhere else. At risk of getting to meta, this piece seems to pop up everywhere. I don't mean that in a bad way, but this is at least the fifth time over the course of many years that I have seen this piece pop up on completely unrelated sites.

Not to mention it's been here on HN at least 8 times, probably 10 or more. I've stopped bothering to direct people to previous conversations - they just say the same things over and over again anyway.

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

#44

Post by hcarvalhoalves »

Reflects my experience. During school I had interest and good grades in all classes, including physics and geometry (those are separate from math in Brazil), the only exception being math (which covers algebra, polynomials, etc.). How a kid can get an A in physics and a D in math is beyond my comprehension, but I did. I only started appreciating math much later in life.

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

#45

Post by gizmo686 »

During high school, at the end of the year everyone in my Calculus class had to make a math presentation (to go along with a paper). During lunch one day we stood with our posters to explain our project the the students that choice/were encouraged to attend. I explained my topic (re-ordering conditionally convergent series) to a group of students. They seemed to understand what I was saying, showed awe at some of the key insights/tricks, and even interupted me to excitadly finish the arguement. Then, when I was done, they pointed to the equations and asked me to explain them. My response was that those equations are exactly what I had just said, and I repeated the arguement while showing them where it is in the equations.

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

#46

Post by ef4 »

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 demanding task.

The right question is, how do you inspire people to want to learn?

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

#47

Post by coldtea »

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…

>"Mathematics of motion", which makes it sound so simple, has in fact perplexed philosophers and mathematicians for centuries and continues to perplex a great many people even today, consider for example the Zeno paradox (...) The ideas of Newton and Leibniz were hardly simple

All of which is besides the point (he makes), that they are simpler than the current formalism.

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

#48

Post by dnautics »

saraid216 wrote: post #25
dnautics wrote: post #20

As an erstwhile math major (I couldn't hack the honors basic algebra class - the difference between a euclidean domain and a principal ideal domain got too confusing; but I rocked proofs in analysis) I have to say that the author is confusing Mathematics (which is an art) and Arithmetic (which is a skill). Part of what make the opening farce absurd is that musical skills and painting are not terribly necessary as a m…

> whereas understanding sums and compounding processes ARE [terribly necessary as a matter of life and death, or even to a certain degree, quality of life or death]. That's not actually true.

in an ideal world, I would agree with you. We do however live in the real world.

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

#50

Post by banachtarski »

nsphere wrote: post #27
saraid216 wrote: post #24

Earlier quoted context omitted.

One of the key mistakes of educational strategy is dividing up knowledge into a bunch of subjects like "Language", "Math", and so on. You can find linkages in just about everything; this siloing really only serves to make people think they're particularly good at one thing and not another, when really it's a preference for one perspective over another.

I completely agree! By other's perspectives my hardest semester was when I took PDEs, Geometry Space-time (Minkowski), Algorithms, P-chem (Quantum Mechanics), and Analysis. However there was so much over lap with all the materials and topics. A few weeks after midterms all the course work just fit together like a 100 piece puzzle.

Taking as many physics courses as I have, I was getting worried for a while that there was nothing more to life than solving a boundary value problem in some domain or another.
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