There are no rules in math
hardmath123.github.io
There are no rules in math
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Re: There are no rules in math
#2Having earned an undergraduate degree in math I've often had similar thoughts about US elementary math education's emphasis on rules and mechanical calculation and memorization rather than more abstract concepts like pattern matching.
Turns out there was a thing called "New Math" (https://en.wikipedia.org/wiki/New_Math) in the 1960s where public elementary schools tried to teach concepts from set theory and abstract algebra. Basically everyone hated it.
Perhaps there was just a curriculum failure, or perhaps teachers weren't well-equipped enough to teach the material. But we can't ignore the attempt and need to come up with an answer for why New Math failed before we can try it again.
Re: There are no rules in math
#3My high school math teacher used to give us extra classes that weren't directly connected to the curriculum. They were always about structure, elegance, and beauty. Quite a lot of time was also spent on history: who was studying what, when, and why. (Also there was a cult of Leonard Euler, which maybe is not so surprising if you did high school math.)
I found it to be the most important glue in my math education. In fact, all the natural science ought to be taught in this way. Kinda like Bill Bryson's Brief History of Everything, plus actual calculations.
We won a math contest in my last year. I was expecting it to stay interesting.
Unfortunately when I got to university math (and the rest of engineering) was taught in a very utilitarian way. There was very little context, just a lot of similar looking derivations.
I blame the exam culture. In a way it's good because it motivates you to learn something, but it's bad because you end up learning it in a way that isn't useful. At the end of your college days, you are unlikely to remember just how Stoke's theorem works or the coefficients in Runge-Kutta. That's just because the size of the curriculum is huge. But if you had a context, a set of stories about when and why something was studied, you'd have a much better chance of being able to recall that it even exists.
Re: There are no rules in math
#4Having earned an undergraduate degree in math I've often had similar thoughts about US elementary math education's emphasis on rules and mechanical calculation and memorization rather than more abstract concepts like pattern matching. Turns out there was a thing called "New Math" ( https://en.wikipedia.org/wiki/New_Math ) in the 1960s where public elementary schools tried to teach concepts from set theory and abstrac…
I was taught the "New Math" as a child and did not hate it. It was wonderful. When I look at math blogs today, they use notation and terminology I learned back then. This is a tremendous advantage (or so it seems to me).
Re: There are no rules in math
#5That problem is actually very easy to solve. If you number the cells in binary, patterns fall out enough that it's easy to convert back and forth from the original numbering to the final numbering.
If he wants to just work it out by hand, well, maybe he doesn't understand math as well as he thinks. If you want to use math to "build hammers", it help to know what a nail is first.
Re: There are no rules in math
#6My high school math teacher used to give us extra classes that weren't directly connected to the curriculum. They were always about structure, elegance, and beauty. Quite a lot of time was also spent on history: who was studying what, when, and why. (Also there was a cult of Leonard Euler, which maybe is not so surprising if you did high school math.) I found it to be the most important glue in my math education. In…
I had a college geometry professor who taught all of his classes this way. He taught me things about math, structure, elegance, and beauty that unfolded into a much better understanding of why math is so powerful in science. Studying history of math and Euclid did more to enhance my understanding of Physics and Math than any of the actual required courses, because they taught me the context in which the thinking is grown, which is far more powerful than the thinking itself.
Re: There are no rules in math
#7Totally agree with the author. In high-school, I was interested in physics more than math and whenever I took interest in math it was because it would help me understand some specific aspect of the physics better. As I got into engineering, my interest in math again were only in areas where it was directly useful to me (like signal/image processing, operations research etc.) As a CS engineer, I've used very little math I was forced to learn by rote to write exams. Only use that came of it I think is training my brain muscles to do pattern recognition and fast memory recall.
Re: There are no rules in math
#8Having earned an undergraduate degree in math I've often had similar thoughts about US elementary math education's emphasis on rules and mechanical calculation and memorization rather than more abstract concepts like pattern matching. Turns out there was a thing called "New Math" ( https://en.wikipedia.org/wiki/New_Math ) in the 1960s where public elementary schools tried to teach concepts from set theory and abstrac…
I was taught the "New Math" as a child and did not hate it. It was wonderful. When I look at math blogs today, they use notation and terminology I learned back then. This is a tremendous advantage (or so it seems to me).
And everyone else just curses when they open a Wikipedia article for smth that is supposedly (and actually) not that complex, but is explained in those terms, still :)
Re: There are no rules in math
#9That problem is actually very easy to solve. If you number the cells in binary, patterns fall out enough that it's easy to convert back and forth from the original numbering to the final numbering. If he wants to just work it out by hand, well, maybe he doesn't understand math as well as he thinks. If you want to use math to "build hammers", it help to know what a nail is first.
That's not what the article is about.
Re: There are no rules in math
#10That problem is actually very easy to solve. If you number the cells in binary, patterns fall out enough that it's easy to convert back and forth from the original numbering to the final numbering. If he wants to just work it out by hand, well, maybe he doesn't understand math as well as he thinks. If you want to use math to "build hammers", it help to know what a nail is first.
That's not what the article is about.
What is it about? (other than the statement "there are no rules in math" which I think is so outrageously wrong I can't even argue against it here)