Some Fundamental Theorems in Mathematics (2019) [pdf] • Hacker News Board

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#21

Post by agumonkey » Wed, Aug 05, 2020, 3:29 PM UTC

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

I'd say wrong and wrong :)

respectfully of course.

School removes the pragmatic nature of math thus cannot even teach it as a tool because there's no concrete goal (worded problemes are not in situ enough).

The beauty may evade some souls, they're just not in tune with the subject at that time.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#22

Post by jimhefferon » Wed, Aug 05, 2020, 3:41 PM UTC

laichzeit0 wrote: post #7

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

I'm convinced that if Book of Proof [1] was taught in high school, most people would (a) understand math, and (b) not hate it. http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

That's a fine book. But to answer that question surely calls for emperical data?

Generations of teachers of mathematics-- surely not all incompetent-- have found that many people, perhaps most people, do not love math. There are very good teachers (I had a few), and very good ways to teach it (shout out to the Mr Barton Maths podcast), but experience shows that it is a hard go much of the time.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#23

Post by domnomnom » Wed, Aug 05, 2020, 3:56 PM UTC

_f9cu wrote: post #13

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

Floating points are absurd. It helps the scientific community and slows us down to solve interesting frictionless problems. Floating points take too much computation power. The amount of power we spend for floating point math and return on knowledge gained doesn't make sense. A: Hey, but floating points are main thing in scientific problems. Me: Ignore scientific problems, it doesn't amount to nothing and scientific…

We make circular cpus and do everything in base pi! Yes!

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#24

Post by golem14 » Wed, Aug 05, 2020, 3:57 PM UTC

butterthebuddha wrote: post #17

idclip wrote: post #14

Earlier quoted context omitted.

I disagree. Mathematics is a tool to practice our hobbies .. see Feynman‘s biography. Rot mathematics is where it goes wrong. Meta mathematics, abstract, detached from real life, as alot of the academy with its publish pr perish thinking ... that produces pain. Existential voids filled with an exercise that does not help many to move forward optimally. saying weirdos hate logic is extremely dismissive to a lot of wha…

> Rot mathematics is where it goes wrong. Not sure what you mean by "rot mathematics". > Meta mathematics, abstract, detached from real life, as alot of the academy with its publish pr perish thinking ... that produces pain. Some (including me) would say that the meta and abstract mathematics is most beautiful of all... > saying weirdos hate logic is extremely dismissive to a lot of what I would call the human experi…

rote

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#25

Post by Scarbutt » Wed, Aug 05, 2020, 4:18 PM UTC

laichzeit0 wrote: post #7

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

I'm convinced that if Book of Proof [1] was taught in high school, most people would (a) understand math, and (b) not hate it. http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

Would you classify that book as good introduction to discrete math?

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#26

Post by JackFr » Wed, Aug 05, 2020, 4:29 PM UTC

cinntaile wrote: post #4

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

(Here I am focusing on math outside of the math taught in pure mathematics programs.) If anything the focus on math being a tool should be even bigger than it is today if you ask me. Most if not all of the math you get taught in school is math that was invented to solve a problem, it was not created as art. Introducing this historical context would probably help students in understanding why learning math is useful i…

Replace arithmetic with “math appreciation”? No thanks.

I’m still disappointed by the way music and art are taught at the elementary and middle school levels. Singing, playing an instrument, drawing are all things which can effectively be taught and are so much more useful than useless watered down “art” and “music” I had to take in grade and middle school.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#27

Post by domnomnom » Wed, Aug 05, 2020, 4:35 PM UTC

Konohamaru wrote: post #3

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

You cannot teach people--even people at a young age--to enjoy mathematics because mathematics is based on logic and almost everyone except for a few weirdos hates logic. Mr. Spock was designed to point out how unusual people who like logic are, but as a character from a minstrel show, not as a role model....

Not true, logic is great. It's just taught in a tortured way and mostly goes by another name.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#28

Post by domnomnom » Wed, Aug 05, 2020, 4:36 PM UTC

jimhefferon wrote: post #22

laichzeit0 wrote: post #7

Earlier quoted context omitted.

I'm convinced that if Book of Proof [1] was taught in high school, most people would (a) understand math, and (b) not hate it. http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

That's a fine book. But to answer that question surely calls for emperical data? Generations of teachers of mathematics-- surely not all incompetent-- have found that many people, perhaps most people, do not love math. There are very good teachers (I had a few), and very good ways to teach it (shout out to the Mr Barton Maths podcast), but experience shows that it is a hard go much of the time.

Good, keep all the maths for me.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#29

Post by dorchadas » Wed, Aug 05, 2020, 4:39 PM UTC

GaussBonnet wrote: post #9

perfunctory wrote: post #2

Something went wrong with the way math is taught at school. We teach math as a tool and not as something that can be appreciated and enjoyed the way we appreciate and enjoy art. Some math theorems and their proofs are a thing of beauty. Often one doesn't even have to understand all the nitty-gritty details to see that beauty. Some basic understanding of fundamental principals often suffices.

The problem isn't that grade school teachers are sitting on a secret stash of cool theorems, and instead diabolically choose to have students solve quadratic equations year after year. It's that no one in the grade school pipeline has any experience with actual, modern, proof based mathematics. They've never even heard of analysis or group theory. Their knowledge does not extend beyond the latest meme textbook with M…

Yes, yes, and absolutely yes! I'm a high school math and physics teacher (who majored in physics, not education, and is now doing self-study in more proof-based mathematics), and so much the issue is in grade school, in my opinion. The teachers there don't appreciate math. And, more than that, they don't understand math. Lots of them don't have a good well-developed number sense, so it's no wonder our kids don't either!

Then the problems compound when they just give kids calculators without the kids understanding why the calculator works, and by the time they get to high school hope is lost because they have no number sense and we're trying to explain variables and such...often divorced from real life. I've found my kids get a much more intuitive sense of slope when I explain it as the rate of change rather than "rise over run" that they're so often taught in middle school. Give them examples, like amusement park tickets (it cost $50 to get there, then $70 per person) and have them incorporate that into a slope-intercept form. It just makes things so much clearer that they often don't get because they don't have the number sense and because many teachers don't understand/appreciate math.

Re: Some Fundamental Theorems in Mathematics (2019) [pdf]

#30

Post by domnomnom » Wed, Aug 05, 2020, 4:40 PM UTC

bryanrasmussen wrote: post #19

laichzeit0 wrote: post #7

Earlier quoted context omitted.

I'm convinced that if Book of Proof [1] was taught in high school, most people would (a) understand math, and (b) not hate it. http://www.people.vcu.edu/~rhammack/BookOfProof/index.html

the beginning part on Sets is definitely enjoyable reading. thanks for putting that here for me to find.

You'll love Russell then.

https://users.drew.edu/~jlenz/br-ml-ch5.html#n8

He gets deep into some stuff, so read the parts that interest you. I also highly recommend his book, the problems of philosophy. It's really what I think math is all about.