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Some Fundamental Theorems in Mathematics (2019) [pdf]

people.math.harvard.edu

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

#11

Post by bryanrasmussen »

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....

These design requirements in regards to Spock that you remark on - I can't really find them here https://en.wikipedia.org/wiki/Development_of_Spock and though never a Trekkie I don't think this sounds like something Roddenberry would have considered.

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

#13

Post by _f9cu »

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 problems doesn't bring a smile on face. By the time we solve, we would have lost our sense of self. And that's why it is meaningless.

A: What do you propose? Me: Not proposing anything. Just putting my thoughts out. Chase only whole numbers. Even try to cut out division. It is the root cause of all the problems.

Me: Addition makes sense, Multiplication makes sense. Subtraction doesn't make sense. It is used to check the correctness not for real math. You may call, just like multiplication is repeated addition, division is repeated subtraction. I'll stop right there. Division gives two answers - reminder and a quotient. Both are useless.

IF YOU HAD FUN, I'm glad.

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

#14

Post by idclip »

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....

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 what I would call the human experience.

The same stuff can be taught with soul and purpose If we actually show children how they can apply mathematics to improve and enhance what they’re actually doing whether it is building castles in Lego, Or designing faster toy car, A better school project volcano, etc

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

#15

Post by irontinkerer »

idclip wrote: post #14
Konohamaru wrote: post #3

Earlier quoted context omitted.

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....

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…

> Mathematics is a tool to practice our hobbies .. see Feynman‘s biography

I think pointing to a math/physics expert's life story to defend your premise is a bit of a circular reasoning

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

#16

Post by curiousllama »

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…

Not OP, but I agree with OP, assuming by "people" they mean "people already inclined towards math." Self-evidently, IMO, most students need numeracy much more than they need pure math.

In school, I struggled with memorization & attention to detail. For the life of me, I couldn't quite finish an algebra-heavy problem without writing 3*4=15 or outright skipping a step in a conic rotation or whatever. I'd get dinged every... single... time, and got relatively bad grades.

Shortly later, when I arrived back at higher level math through cs & stats, I could ruin the curve in my applied classes. I'd relied so much on mathematical intuition early on to compensate for a lack of memorization ("what are the steps again? Whatever - I'll just think it through now") that I was quite good at putting pieces together in odd ways to solve data science problems.

Not to mention - with proper context, as you say, all that linear algebra that so annoyed me all the sudden seemed intuitive. "OHHHH so THAT'S why this exists"

I was first driven out of math by a relentless focus on math-as-a-tool, and was able to return at a level where it became more about creating new logic. I'm convinced that I would have thrived in an earlier class that focused on elegance & logic - what makes a good proof? - and I'd have stuck with it.

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

#17

Post by butterthebuddha »

idclip wrote: post #14
Konohamaru wrote: post #3

Earlier quoted context omitted.

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....

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 experience.

I think you misread the parent comment (although to be clear, I'm not defending it).

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

#19

Post by bryanrasmussen »

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

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

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

#20

Post by francasso »

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....

Mathematics is as much logic as poetry is grammar. Sadly most people don't know that because they never get exposed to the creative/discovery side of math. Logic is just a tool to check correctness and enable communication.
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