Mathematics is hard for mathematicians to understand too
1–10 of 152 posts
Re: Mathematics is hard for mathematicians to understand too
#2I thought we were well past trying to understand mathematics. After all, John von Neumann long ago said "In mathematics we don't understand things. We just get used to them."
Re: Mathematics is hard for mathematicians to understand too
#3I was writing a small article about [Set, Set Builder Notation, and Set Comprehension](https://adropincalm.com/blog/set-set-builder-natatio-set-com...) and while i was investigating it surprised me how many different ways are to describe the same thing. Eg: see all the notation of a Set or a Tuple.
One last rant point is that you don't have "the manual" of math in the very same way you would go on your programming language man page and so there is no single source of truth.
Everybody assumes...
Re: Mathematics is hard for mathematicians to understand too
#4I thought we were well past trying to understand mathematics. After all, John von Neumann long ago said "In mathematics we don't understand things. We just get used to them."
Just because someone said it doesn't mean we all agree with it, fortunately.
You know the meme with the normal distribution where the far right and the far left reach the same conclusion for different reasons, and the ones in the middle have a completely different opinion?
So on the far right you have people on von Neumann who says "In mathematics we don't understand things". On the far left you have people like you who say "me no mats". Then in the middle you have people like me, who say "maths is interesting, let me do something I enjoy".
Re: Mathematics is hard for mathematicians to understand too
#5Mathematics is such an old field, older than anything except arguably philosophy, that it's too broad and deep for anyone to really understand everything. Even in graduate school I often took classes in things discovered by Gauss or Euler centuries before. A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. So, you end up having to spend years specializing and then struggle to find other with the same background.
All of which is compounded by the desire to provide minimal "proofs from the book" and leave out the intuitions behind them.
Re: Mathematics is hard for mathematicians to understand too
#6I thought we were well past trying to understand mathematics. After all, John von Neumann long ago said "In mathematics we don't understand things. We just get used to them."
Just because someone said it doesn't mean we all agree with it, fortunately. You know the meme with the normal distribution where the far right and the far left reach the same conclusion for different reasons, and the ones in the middle have a completely different opinion? So on the far right you have people on von Neumann who says "In mathematics we don't understand things". On the far left you have people like you…
Of course. I just find it hilarious that someone like von Neumann would say that.
Re: Mathematics is hard for mathematicians to understand too
#7Mathematics is such an old field, older than anything except arguably philosophy, that it's too broad and deep for anyone to really understand everything. Even in graduate school I often took classes in things discovered by Gauss or Euler centuries before. A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old. So, you end up having to spe…
> A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old.
Do you know the reason for that? The reason is that those problems are open and easy to understand. For the rest of open problems, you need an expert to even understand the problem statement.
Re: Mathematics is hard for mathematicians to understand too
#8I was writing a small article about [Set, Set Builder Notation, and Set Comprehension]( https://adropincalm.com/blog/set-set-builder-natatio-set-com... ) and while i was investigating it surprised me how many different ways are to describe the same thing. Eg: see all the notation of a Set or a Tuple. One last rant point is that you don't have "the manual" of math in the very same way you would go on your programming…
I find it strange to compare "math" with one programming language. Mathematics is a huge and diverse field, with many subcommunities and hence also differing notation.
Your rant would be akin to this if the sides are reversed: "It's surprising how many different ways there are to describe the same thing. Eg: see all the notations for dictionaries (hash tables? associative arrays? maps?) or lists (vectors? arrays?).
You don't have "the manual" of programming languages. "
Re: Mathematics is hard for mathematicians to understand too
#9Earlier quoted context omitted.
Just because someone said it doesn't mean we all agree with it, fortunately. You know the meme with the normal distribution where the far right and the far left reach the same conclusion for different reasons, and the ones in the middle have a completely different opinion? So on the far right you have people on von Neumann who says "In mathematics we don't understand things". On the far left you have people like you…
Of course. I just find it hilarious that someone like von Neumann would say that.
von Neumann liked saying things that he knew would have an effect like "so deep" and "he's so smart". Like when asked how he knew the answer, claiming that he did the sum in his head when undoutedly he knew the closed-form expression.
Re: Mathematics is hard for mathematicians to understand too
#10Just the other day I was listening to EconTalk on this: https://www.econtalk.org/a-mind-blowing-way-of-looking-at-ma...