31–40 of 104 posts
> The distinction between the three types of errors can lead to the phenomenon ... of a mathematical argument by a post-rigorous mathematician which locally contains a number of typos and other formal errors, but is globally quite sound, with the local errors propagating for a while before being cancelled out by other local errors I was initially amazed at this when I was in graduate school, but with enough experienc…
> One can roughly divide mathematical education into three stages: Similarly with programming. 1. Write programs that you think are cool 2. Learn about data structures and algorithms and complexity and software organization. 3. Write programs that you think are cool. But since you know more, you can write more cool programs. If things are working as they should, the end stage of mathematics and programming should be…
1. Start by writing programs with vectors and maps.
2. Learn all about data structures, algorithms, cache misses, memory efficiency etc
3. And then write programs with vectors and maps.
Is there?
“Before I learned the art, a punch was just a punch, and a kick, just a kick. After I learned the art, a punch was no longer a punch, a kick, no longer a kick. Now that I understand the art, a punch is just a punch and a kick is just a kick.” - Bruce Lee
Earlier quoted context omitted.
Absolutely. We have machines that can crank out true theorems, rigorously proven, all day. It takes a mathematician to know what is worth working on. And that is fundamentally an intuitive decision. Computers don't care whether a proof is interesting or not.
It’s a bit tautological since we are defining interesting as what human mathematicians work on. Perhaps if computers ran the show they wouldn’t agree with our definition.
> One can roughly divide mathematical education into three stages: Similarly with programming. 1. Write programs that you think are cool 2. Learn about data structures and algorithms and complexity and software organization. 3. Write programs that you think are cool. But since you know more, you can write more cool programs. If things are working as they should, the end stage of mathematics and programming should be…
Also (in C++ lingo): 1. Start by writing programs with vectors and maps. 2. Learn all about data structures, algorithms, cache misses, memory efficiency etc 3. And then write programs with vectors and maps.
1. Start by doing everything in ReaderT Env IO
2. Learn all about mtl (or monad transformers, free monads, freer monads, algebraic effects, whatever)
3. Do everything in ReaderT Env IO
> One can roughly divide mathematical education into three stages: Similarly with programming. 1. Write programs that you think are cool 2. Learn about data structures and algorithms and complexity and software organization. 3. Write programs that you think are cool. But since you know more, you can write more cool programs. If things are working as they should, the end stage of mathematics and programming should be…
Also (in C++ lingo): 1. Start by writing programs with vectors and maps. 2. Learn all about data structures, algorithms, cache misses, memory efficiency etc 3. And then write programs with vectors and maps.
But the maps this time are absl::flat_hash_map (or another C++ alternative hash map such as Folly F14, etc) instead of std::map (or even std::unordered_map).
“Before I learned the art, a punch was just a punch, and a kick, just a kick. After I learned the art, a punch was no longer a punch, a kick, no longer a kick. Now that I understand the art, a punch is just a punch and a kick is just a kick.” - Bruce Lee
People have pointed out similarities to a few things in this thread now. It's pretty much the bell curve meme: https://knowyourmeme.com/memes/iq-bell-curve-midwit
I've known the Dogen saying for years. Have even meditated on it.
I've been enjoying Bell Curve meme for sometime. Very funny.
Never put together that these were the same thing.
Today I am awakened.
The worst thing is when someone who thinks that "math is 100% infallible and all about rigor, you gotta show your work and include all the steps" yet they think that set theory is good enough and it doesnt have problems they say things like "Everything in math is a set," but then you ask them "OK, what's a theorem and what's a proof?" they'll either be confused by this question or say something like "It's a different…
Earlier quoted context omitted.
Absolutely. We have machines that can crank out true theorems, rigorously proven, all day. It takes a mathematician to know what is worth working on. And that is fundamentally an intuitive decision. Computers don't care whether a proof is interesting or not.
It’s a bit tautological since we are defining interesting as what human mathematicians work on. Perhaps if computers ran the show they wouldn’t agree with our definition.
Ultimately though this is all funded by, in the end, the belief that they’ll be able to dumb down the good stuff for us scientists, engineers, and other folks who build actual physical things when we hit the point that we need it. (Of course it is an exploration process so not everything needs to be directly applicable).
If computers ran the show, we would probably stop plugging them in if they used more power than their theories saved us, or whatever.