3 ms·

The same can be said about programming. Reference and theory are very useful, but context is how they are tied together in implementation.

Mathnerd314 10y ago
By the Curry–Howard correspondence, programming is in fact (formal) theorem proving. Mathematics got a lot less interesting after I realized it amounted to a giant, informally-specified, mostly undocumented body of code designed to run on the human brain... from that perspective it's hard to see why one should prefer mathematics to a well-written software program that does the same thing.
- mathgenius 10y ago
  > code designed to run on the human brain So it's legacy code that runs on the oldest hardware that we have.. Plenty of people are interested in updating this code so that it runs on more modern platforms. Actually, this is my favorite way to drill into a piece of mathematics: port it to python.
- skybrian 10y ago
  Is Curry-Howard interesting if you're not programming with advanced type systems? It's my understanding that writing a function that returns an integer (for example) corresponds to proving that an integer exists. Whoop-de-do? This would imply that unless you're constructing a sophisticated return type, you're not proving anything interesting.
- deleted 10y ago
  [deleted]
- mrout 10y ago
  Yeah sorry, you don't at all understand mathematics.
- bjl 10y ago
  That's not quite true. Curry-Howard only applies to constructivist mathematics, which is a very tiny subset of mathematics proper.
  - gergoerdi 9y ago
    That is a much more complicated question than you make it sound: https://cstheory.stackexchange.com/q/5245/1802 https://cstheory.stackexchange.com/q/5245/1802
lolive 10y ago
My first programmation book was the K&R book. I hated reading it and was pretty sure that was nothing I would ever understand (or use). 25 years later, I now understand all the details of the book. And now I hate ... the C language itself (with passion!). Fortunately, nowadays, there is so much learning material that you have the opportunity to choose the one that suits you. For example, I know that I cannot apply a theory upon reality. I have to start with examples and build my own vision by abstracting from a lot of examples. So I choose my learning material accordingly. My current interest, at the moment, is monad. Believe me, there is a lot of abstract articles about that. But my entry point was a tutorial about implementing some stuff in Javascript, that happened to be functors, monads, etc. Believe it or not, but I used that knowledge the week after in one of my Java projects. And my colleagues considered it was "a nice trick" (which is true!). In one word, the learning process must be fluid. Don't try to force anything. If the book medium does not suit you, don't blame the book. Or yourself. Try to find another resource and keep learning.
VLM 10y ago
There exist purely theoretical computer science topics. Ullman's automata theory lectures are freely (legally?) available online. There are also authors like Knuth who are surprisingly practical. This problem goes way beyond math and programming and into physics and general engineering. There are a surprising number of engineers who can manipulate the linear algebra tools but can't actually engineer structures or figure out linear circuits. EE filter design is another good example. If you look at higher ed vocational training as kind of a prep-school or maybe a qualification filter for an apprenticeship it makes more sense. Once you figure out linear algebra you're qualified to apprentice to someone to teach you how to actually use it.

Mathnerd314 10y ago

By the Curry–Howard correspondence, programming is in fact (formal) theorem proving. Mathematics got a lot less interesting after I realized it amounted to a giant, informally-specified, mostly undocumented body of code designed to run on the human brain... from that perspective it's hard to see why one should prefer mathematics to a well-written software program that does the same thing.

mathgenius 10y ago
> code designed to run on the human brain So it's legacy code that runs on the oldest hardware that we have.. Plenty of people are interested in updating this code so that it runs on more modern platforms. Actually, this is my favorite way to drill into a piece of mathematics: port it to python.
skybrian 10y ago
Is Curry-Howard interesting if you're not programming with advanced type systems? It's my understanding that writing a function that returns an integer (for example) corresponds to proving that an integer exists. Whoop-de-do? This would imply that unless you're constructing a sophisticated return type, you're not proving anything interesting.
deleted 10y ago
[deleted]
mrout 10y ago
Yeah sorry, you don't at all understand mathematics.
bjl 10y ago
That's not quite true. Curry-Howard only applies to constructivist mathematics, which is a very tiny subset of mathematics proper.
- gergoerdi 9y ago
  That is a much more complicated question than you make it sound: https://cstheory.stackexchange.com/q/5245/1802 https://cstheory.stackexchange.com/q/5245/1802

lolive 10y ago

My first programmation book was the K&R book. I hated reading it and was pretty sure that was nothing I would ever understand (or use). 25 years later, I now understand all the details of the book. And now I hate ... the C language itself (with passion!). Fortunately, nowadays, there is so much learning material that you have the opportunity to choose the one that suits you. For example, I know that I cannot apply a theory upon reality. I have to start with examples and build my own vision by abstracting from a lot of examples. So I choose my learning material accordingly. My current interest, at the moment, is monad. Believe me, there is a lot of abstract articles about that. But my entry point was a tutorial about implementing some stuff in Javascript, that happened to be functors, monads, etc. Believe it or not, but I used that knowledge the week after in one of my Java projects. And my colleagues considered it was "a nice trick" (which is true!). In one word, the learning process must be fluid. Don't try to force anything. If the book medium does not suit you, don't blame the book. Or yourself. Try to find another resource and keep learning.

VLM 10y ago

There exist purely theoretical computer science topics. Ullman's automata theory lectures are freely (legally?) available online. There are also authors like Knuth who are surprisingly practical. This problem goes way beyond math and programming and into physics and general engineering. There are a surprising number of engineers who can manipulate the linear algebra tools but can't actually engineer structures or figure out linear circuits. EE filter design is another good example. If you look at higher ed vocational training as kind of a prep-school or maybe a qualification filter for an apprenticeship it makes more sense. Once you figure out linear algebra you're qualified to apprentice to someone to teach you how to actually use it.