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The qualifier was important. If, by arguing that math skills are important to programming, you mean "skills in post-Calculus math" than say so. If you say "mat

The qualifier was important. If, by arguing that math skills are important to programming, you mean "skills in post-Calculus math" than say so. If you say "math," people will continue to believe that you mean math in the way that they experienced it, i.e. math ending at or shortly after calculus. Lots of mathematicians freely admit that they're terrible at computation. Which is precisely my point - the two represent different skills. Being good at symbol manipulation (i.e. "math" as represented by your high school transcript, SAT, ACT, and college transcript if not a math major) is not a determinant of your aptitude as a programmer. Is it useful to study math beyond calculus? Of course! I know (abstractly) that things like the typed lambda calculus and set theory exist and are the foundation for much of what we do. However, it is ignorant to talk about these things like they're related to your aptitude for pre-Analysis math. But what it isn't is rational to to use performance in lower math classes to screen (computer science undergrad applicants|interns|programmers), or to encourage people to choose or not choose programming as a career path based on their performance in mathematics classes. Basically, I side with Lockhart's Lament. https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament....

j2kun 12y ago
Your comment made it very unclear whether you believed what you were saying about mathematics or not. Rereading, it still seems like you think conjecture and proof is more like physics than math. And you claim that math is irrelevant to compiler design. It's not "abstractly" relevant, it's directly relevant. Parsing is formal language recognition. Register allocation is literally graph coloring. These things are not third-generation applications of mathematics. You seem to think that mathematics makes you good at computing, when in truth most mathematicians are bad at computing things by hand. The root misunderstanding might be that most people wouldn't know math if it hit them in the head, but changing my definition of math to fit their misconceptions is certainly not going to fix the problem. I would even prefer it if people thought, "math? yeah I have no idea what goes on in that subject" to what you describe. Because distinguishing between "math" and "post-Calculus math" (the latter of which is almost all of math) won't help anyone.
- seanmcdirmid 12y ago
  Dammit: http://xkcd.com/435/ http://xkcd.com/435/ You are basically claiming that everything is math, which is true, but useless. Programming is more like chemistry or biology in the purity access...not "like them" but at a similar level. Writing parsers, which I do a lot, requires very little parsing theory...ya, they make for good academic papers, but nothing beats good ole simple recursive descent in flexibility for error handling. And for register allocation, you might use - gasp - an algorithm, but that doesn't dominate your work - writing a compiler involves some math (among other tasks), but is not mathematical activity. Mathematicians can be bad or good at programming, just like musicians can be...there is no strong correlation to their aptitude based on their previous training. > The root misunderstanding might be that most people wouldn't know math if it hit them in the head, but changing my definition of math to fit their misconceptions is certainly not going to fix the problem. Math can be defined so broadly as to basically be a useless word. Is sociology math? Is chemistry math? Is physics math? Is engineering math? Is implementing an algorithm math? Meh, if so, then whatever, we haven't made any progress.
  - auggierose 12y ago
    If you still write parsers as recursive descent parser by hand, then this is because NOT ENOUGH MATH IS APPLIED IN PRACTICE (by programmers who think they don't need it).
    - seanmcdirmid 12y ago
      No, its because incremental performance and error recovery are more important than raw performance and expressiveness. If you think Dr. Odersky doesn't know enough math...not to mention most production compilers out there written by the best professionals in the field. Reality is a harsh mistress. My parsers, by the way, do things only your parsers could dream of: http://research.microsoft.com/en-us/people/smcdirm/liveprogramming.aspx?2 http://research.microsoft.com/en-us/people/smcdirm/liveprogr...
      - loup-vaillant 12y ago

j2kun 12y ago

Your comment made it very unclear whether you believed what you were saying about mathematics or not. Rereading, it still seems like you think conjecture and proof is more like physics than math. And you claim that math is irrelevant to compiler design. It's not "abstractly" relevant, it's directly relevant. Parsing is formal language recognition. Register allocation is literally graph coloring. These things are not third-generation applications of mathematics. You seem to think that mathematics makes you good at computing, when in truth most mathematicians are bad at computing things by hand. The root misunderstanding might be that most people wouldn't know math if it hit them in the head, but changing my definition of math to fit their misconceptions is certainly not going to fix the problem. I would even prefer it if people thought, "math? yeah I have no idea what goes on in that subject" to what you describe. Because distinguishing between "math" and "post-Calculus math" (the latter of which is almost all of math) won't help anyone.

seanmcdirmid 12y ago
Dammit: http://xkcd.com/435/ http://xkcd.com/435/ You are basically claiming that everything is math, which is true, but useless. Programming is more like chemistry or biology in the purity access...not "like them" but at a similar level. Writing parsers, which I do a lot, requires very little parsing theory...ya, they make for good academic papers, but nothing beats good ole simple recursive descent in flexibility for error handling. And for register allocation, you might use - gasp - an algorithm, but that doesn't dominate your work - writing a compiler involves some math (among other tasks), but is not mathematical activity. Mathematicians can be bad or good at programming, just like musicians can be...there is no strong correlation to their aptitude based on their previous training. > The root misunderstanding might be that most people wouldn't know math if it hit them in the head, but changing my definition of math to fit their misconceptions is certainly not going to fix the problem. Math can be defined so broadly as to basically be a useless word. Is sociology math? Is chemistry math? Is physics math? Is engineering math? Is implementing an algorithm math? Meh, if so, then whatever, we haven't made any progress.
- auggierose 12y ago
  If you still write parsers as recursive descent parser by hand, then this is because NOT ENOUGH MATH IS APPLIED IN PRACTICE (by programmers who think they don't need it).
  - seanmcdirmid 12y ago
    No, its because incremental performance and error recovery are more important than raw performance and expressiveness. If you think Dr. Odersky doesn't know enough math...not to mention most production compilers out there written by the best professionals in the field. Reality is a harsh mistress. My parsers, by the way, do things only your parsers could dream of: http://research.microsoft.com/en-us/people/smcdirm/liveprogramming.aspx?2 http://research.microsoft.com/en-us/people/smcdirm/liveprogr...
    - loup-vaillant 12y ago