Why there is no Hitchhiker’s Guide to Mathematics for Programmers
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Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#2tl;dr: i'm a snobby research student who is trying to trash developers who didn't need college.
(yeah. that was an ad hominem. come at me.)
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#3tl;dr: i'm a snobby research student who is trying to trash developers who didn't need college. (yeah. that was an ad hominem. come at me.)
That's not at all what the author is trying to say. He's pointing out the shortcomings of mathematics notation and why that can be off-putting to otherwise motivated programmers.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#4Actually, there is something that comes pretty close to this--it's called The Princeton Companion to Mathematics, curated by T. Gowers but mostly written by about a hundred of the top mathematicians in their respective fields, and is one of the most beautiful books I've ever read.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#5> Perhaps one of the most prominent objections to devoting a lot of time to mathematics is that it can be years before you ever apply mathematics to writing programs. On one hand, this is an extremely valid concern. If you love writing programs and designing software, then mathematics is a nothing more than a tool to help you write better programs.
Calling it an "extremely valid concern" is understating it. The dilemma is that programmers have many, many roads to follow if they want to improve their product, all of them discrete, deep fields in their own. Math is great, and certainly studying it will expand your mind...but so will studying engineering practices, statistics (which yes, is a kind of math, but not as theoretical as the kind the OP is advocating for), user interface design, and knowledge domains (medicine, legal, earth sciences, etc.)...all of which, as far as most programmers can tell, will yield concrete rewards much more easily than will mastering higher level mathematics.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#6tl;dr: i'm a snobby research student who is trying to trash developers who didn't need college. (yeah. that was an ad hominem. come at me.)
I read the article and did not come away with that impression. :-)
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#7I don't know about the OP's point on the value of proof to programmers. I do optimization and machine learning, and I use all kinds of math on a regular basis. But I don't prove things, and rarely need to follow someone else's proof either. You can get a lot out of applied math without touching a proof. And if it isn't applied, then you really don't need it ;-).
I agree there is value in learning how to read math notation, so there is a valid point in there somewhere.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#8I've come up against this recently and I think a lot of imperative programmers will. For me, the basic pattern, starting from a career based on perl/php/java was this series of realizations:
- EECS circuit design is based on a conceit that gives chips a speed limit
- as a result, chips aren't getting much faster and that multi-cores are happening instead
- parallel programming will become more and more essential to make a buck as a programmer
- imperative languages aren't great for parallel programming due to mutable variables
- functional languages are better for parallel programming due to immutable variables
- functional languages are a lot closer to math concepts than imperative languages
- uh-oh
So for me it's been a fun few months of stumbling through self-directed study in stats, probability, and math. Bayesian probability from some articles by Yudkowsky. Fast, clumsy review of 0th-order, 1st-order, and zfc set theory. Anki decks out the wazoo. Now I'm plodding through Learn You A Haskell.
I would like to work more with actual mathematical proofs but I'm finding that tough to get into myself. It was fun paging through metamath for a few days, though.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#9This seems like a problem of terminology. It is valid to desire a better acquaintance with the theorems others have proven, just as it is valid to desire a better acquaintance with the user-facing features of Chrome, iTunes, Excel, etc. I guess "using math" is different than "doing math", and most people are more interested in the the former.
There is a bit of a continuum, though. Using Excel effectively involves a smidgen of programming, similar to how "using math" effectively really means using other peoples' theorems to "prove" things, very informally, about your own domain. Maybe that's why people are more likely to get confused between "using" math and "doing" math.
Re: Why there is no Hitchhiker’s Guide to Mathematics for Programmers
#10> Perhaps one of the most prominent objections to devoting a lot of time to mathematics is that it can be years before you ever apply mathematics to writing programs. On one hand, this is an extremely valid concern. If you love writing programs and designing software, then mathematics is a nothing more than a tool to help you write better programs. Calling it an "extremely valid concern" is understating it. The dilem…
This is a very succinct breakdown of the problem as I see it. If only it were so easy as being able to rationally and empirically determine that X is the most efficient investment of time and energy.