The thing is the answer is YES, but you won't even understand why unless you have the appropriate math knowledge.
There would be a lot less terrible code written out there if people had a better grasp of discrete math, knew how to make their O(n) analysis, knew how to create and implement provably correct algorithms, knew lambda calculus and e.t.c. and that's just for general programming. I would say a basic grasp of set theory and graph theory applies to almost everything too.
I have discrete under my belt. And a bunch of other stuff too (came a bit short of having a minor in math in college).
And... well, I can't say that I've ever explicitly used any of it in programming. I suspect you're falling into the trap of generalizing from a field you're familiar with to all fields, and that's a generalization that doesn't hold up.
In part the key word here is "explicitly." I have a PhD in Combinatorics and Graph Theory, and I have lectured in Calculus, Group Theory, Functional Analysis and Topology. In my daily work for the past 18 years I have explicitly used that background exactly once.
But the ongoing influence, the style of thought, the ability to visualise and the ability to abstract away from the details - these things I use all the time, every day. They have been enhanced and honed by all that math.
I use my math background implicitly all the time, and I don't know how I'd do what I do without it.
And this is perhaps the most important point about studying math. Often the greatest take-away is the abstract problem solving capability, not the material itself. I've never had to analyse the genus of a manifold in real life, but I have thought about objects moving in an 11 dimensional space with holes, because while everyone else was stuch in the detail, I was seeing things differently. It turned out that the combination of styles was critical to solving the problem.
Often the greatest take-away is the abstract problem solving capability, not the material itself.
That's why I got a degree in philosophy.
OK, not the only reason, but one of them...
Meanwhile, I think my point stands. Too many people seem to have an "OMG you don't use linear algebra every day? What kind of crap programmer are you?" attitude.
I suspect that you've had opportunities to use your math, and had you seen those opportunities you would recognize the potential utility.
I say this as someone who periodically finds yet another way to use my math background to help me do things while my co-workers in the same job don't. Which is why I'm the one who got to do the statistics for evaluating A/B testing, eliminated multiple performance problems others had come to accept, and gets tapped to tackle complex "how do we figure this out" problems from time to time.
And yes, I've had the fun of seeing co-workers who theoretically had the same job as me argue that math wasn't useful for programming, while I was sitting there with a list of examples of how I'd recently used my math background. (But then I got promoted into a different job title and in those discussions those programmers were able to respond that of course I needed more math for reporting, but they didn't need it as web developers. Never mind that I was the guy who got asked to help when the database had trouble scaling at peak traffic of several million pages/hour...)
Really this seems to me to be a variant of the blub paradox. If you haven't learned to reflexively see the benefits of thinking in some new way, you won't recognize how thinking that way could help with the problems you are solving day in and day out. Conversely if you have gained those mental skills, you recognize their utility in situations that other people wouldn't dream they are applicable for.
Comments
The thing is the answer is YES, but you won't even understand why unless you have the appropriate math knowledge.
There would be a lot less terrible code written out there if people had a better grasp of discrete math, knew how to make their O(n) analysis, knew how to create and implement provably correct algorithms, knew lambda calculus and e.t.c. and that's just for general programming. I would say a basic grasp of set theory and graph theory applies to almost everything too.
I have discrete under my belt. And a bunch of other stuff too (came a bit short of having a minor in math in college).
And... well, I can't say that I've ever explicitly used any of it in programming. I suspect you're falling into the trap of generalizing from a field you're familiar with to all fields, and that's a generalization that doesn't hold up.
In part the key word here is "explicitly." I have a PhD in Combinatorics and Graph Theory, and I have lectured in Calculus, Group Theory, Functional Analysis and Topology. In my daily work for the past 18 years I have explicitly used that background exactly once.
But the ongoing influence, the style of thought, the ability to visualise and the ability to abstract away from the details - these things I use all the time, every day. They have been enhanced and honed by all that math.
I use my math background implicitly all the time, and I don't know how I'd do what I do without it.
And this is perhaps the most important point about studying math. Often the greatest take-away is the abstract problem solving capability, not the material itself. I've never had to analyse the genus of a manifold in real life, but I have thought about objects moving in an 11 dimensional space with holes, because while everyone else was stuch in the detail, I was seeing things differently. It turned out that the combination of styles was critical to solving the problem.
Often the greatest take-away is the abstract problem solving capability, not the material itself.
That's why I got a degree in philosophy.
OK, not the only reason, but one of them...
Meanwhile, I think my point stands. Too many people seem to have an "OMG you don't use linear algebra every day? What kind of crap programmer are you?" attitude.
I suspect that you've had opportunities to use your math, and had you seen those opportunities you would recognize the potential utility.
I say this as someone who periodically finds yet another way to use my math background to help me do things while my co-workers in the same job don't. Which is why I'm the one who got to do the statistics for evaluating A/B testing, eliminated multiple performance problems others had come to accept, and gets tapped to tackle complex "how do we figure this out" problems from time to time.
And yes, I've had the fun of seeing co-workers who theoretically had the same job as me argue that math wasn't useful for programming, while I was sitting there with a list of examples of how I'd recently used my math background. (But then I got promoted into a different job title and in those discussions those programmers were able to respond that of course I needed more math for reporting, but they didn't need it as web developers. Never mind that I was the guy who got asked to help when the database had trouble scaling at peak traffic of several million pages/hour...)
Really this seems to me to be a variant of the blub paradox. If you haven't learned to reflexively see the benefits of thinking in some new way, you won't recognize how thinking that way could help with the problems you are solving day in and day out. Conversely if you have gained those mental skills, you recognize their utility in situations that other people wouldn't dream they are applicable for.