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As someone who has done a fair bit of both math and programming, I will agree that having some math knowledge has definitely helped at various times when progra

As someone who has done a fair bit of both math and programming, I will agree that having some math knowledge has definitely helped at various times when programming, but I don't think these specific instances (e.g. the 10 examples given in the article) constitute the primary reason it's a good idea to learn math. For the purposes of handling those specific situations, I think you would do fine to just learn the math as you encounter the need for it (and 95+% of the time you don't need anything beyond high school). To me, the primary value of math for programming is that it is a pure form of exercising many of the skills that help you write good code. For example: - fluency in logical reasoning - turning vague intuitions into precise statements (translating business requirements into code) - formalizing proofs (covering all cases, establishing invariants) - developing abstractions to succinctly describe relationships - solving a problem systematically You can also learn these skills by programming, of course, but probably not as quickly, because you will be distracted with other tasks such as debugging, setting up your dev environment, waiting for your program to run, etc. So in my opinion, what's important is not so much the immutability of the math itself, but rather the process of doing the math. I would be interested to know if others have had similar experiences.

adrianratnapala 10y ago
This comment sums up my own thinking better than I could have. Though if the pure functional approach gains more ground, the link between maths will become more direct -- writing a Haskell program feels a lot like writing a formal proof of an algorithm. And all proofs are maths. That said: this might be a reason to teach less maths in schools. If someone can invent a good informatics curriculum for children, then it's OK if it eats into class time for maths, because the (hypothetical good) IT subject will teach them some of the most skills underpinning maths.
- noelwelsh 10y ago
  Agree 100%. The strong connections between FP and maths make the programming in an FP language very much like doing maths. Usually very simple maths, but that's a good thing. You might like the Bootstrap curriculum: http://www.bootstrapworld.org/ http://www.bootstrapworld.org/ It's developed by the PLT research group behind Racket and How to Design Programs. Very good stuff.
henrik_w 10y ago
Exactly! Keith Devlin also made this point in an article (from 2003) in Communications of the ACM called "Why universities require computer science students to take math" (pdf) ftp://ftp.gunadarma.ac.id/.upload/Communication-ACM/September-2003/p36-devlin.pdf Sample quote: "Once you realize that computing is all about constructing, manipulating, and reasoning about abstractions, it becomes clear that an important prerequisite for writing (good) computer programs is the ability to handle abstractions in a precise manner."
sklogic 10y ago
Exactly. Programming is mathematics, all of it. It is not just overlaping with mathematics in few peculiar areas but it is nothing but mathematics and must be treated as such.
kaeluka 10y ago
I agree with what you say, but it seems obvious to me. On the other hand, what gets overlooked, IMO, is the "other stuff". Humanities, law, business, biology, take your pick! When faced with a problem, a programmer is always looking at at least two issues: 1. to implement, 2. to understand the problem domain. I see math being exceptionally helpful in 1), but at most somewhat helpful in 2) -- because at the end of the day, programs that we write tend not to be about math, or logic. Category theory does not help you understand the contract your company signed with some other company 12 years ago, and the amendments they made 7 years ago. It does help you implement these things concisely and correctly. What'd would help you understand would be for a programmer to know something about contracts. Most programmers that I know have a certain talent for and knowledge about math. Most programmers that I know, also don't know a lot about the world outside of computers. That includes me, fwiw. I think that their careers would profit from considering learning some non-mathematical domains more than from learning more math. I'm not arguing against math, but I'm arguing for a good balance. To know at least the basics of some other domains, before you set out to learn a lot about one.
- pigged 10y ago
  I disagree, I would say most programmers know too little math and even too little computer science. As a field we are way behind most other fields in how well we know our own field. Yet most programmers are somewhat familiar with many other fields because they spend a lot of time reading about stuff on the internet. I think the reality is the opposite of what you suggest, programmers are in no way an example of a profession where most practitioners have a deep and extensive knowledge. For most programmers, the learning method is finding out how to DO things (as in, find an example on the internet, try it, it works, I'm done) without actually understanding anything. You must be very lucky in where you work if you think programmers know a lot of math and even know what "category theory" is.
  - kaeluka 10y ago
    I don't think that reading about stuff online leads to knowledge, just like repeating writing the same boring CRUD app over and over again won't make you a much better programmer. > As a field we are way behind most other fields in how well we know our own field. I'd be surprised if that was so. I think we have a tendency to idealise other fields' achievements :) Additionally, I think you're using a scientist as a role model for a programmer. I don't think that's a good role model. Most programmers are technicians, not scientists. They produce products, not knowledge. > You must be very lucky in where you work Hm. It is the case that I'm lucky! I work at a University, in a PL group. So the people around me daily have better math foundations than most. I'll admit that there is bias in what I say.
InclinedPlane 10y ago
For me I found that having an education in math made me a better scientist, and being a better scientist made me a better developer. Having a background in mathematics makes you very sensitive to when and where assumptions get made, as well as very exacting about the line of reasoning between evidence and conclusions. It's surprising how common unchallenged assumptions can be in science, but in development work it's practically a disease. Troubleshooting and root cause analysis are extremely important parts of dev work, and it's amazing how bad the average dev is at it. Prone to jumping to conclusions and ready to blame the usual suspects even when the evidence doesn't match.

adrianratnapala 10y ago

This comment sums up my own thinking better than I could have. Though if the pure functional approach gains more ground, the link between maths will become more direct -- writing a Haskell program feels a lot like writing a formal proof of an algorithm. And all proofs are maths. That said: this might be a reason to teach less maths in schools. If someone can invent a good informatics curriculum for children, then it's OK if it eats into class time for maths, because the (hypothetical good) IT subject will teach them some of the most skills underpinning maths.

noelwelsh 10y ago
Agree 100%. The strong connections between FP and maths make the programming in an FP language very much like doing maths. Usually very simple maths, but that's a good thing. You might like the Bootstrap curriculum: http://www.bootstrapworld.org/ http://www.bootstrapworld.org/ It's developed by the PLT research group behind Racket and How to Design Programs. Very good stuff.

henrik_w 10y ago

Exactly! Keith Devlin also made this point in an article (from 2003) in Communications of the ACM called "Why universities require computer science students to take math" (pdf) ftp://ftp.gunadarma.ac.id/.upload/Communication-ACM/September-2003/p36-devlin.pdf Sample quote: "Once you realize that computing is all about constructing, manipulating, and reasoning about abstractions, it becomes clear that an important prerequisite for writing (good) computer programs is the ability to handle abstractions in a precise manner."

sklogic 10y ago

Exactly. Programming is mathematics, all of it. It is not just overlaping with mathematics in few peculiar areas but it is nothing but mathematics and must be treated as such.

kaeluka 10y ago

I agree with what you say, but it seems obvious to me. On the other hand, what gets overlooked, IMO, is the "other stuff". Humanities, law, business, biology, take your pick! When faced with a problem, a programmer is always looking at at least two issues: 1. to implement, 2. to understand the problem domain. I see math being exceptionally helpful in 1), but at most somewhat helpful in 2) -- because at the end of the day, programs that we write tend not to be about math, or logic. Category theory does not help you understand the contract your company signed with some other company 12 years ago, and the amendments they made 7 years ago. It does help you implement these things concisely and correctly. What'd would help you understand would be for a programmer to know something about contracts. Most programmers that I know have a certain talent for and knowledge about math. Most programmers that I know, also don't know a lot about the world outside of computers. That includes me, fwiw. I think that their careers would profit from considering learning some non-mathematical domains more than from learning more math. I'm not arguing against math, but I'm arguing for a good balance. To know at least the basics of some other domains, before you set out to learn a lot about one.

pigged 10y ago
I disagree, I would say most programmers know too little math and even too little computer science. As a field we are way behind most other fields in how well we know our own field. Yet most programmers are somewhat familiar with many other fields because they spend a lot of time reading about stuff on the internet. I think the reality is the opposite of what you suggest, programmers are in no way an example of a profession where most practitioners have a deep and extensive knowledge. For most programmers, the learning method is finding out how to DO things (as in, find an example on the internet, try it, it works, I'm done) without actually understanding anything. You must be very lucky in where you work if you think programmers know a lot of math and even know what "category theory" is.
- kaeluka 10y ago
  I don't think that reading about stuff online leads to knowledge, just like repeating writing the same boring CRUD app over and over again won't make you a much better programmer. > As a field we are way behind most other fields in how well we know our own field. I'd be surprised if that was so. I think we have a tendency to idealise other fields' achievements :) Additionally, I think you're using a scientist as a role model for a programmer. I don't think that's a good role model. Most programmers are technicians, not scientists. They produce products, not knowledge. > You must be very lucky in where you work Hm. It is the case that I'm lucky! I work at a University, in a PL group. So the people around me daily have better math foundations than most. I'll admit that there is bias in what I say.

InclinedPlane 10y ago

For me I found that having an education in math made me a better scientist, and being a better scientist made me a better developer. Having a background in mathematics makes you very sensitive to when and where assumptions get made, as well as very exacting about the line of reasoning between evidence and conclusions. It's surprising how common unchallenged assumptions can be in science, but in development work it's practically a disease. Troubleshooting and root cause analysis are extremely important parts of dev work, and it's amazing how bad the average dev is at it. Prone to jumping to conclusions and ready to blame the usual suspects even when the evidence doesn't match.