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So true. People at my school don't always realize that computer science isn't just about programming, it's truly a subset of mathematics.

scott_s 13y ago
HN discussion on an essay I wrote, "Computer Science is Not Math": https://news.ycombinator.com/item?id=3928276 https://news.ycombinator.com/item?id=3928276
chas 13y ago
Homotopy type theory[1] is essentially working to show that math is (or can be viewed as) an interesting application of computer science. [1] http://homotopytypetheory.org/2013/06/20/the-hott-book/ http://homotopytypetheory.org/2013/06/20/the-hott-book/
- hackinthebochs 13y ago
  Very interesting! I've often got into nasty arguments with people online when I dared to say that Computer science (Computing) was not a subset of math, but rather could be viewed more naturally as a superset. It is good to see serious academic work being done along these lines.
  - eru 13y ago
    You can have the same debate about logic and mathematics, or to some extent philosophy and mathematics.
    - kriro 13y ago
      You could throw set theory into the ring as well :)
  - davorak 13y ago
    I did not get the impression, from the blog posts, that HOTT was putting forth that CS could or is a super set of math just that it can be used as a foundation for all mathematics, just like set theory or category theory can be.
    - hackinthebochs 13y ago
      I think this is where terminology breaks down a bit, but my reading of "basis of" is taken as being loosely equivalent to saying a superset of. In this same sense, logic can be seen as the basis for all mathematics. Anything that is math is also strictly logic, hence math is a subset of logic.
      - cwzwarich 13y ago
        Mathematics existed long before logic came to explain it, and most practicing mathematicians don't care that much about formal logic or think about it in their day-to-day work. The incompleteness theorems add a further disconnect.
        hackinthebochs 13y ago
        I don't think it makes sense to say one can do mathematics without logic. Even if early math users didn't have a concept of formal logic, their mathematical reasoning was still dependent on it.
      - SatvikBeri 13y ago
        This is a fairly interesting philosophical question. Personally I view (and use) Math as a set of abstractions to understand the world, and use Mathematical Logic to help make Math more rigorous and proofs more checkable. But if it turned out that Mathematical Logic had some flaws as it is formalized today, I wouldn't throw out Probability Theory or Algebra. Instead I would seek a formalization of Mathematical Logic that made those things useful. I don't think that there's any formal system you can use as the basis of all Math, though. For example, ZFC can't talk about proper classes, but we'd like to be able to make statements about the class of all sets, and the collection of all classes, etc.
- decasteve 13y ago
  HoTT even more than that. Type theory does what you describe without the "homotopy". See: http://golem.ph.utexas.edu/category/2013/06/the_hott_book.html http://golem.ph.utexas.edu/category/2013/06/the_hott_book.ht...
  - tome 13y ago
    It will be easier to convince mathematicians that homotopy theory is maths than it will be to convince them that type theory is (in general).
chengiz 13y ago
Ok I'll bite. Why is "creating the right model for thinking about a problem and devising the appropriate mechanizable techniques to solve it" a subset of mathematics?
- RockyMcNuts 13y ago
  Computer science is the study of algorithms, information systems and anything that is computable. Mathematics is the study of formal systems, eg proofs that can be derived from axioms using algorithms, i.e. a specific type of computable system. Therefore, mathematics is a subset of computer science.
  - Retric 13y ago
    Math includes the study of non computable things. Also, Math includes chaos theory which is more than just a formal system. EX: computable numbers are a subset of all numbers. http://en.wikipedia.org/wiki/Computable_number http://en.wikipedia.org/wiki/Computable_number
    - RockyMcNuts 13y ago
      mostly kidding. but presumably the theorems about non-computable numbers are computable and therefore you're still working with computable things?
- TeMPOraL 13y ago
  Because the mathematics is basically distilled, formalized art of precise thinking. It's the art of manipulating and morphing mental models. It's as much about numbers as astronomy is about telescopes ;).
  - seanmcdirmid 13y ago
    Forming a model might not involve precise thinking, it often involves lateral thinking, at least with me. I heard that computer science was more of a subset of music than math.
mtdewcmu 13y ago
Computer science is a big tent. It's an amalgamation of a lot of different things. If you ask "Is computer science X?" the answer is usually yes.
- alexchamberlain 13y ago
  Is computer science the study of political figures of the past? No... but it is the study of validating X.

scott_s 13y ago

HN discussion on an essay I wrote, "Computer Science is Not Math": https://news.ycombinator.com/item?id=3928276 https://news.ycombinator.com/item?id=3928276

chas 13y ago

Homotopy type theory[1] is essentially working to show that math is (or can be viewed as) an interesting application of computer science. [1] http://homotopytypetheory.org/2013/06/20/the-hott-book/ http://homotopytypetheory.org/2013/06/20/the-hott-book/

hackinthebochs 13y ago
Very interesting! I've often got into nasty arguments with people online when I dared to say that Computer science (Computing) was not a subset of math, but rather could be viewed more naturally as a superset. It is good to see serious academic work being done along these lines.
- eru 13y ago
  You can have the same debate about logic and mathematics, or to some extent philosophy and mathematics.
  - kriro 13y ago
    You could throw set theory into the ring as well :)
- davorak 13y ago
  I did not get the impression, from the blog posts, that HOTT was putting forth that CS could or is a super set of math just that it can be used as a foundation for all mathematics, just like set theory or category theory can be.
  - hackinthebochs 13y ago
    I think this is where terminology breaks down a bit, but my reading of "basis of" is taken as being loosely equivalent to saying a superset of. In this same sense, logic can be seen as the basis for all mathematics. Anything that is math is also strictly logic, hence math is a subset of logic.
    - cwzwarich 13y ago
      Mathematics existed long before logic came to explain it, and most practicing mathematicians don't care that much about formal logic or think about it in their day-to-day work. The incompleteness theorems add a further disconnect.
      - hackinthebochs 13y ago
        I don't think it makes sense to say one can do mathematics without logic. Even if early math users didn't have a concept of formal logic, their mathematical reasoning was still dependent on it.
    - SatvikBeri 13y ago
      This is a fairly interesting philosophical question. Personally I view (and use) Math as a set of abstractions to understand the world, and use Mathematical Logic to help make Math more rigorous and proofs more checkable. But if it turned out that Mathematical Logic had some flaws as it is formalized today, I wouldn't throw out Probability Theory or Algebra. Instead I would seek a formalization of Mathematical Logic that made those things useful. I don't think that there's any formal system you can use as the basis of all Math, though. For example, ZFC can't talk about proper classes, but we'd like to be able to make statements about the class of all sets, and the collection of all classes, etc.
decasteve 13y ago
HoTT even more than that. Type theory does what you describe without the "homotopy". See: http://golem.ph.utexas.edu/category/2013/06/the_hott_book.html http://golem.ph.utexas.edu/category/2013/06/the_hott_book.ht...
- tome 13y ago
  It will be easier to convince mathematicians that homotopy theory is maths than it will be to convince them that type theory is (in general).

chengiz 13y ago

Ok I'll bite. Why is "creating the right model for thinking about a problem and devising the appropriate mechanizable techniques to solve it" a subset of mathematics?

RockyMcNuts 13y ago
Computer science is the study of algorithms, information systems and anything that is computable. Mathematics is the study of formal systems, eg proofs that can be derived from axioms using algorithms, i.e. a specific type of computable system. Therefore, mathematics is a subset of computer science.
- Retric 13y ago
  Math includes the study of non computable things. Also, Math includes chaos theory which is more than just a formal system. EX: computable numbers are a subset of all numbers. http://en.wikipedia.org/wiki/Computable_number http://en.wikipedia.org/wiki/Computable_number
  - RockyMcNuts 13y ago
    mostly kidding. but presumably the theorems about non-computable numbers are computable and therefore you're still working with computable things?
TeMPOraL 13y ago
Because the mathematics is basically distilled, formalized art of precise thinking. It's the art of manipulating and morphing mental models. It's as much about numbers as astronomy is about telescopes ;).
- seanmcdirmid 13y ago
  Forming a model might not involve precise thinking, it often involves lateral thinking, at least with me. I heard that computer science was more of a subset of music than math.

mtdewcmu 13y ago

Computer science is a big tent. It's an amalgamation of a lot of different things. If you ask "Is computer science X?" the answer is usually yes.

alexchamberlain 13y ago
Is computer science the study of political figures of the past? No... but it is the study of validating X.