My view is quite unconventional, but I believe, computer science is a branch of mathematics that deals with large but finite structures (so they need an algorithmic description). Compare with most of "legacy" mathematics, which studies countable structures (so the description can use arbitrary series). Of course, there are larger sets, but they mostly serve as a theater (just like countable infinity is just a theater…
This is a strange claim since the entire field was founded upon the investigation of potentially (and often actually) infinite computations.
> Compare with most of "legacy" mathematics, which studies countable structures (so the description can use arbitrary series).
Define "most". Do it in a way that makes real and complex analysis and topology (and probably many other branches) the smaller part of mathematics.
Most importantly though, my problem with this kind of discussion is that the question itself is meaningless. Not everything can be classified into neat " X is a Y" relationships. Not everything needs to be classified into such relationships. Even if the discussion reached a consensus, that consensus would be meaningless. Computer science is a part of math? OK, but so what? Computer science is not a part of math? OK, but so what? Neither conclusion would tell us anything useful.