2 ms·

I'm sure this course is great. Sipser is a terrific teacher and his textbook on the subject looks excellent. I used to be into the subject myself and still ha

I'm sure this course is great. Sipser is a terrific teacher and his textbook on the subject looks excellent. I used to be into the subject myself and still hang around Scott Aaronson's blog where CS nerds tend to congregate. But, I think there was an era when being a good programmer meant knowing a lot about algorithms, and the pinnacle of the programmer's art was supposed to be knowing how to write a compiler (look at the intended outline of Knuth's TAOCP as written in the 1960's: it was to be a 7 volume buildup finishing with stuff like parsers). These days, I think CS algorithms are pretty well packaged in code you can download, they're not even that relevant to most problems most of us face in our work, and being really clueful instead involves more traditional math than CS per se. This might be something like a cycle returning to where it started. I find myself wishing I knew more about probability and statistics (useful all over the place), abstract algebra (fancy type systems use it), a reasonable amount of mathematical logic (program verification), number theory (cryptography), geometry and maybe even functional analysis and PDE's (machine learning), etc. I'm probably more into math than the average programming geek but I still feel like a helpless little kid when I try to understand these topics. This is me, wagging my tail in the picture (j/k): https://www.starshipnivan.com/blog/wp-content/uploads/2009/06/lars0896.gif https://www.starshipnivan.com/blog/wp-content/uploads/2009/0... but in all sorts of areas of programming, it always seems like there is a "doorknob principle" just outside my reach. To the extent that I have any motivation to study math these days, I think the above subjects are more likely to be useful than CS theory per se. YMMV.

Hoskq 5y ago
This is why learning to work with others, getting into the right teams etc matters. We all have 6 inch chimp brains. The universe will not fit into it no matter what you do individually. Groups of chimps > Single chimp roaming the jungle in the darkness.
- throwaway81523 5y ago
  The math I mentioned is all pretty accessible to the average math grad student who wants to study it. An actual research mathematician would have a good grounding in all of it except for maybe logic. That is unfortunate since logic is important and every technical person should probably study some (i.e. the equivalent of an undergrad class where you study things like the Gödel incompleteness theorem). If I look at mathoverflow with my 6 inch brain, it somehow seems like everyone over there managed to get a 12 inch brain or larger, except under the lo.logic tag. There, tons of the questions are at the basic undergraduate level, which is good for me because I can sometimes understand them, but they are nowhere near the research level expected on the rest of that site. I do like your formulation about the 6 inch chimp brain.
  - Joan2 5y ago
    Math overflow is NOT a learning environment. Its more a Library than a School. There are many difference between those two spaces. Think about why no one, anywhere in the world, across all cultures, drops their kids of at a library instead of a school...
    - throwaway81523 5y ago
      I agree about mathoverflow not being a learning space per se, but I've learned a lot there, and I also learned a lot in libraries (probably more than I did in school).
  - hdjjhhvvhga 5y ago
    > An actual research mathematician would have a good grounding in all of it except for maybe logic. That is unfortunate since logic is important Really? I took two courses in discrete math and both started with logic. How can you move on to proofs without logic? I can't imagine a "research mathematician" without a sound basis in it.
    - throwaway81523 5y ago
      I mean mathematical logic, where you study proofs as mathematical objects, among other things. The topic used to be called "metamathematics". An old fashioned intro class would usually build up the machinery to prove Gödel's incompleteness theorem, do a little model theory, maybe some set theory, etc. I think a lower level discrete math class wouldn't touch any of this. See: https://en.wikipedia.org/wiki/Mathematical_logic https://en.wikipedia.org/wiki/Mathematical_logic

Hoskq 5y ago

This is why learning to work with others, getting into the right teams etc matters. We all have 6 inch chimp brains. The universe will not fit into it no matter what you do individually. Groups of chimps > Single chimp roaming the jungle in the darkness.

throwaway81523 5y ago
The math I mentioned is all pretty accessible to the average math grad student who wants to study it. An actual research mathematician would have a good grounding in all of it except for maybe logic. That is unfortunate since logic is important and every technical person should probably study some (i.e. the equivalent of an undergrad class where you study things like the Gödel incompleteness theorem). If I look at mathoverflow with my 6 inch brain, it somehow seems like everyone over there managed to get a 12 inch brain or larger, except under the lo.logic tag. There, tons of the questions are at the basic undergraduate level, which is good for me because I can sometimes understand them, but they are nowhere near the research level expected on the rest of that site. I do like your formulation about the 6 inch chimp brain.
- Joan2 5y ago
  Math overflow is NOT a learning environment. Its more a Library than a School. There are many difference between those two spaces. Think about why no one, anywhere in the world, across all cultures, drops their kids of at a library instead of a school...
  - throwaway81523 5y ago
    I agree about mathoverflow not being a learning space per se, but I've learned a lot there, and I also learned a lot in libraries (probably more than I did in school).
- hdjjhhvvhga 5y ago
  > An actual research mathematician would have a good grounding in all of it except for maybe logic. That is unfortunate since logic is important Really? I took two courses in discrete math and both started with logic. How can you move on to proofs without logic? I can't imagine a "research mathematician" without a sound basis in it.
  - throwaway81523 5y ago
    I mean mathematical logic, where you study proofs as mathematical objects, among other things. The topic used to be called "metamathematics". An old fashioned intro class would usually build up the machinery to prove Gödel's incompleteness theorem, do a little model theory, maybe some set theory, etc. I think a lower level discrete math class wouldn't touch any of this. See: https://en.wikipedia.org/wiki/Mathematical_logic https://en.wikipedia.org/wiki/Mathematical_logic