Great Reading in Computer Science | Hacker News Reader

Great Reading in Computer Science

cs.virginia.edu

52 pointspetercooper15 comments

I would add Shannon's paper from 11 years later than his thesis, "A Mathematical Theory of Communication": http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pd... .

Is it weird that I think Principia Mathematica should be on this list?

I feel that as a programmer my job is to very carefully axiomatize a little chunk of the world.

also, while I remember, Google cache (link was not workign when I came along):

http://webcache.googleusercontent.com/search?q=cache:n25iPlE...

Robert Constable gave a talk at the recent Principia Mathematica anniversary symposium [1] about its impact on computer science; the text is available online. [2] (There was a recent thread on all this. [3])

[1] http://www.srcf.ucam.org/principia/

[2] http://www.srcf.ucam.org/principia/files/rc.pdf

[3] http://news.ycombinator.com/item?id=1941966

Have you read principia mathematica?

yes, i was a philosophy major

OK. Did you quickly skim it or read it carefully and understand all the proofs? (somehow I doubt the latter, because the authors themselves said years after writing the book that 6 people had read it).

It seems to me a huge waste of time to study an antiquated system of mathematics. If you're interested in this kind of stuff, study a modern book on logic or set theory.

Neither?

I didn't quickly skim it, but I didn't understand all of the proofs either. It is a couple thousand pages, so there is a large grey area between perfect understanding and having skimmed.

'Modern' books on logic or set theory are not nearly as well constructed as Principia Mathematica. (And the interesting part for me is the way that it is constructed).

I don't think Russel and Whitehead wrote it as a textbook...

In what way is Principia Mathematica better constructed?

The way I learned mathematics seems pretty well constructed. You first learn about sets, then you build natural numbers out of sets, then the integers, then rational numbers, from the rational numbers you build real numbers via Cauchy sequences. And you can construct all of this in less time than Principia Mathematica takes to get to 1+1=2.

Set theory is generally accepted as a better foundation for mathematics than Principia's type theory, but if you wrote all those ZFC proofs with full formality they'd be pretty long too. This answer on Math Overflow is pretty indicative.

http://mathoverflow.net/questions/14356/bourbakis-epsilon-ca...

Usually mathematical arguments are relatively informal; every time you use set comprehension notation, for example, you're skipping a few steps in your proof (and note, of course, that the impredicative definitions one can use with it are open to e.g. Russell's paradox, which is why we have axiomatic set theory in the first place).

If you want to do everything perfectly formally you're better off studying a computer based theorem prover like Coq. Not only if everything proven perfectly formally, the proof is also checked by a computer. This also allows conciser proofs because the theorem prover can often generate parts of your proof.

Man, I had his "Good Quotations" page [1] bookmarked for the longest time, like seven years ago.

[1] http://www.cs.virginia.edu/~robins/quotes.html

The link hasn't worked for me since last night. I can see a cached copy, but that's it.

He didn't even include the Art of Computer Programming by Don Knuth!

Considering it's "supplemental reading" for students, maybe he uses TAOCP in his courses already so doesn't need to mention it? :)

gary numan has a more interesting website than i had thought.

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