
Great Reading in Computer Science - petercooper
http://www.cs.virginia.edu/~robins/CS_readings.html
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llimllib
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...](http://cm.bell-
labs.com/cm/ms/what/shannonday/shannon1948.pdf) .

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ohyes
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...](http://webcache.googleusercontent.com/search?q=cache:n25iPlEGp1sJ:www.cs.virginia.edu/~robins/CS_readings.html+http://www.cs.virginia.edu/~robins/CS_readings.html&cd=1&hl=en&ct=clnk&gl=us)

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jules
Have you read principia mathematica?

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ohyes
yes, i was a philosophy major

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jules
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.

~~~
ohyes
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...

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jules
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.

~~~
ionfish
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...](http://mathoverflow.net/questions/14356/bourbakis-epsilon-calculus-
notation/31778#31778)

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).

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jules
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.

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jcsalterego
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>

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

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

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

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

