Ask HN: Older textbooks/papers you consider classics still worth studying today? - webmaven
======
jessriedel
Claude Shannon's original 1948 paper "A Mathematical Theory of Communication"
launched the entire field of information theory. It's 50 pages, highly
readable, and pedagogical. The source of its magic is that Shannon introduces
and concretely grounds an essentially new ontological concept of vast
applicability. And it has _100,000 citations_.

[http://math.harvard.edu/~ctm/home/text/others/shannon/entrop...](http://math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf)

~~~
laxatives
This could have easily been 3-4 landmark papers, but instead its packed into
one cogent idea.

That common interview question about query autocomplete/sentence completion?
Shannon solved it and demonstrates it in this paper, almost a decade before
FORTRAN existed. New grads still struggle with that problem. PhD's still
struggle with that problem.

Pretty much every machine learning classifier is using a loss function
described in that paper.

------
erikig
"The Art of Electronics" Paul Horowitz, Winfield Hill. Electronics for people
who want to do stuff.

I loved this book as a teenager and recently got reacquainted with this after
years by the almighty AvE on youtube when he took apart this an old Helicopter
Radio/Telephone here:
[https://www.youtube.com/watch?v=6eoBj5W7Vdc](https://www.youtube.com/watch?v=6eoBj5W7Vdc)

~~~
jbay808
Great book. Do get the most recent edition, because the recommend parts in the
older ones are quite outdated.

------
The_suffocated
_Modern Higher Algebra_ by A. Adrian Albert (1937, Dover/Cambridge). It covers
both abstract algebra and linear algebra.

Most modern textbooks tend to approach linear algebra from geometric
perspectives. Albert's text is one of the few that introduce the subject in a
purely algebraic approach. With a solid algebraic foundation, the author was
able to produce some elegant proofs or results that you don't often see in
modern texts.

E.g. Albert's proof of Cayley-Hamilton theorem is essentially a one-liner.
Some modern textbooks (such as Jim Hefferon's _Linear Algebra_ ) try to
reproduce the same proof, but without setting up the proper algebraic
framework, their proofs become much longer and much harder to understand.
Readers of these modern textbooks may not realize that the theorem is simply a
direct consequence of Factor Theorem for polynomials over non-commutative
rings.

With only about 300 pages, the book's coverage is amazingly wide. When I first
read the table of content, I was surprised to see that it not only covers
undergraduate topics such as group, ring, field and Galois theory, but also
advanced topics such as p-adic numbers. I haven't read the part on abstract
algebra in details. However, if you want to re-learn linear algebra, this book
may be an excellent choice.

~~~
jimhefferon
Sorry about that. I shall try to do better.

~~~
The_suffocated
For those who are reading this, let me stress that it is not that Prof.
Hefferon's proof of Cayley-Hamilton theorem is bad (it is actually better than
some really horrible proofs that appear in some well-received textbooks), but
that Albert's treatment is superb --- it is far better than the treatments of
the theorem in most modern textbooks, including Prof. Hefferon's. Also, I was
certainly not commenting on the overall quality of Prof. Hefferon's book, and
I thank him for offering his textbook for free.

~~~
jimhefferon
Oh, forgive me, no offense taken. I should have put a smiley. I read your post
with interest and shall check out the book.

(As you no doubt know, different books have different audiences. Before I
wrote my Linear book, when I looked at the available textbooks I thought that
there were low-level computational books that suited people with weak
backgrounds, and high-level beautiful books that show the power of big,
exciting, ideas. I had a room with students who were not ready for high. I
wrote the book hoping that it could form part of an undergraduate program that
deliberately worked at bringing students along to where they would be ready
for such things. Naturally, with that mindset I read your post as meaning that
the audience for the book you described is just different. Anyway, thanks
again for the pointer.)

------
glun
When I was an undergrad (enrolled in 2011) I decided to screw my professors
book recommendations and lookup what the internet seemed to think was the best
book in each subject and read that instead. Most of them were fairly old. Some
examples that I remember off the top of my head:

Intro to CS: SICP (1979)

Algorithms/data structures: CLRS (1989)

Theory of computation: Sipser (1996)

Compilers: Dragon book (1986)

Calculus: Spivak (1967)

Linear Algebra: Dover's by Shilov (1971)

The given year is for the first publication, some of them are still being
updated and I probably read a newer edition.

------
NerDProgrammer
Code: The Hidden Language of Computer Hardware and Software by Charles
Pretzold

Reading the book is the most beautiful and simple way that a person can really
understand what a computer and come to the realization that it is not black
magic.

[https://www.amazon.com/Code-Language-Computer-Developer-
Prac...](https://www.amazon.com/Code-Language-Computer-Developer-Practices-
ebook/dp/B00JDMPOK2)

------
jamieweb
This is a famous one from 1999 - "Why Johnny Can't Encrypt" [1]

There's a couple of follow-ups too, such as "Why Johnny Still Can't Encrypt"
[2], and "Why Johnny Still, Still Can't Encrypt" [3].

[1]
[https://people.eecs.berkeley.edu/~tygar/papers/Why_Johnny_Ca...](https://people.eecs.berkeley.edu/~tygar/papers/Why_Johnny_Cant_Encrypt/OReilly.pdf)

[2] [https://cups.cs.cmu.edu/soups/2006/posters/sheng-
poster_abst...](https://cups.cs.cmu.edu/soups/2006/posters/sheng-
poster_abstract.pdf)

[3] [https://arxiv.org/abs/1510.08555](https://arxiv.org/abs/1510.08555)

------
bookofjoe
"There's Plenty of Room at the Bottom"—Richard P. Feynman (1959)
[http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/Feynman'...](http://www.phy.pku.edu.cn/~qhcao/resources/class/QM/Feynman's-Talk.pdf)

"Zen in the Art of Archery" — Eugen Herrigel
(1953)[http://www.ideologic.org/files/Eugen_Herrigel_-
_Zen_in_the_A...](http://www.ideologic.org/files/Eugen_Herrigel_-
_Zen_in_the_Art_of_Archery.pdf)

"What is it like to be a bat?" — Thomas Nagel (1974)
[https://organizations.utep.edu/portals/1475/nagel_bat.pdf](https://organizations.utep.edu/portals/1475/nagel_bat.pdf)

"The Tragedy of the Commons" — Garrett Hardin (1968)
[https://www.hendrix.edu/uploadedFiles/Admission/GarrettHardi...](https://www.hendrix.edu/uploadedFiles/Admission/GarrettHardinArticle.pdf)

------
yantrams
World of Mathematics - An amazing compendium of accessible content straight
from the masters - Poincare, Jonathan Swift, Neumann, Bishop Berkeley, Cayley
etc [https://www.amazon.com/World-Mathematics-James-Newman-
Hardco...](https://www.amazon.com/World-Mathematics-James-Newman-
Hardcover/dp/B011SKBVXK) I believe it is available on archive.org

What Is Mathematics? by Richard Courant and Herbert Robbins published in 1941.
One of the most beginner friendly yet rigorous books out there for a survey of
many areas in mathematics.

You can find hundreds of gems here from erstwhile Soviet Union -
[https://mirtitles.org/](https://mirtitles.org/)

------
mises
K&R C is still an excellent resource for learning. C may not be the flashiest
new thing, but it's still a very useful skill to have.

~~~
ternaryoperator
For sure get the second edition. The first edition is way, way out of date.

~~~
wglb
But the typesetting took such a dive downhill!

------
atrocious
PAIP - Norvig 1992. It appears to be available online
[https://github.com/norvig/paip-lisp](https://github.com/norvig/paip-lisp)

~~~
throwaway487548
Yes, this is the classic. PDF could be found in bittorrent

------
peterkelly
Structure and Interpretation of Computer Programs (SICP)

[https://mitpress.mit.edu/sites/default/files/sicp/index.html](https://mitpress.mit.edu/sites/default/files/sicp/index.html)

------
whiskers
Computer Graphics: Principles and Practice in C (2nd Edition) is an incredibly
deep look at the cutting edge of computer graphics technology as it stood in
the late 1980s.

It's full of beautiful renderings and diagrams, covers the core algorithms of
2D and 3D graphics, introduces the mathematics required, and many other
related subjects such as user interface design.

Apparently there is a 3rd edition from 2013 which looks at modern GPU-based
rendering, though I don't own a copy.

[https://en.wikipedia.org/wiki/Computer_Graphics:_Principles_...](https://en.wikipedia.org/wiki/Computer_Graphics:_Principles_and_Practice)

~~~
garmaine
I’ve studied both. They are totally different books. The 2nd edition is the
“Art of Computer Programming” for computer graphics. The 3rd edition is a
fantastic overview of GPU based graphics libraries (the fundamentals not the
APIs). Which is to say, they have almost nothing in common.

------
sah2ed
_The Structure of Scientific Revolutions_ (1962) by Thomas Kuhn is a fantastic
book that explores the history of science while also debunking the commonly
held belief that discoveries (of gravity, oxygen gas etc) are instantaneous
observations, instead of a gradual weaving together of several seemingly
contradicting observations.

[https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re...](https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Revolutions)

------
jupiter90000
I worked with an ex-ecology professor on some 'data science' projects at work,
who suggested this older book I enjoyed called "The Ecological Detective:
Confronting Models with Data." Good read imho for ideas about generating
hypotheses, exploring data, and comparing models to explain the data, and not
just in ecology (though that is the context obviously).

[https://press.princeton.edu/titles/5987.html](https://press.princeton.edu/titles/5987.html)

------
ilovecaching
If you haven’t read all of the Turing award papers yet, I highly recommend
forming a study group if you can and working from the beginning.

~~~
epsilon-greedy
Where can I find a list of those papers? I just spent a minute trying to find
something using Google but didn't manage to find anything

~~~
pmcjones
[https://amturing.acm.org/alphabetical.cfm](https://amturing.acm.org/alphabetical.cfm)
links to a page for each awardee, with a link to their lecture.

~~~
epsilon-greedy
Thanks a lot! I totally overlooked the lecture links

------
superasn
The art of getting money (1) by PT Barnum is definitely one of those books.
Even though written in 1880 most of the advice transcends time and technology
and still evergreen as ever.

(1)
[https://books.google.co.in/books/about/Art_of_Money_Getting....](https://books.google.co.in/books/about/Art_of_Money_Getting.html?id=pEbnX5JO7QcC&printsec=frontcover&source=kp_read_button&redir_esc=y)

------
bookofjoe
"Science and Sanity" — Alfred Korzybski (1933)
[http://pialogue.info/books/Science-and-Sanity-
Korzybski.pdf](http://pialogue.info/books/Science-and-Sanity-Korzybski.pdf)

"The Presentation of Self in Everyday Life" — Erving Goffman (1956)
[https://monoskop.org/images/1/19/Goffman_Erving_The_Presenta...](https://monoskop.org/images/1/19/Goffman_Erving_The_Presentation_of_Self_in_Everyday_Life.pdf)

~~~
alok-g
It would help to read your commentary on these.

~~~
yesenadam
Well, I don't know if mine will help. I love Goffman's book, it's super-
readable, enlightening. It's about the different roles and..settings people
operate in, and the rules and customs of those places, e.g. backstage,
shopfront, military ranks, hospitality etc. Full of great stories quoted from
an impressive number of sources, very diverse.

Korzybski's book used to be huge, recommended by all kinds of famous people. I
spent a few hours reading in it one day, to see for myself. (Plus had heard a
fair bit about it before.) Korzybski basically seems a huge crank, who thought
himself and his baby General Semantics[0] as important as Aristotle. The quote
one always hears from it is "the map is not the territory", and well, that's
about the only thing worth quoting from it. Plus he tried to get rid of "is"
from the language, i.e. "A is B".[1] Seemingly because such sentences are
deceptive - if you say "The car is red", well, it's many things besides red,
so the sentence is a lie is many ways. It's a very strange objection. As if
it's bad because it doesn't say everything, just one thing. Aristotle he's
not.

Also there's an interesting contraption featured in the book, made of metal
with holes, strings, plugs, used to make maps of levels of concepts. I don't
know if it's practically useful.

Apart from that, what makes it a big slab of a book, are a host of chapters on
different academic subjects serving as introductions to those subjects, e.g.
one on maths, calculus I think, supposedly illustrating general semantics
applied there. These seem mostly intended to give the impression Korzybski is
a genius polymath. People who didn't know anything about that subject might
learn something from that, and feel the book taught them something. But it's
nothing to do with Korzybski's theories.

[0]
[https://en.wikipedia.org/wiki/General_semantics](https://en.wikipedia.org/wiki/General_semantics)

[1] This was extended by a student of Korzybski's to E-Prime, a language
without any form of the verb 'to be'.
[https://en.wikipedia.org/wiki/E-Prime](https://en.wikipedia.org/wiki/E-Prime)

------
abecedarius
[http://www.feynmanlectures.caltech.edu/](http://www.feynmanlectures.caltech.edu/)

------
ianai
Not sure you’re looking for philosophy, but I keep a translation of the Tao Te
Ching nearby at all times. It’s helped me stay centered and humble.

Just to go meta: whatever book you learned something from originally/in
college you should keep. It might not always be the best, but keeping the
context of your original understanding can really help and speed up
recollection when needed. (This probably applies most to textbooks used for
whole classes as opposed to minor topic references.)

~~~
otohp
Good idea! I am a complete sucker for tracking down CS textbooks from my
courses 20 plus years ago. And I like the hard copy versions. My outlook is,
an engineer is known by the books he keeps.

------
ggaughan
A Relational Model of Data for Large Shared Data Banks (1970)

E. F. CODD

[https://www.seas.upenn.edu/~zives/03f/cis550/codd.pdf](https://www.seas.upenn.edu/~zives/03f/cis550/codd.pdf)

~~~
dwd
Nice choice.

I would add: An Introduction to Database Systems - Date

Also a few unmentioned so far: Discrete Mathematical Structures - Kolman

Introduction To Systems Analysis And Design - Hawryszkiewycz

Modern Operating Systems - Tanenbaum

------
yekanchi
How Computers Work By Roger Young, Here is an online version:
[http://www.fastchip.net/howcomputerswork/p1.html](http://www.fastchip.net/howcomputerswork/p1.html)

anytime worth reading, simply tells you how everything in a computer work like
memory and processor.

------
ohiovr
Mechanics and Thermodynamics of propulsion by Peterson and Hill explains most
of the rocketry systems still in use today and the first edition was published
in 1965. I think it is interesting that fundamental boost rocketry has changed
very little since that time.

------
ww520
The Dragon book - Compilers. I got more out of it reading it after using it in
a university course.

------
bigtimber
Previous posts have nicely covered almost all of the textbooks and papers I
would have mentioned myself, including K&R's _C Programming_, Brooks'
_Mythical Man-Month_, Feynman's Lectures, etc. The only glaring omission was
any mention of the classic (1965) FFT paper by Cooley and Tukey: "An algorithm
for the machine calculation of complex Fourier series." _Mathematics of
Computation_, 19(90), 297–297. doi:10.1090/s0025-5718-1965-0178586-1
([https://www.eit.lth.se/fileadmin/eit/courses/eit085f/Cooley_...](https://www.eit.lth.se/fileadmin/eit/courses/eit085f/Cooley_Tukey_An_Algorithm_for_the_Machine_Calculation_of_Complex_Fourier_Series_Math_of_Comp_1965.pdf))
I might also have added the _CRC Handbook of Chemistry and Physics_ that seems
to have been on every working scientists's and engineer's bookshelf (including
mine) during the mid-to-late 20th century. Still in print, nearing the 100th
edition. Also, some of my old favorite textbooks that I used at University
were not mentioned, including Thomas' _Calculus and Analytical Geometry_. I
still have my red cloth covered Addison-Wesley 3rd edition, no longer in
print, but a much later edition might still be in print.

------
chomp
Very famous paper, one of my favorites -
[https://en.m.wikipedia.org/wiki/No_Silver_Bullet](https://en.m.wikipedia.org/wiki/No_Silver_Bullet)

------
ronald_raygun
Euclid's Elements was a pretty foundational text. Also Philosophiæ Naturalis
Principia Mathematica

~~~
keithpeter
Chandrasekhar's _" Newton's_ Principia _for the common reader "_ is a reading
of Newton's book in modern mathematical notation and with commentary on the
methods Newton was using.

------
cozybear18
"Reflections on Trusting Trust" (1984) by Ken Thompson

------
ChuckMcM
"The Design of the UNIX operating system" by Bach holds up well. Feynman's
lectures on physics (3 volume set). Electrodynamics by Jackson is also up
there.

------
jharohit
Something I had read long time ago and also recently recommended by Ed Witten
is John Wheeler's essay - "INFORMATION, PHYSICS, QUANTUM: THE SEARCH FOR
LINKS" also famously known as the "It from Bit"essay (which now probably is
"It from Q-bit" as our current understanding).

[http://cqi.inf.usi.ch/qic/wheeler.pdf](http://cqi.inf.usi.ch/qic/wheeler.pdf)

------
dr_dshiv
"Mathematics Useful for Understanding Plato", 100AD, by Theon of Smyrna.
Amazing.

------
DyslexicAtheist
_" An incomplete list of classic papers every Software Architect should
read"_, [https://blog.valbonne-consulting.com/2014/06/09/an-
incomplet...](https://blog.valbonne-consulting.com/2014/06/09/an-incomplete-
list-of-classic-papers-every-software-architect-should-read/)

------
emmanueloga_
[1] is a repo of papers people...love. Maybe you can grep for dates to find
the older ones. The nice thing is that they are sorted by category.

1: [https://github.com/papers-we-love/papers-we-
love](https://github.com/papers-we-love/papers-we-love)

------
charlysl
"On the criteria to be used in decomposing systems into modules" (1972) -
because the core principles of modularity haven't changed
[[https://www.win.tue.nl/~wstomv/edu/2ip30/references/criteria...](https://www.win.tue.nl/~wstomv/edu/2ip30/references/criteria_for_modularization.pdf)]

"The Mythical Man Month" (1975) - because human nature hasn't changed
[[https://www.amazon.com/Mythical-Man-Month-Software-
Engineeri...](https://www.amazon.com/Mythical-Man-Month-Software-Engineering-
Anniversary/dp/0201835959)]

"The History of Fortran I, II, and III" (1979) - because this historical piece
by the author of the first high level language brings home the core principles
of language design [[https://archive.org/details/history-of-
fortran](https://archive.org/details/history-of-fortran)]

"The Unix Programming Environment" (1984) - because the core basics of the
command line haven't changed [[https://www.amazon.com/Unix-Programming-
Environment-Prentice...](https://www.amazon.com/Unix-Programming-Environment-
Prentice-Hall-Software/dp/013937681X)]

"Reflections on Trusting Trust" (1984) - because the basic concepts of
software security haven't changed
[[https://www.archive.ece.cmu.edu/~ganger/712.fall02/papers/p7...](https://www.archive.ece.cmu.edu/~ganger/712.fall02/papers/p761-thompson.pdf)]

"The Rise of Worse is Better" (1991) - because many of the tradeoffs to be
made when designing systems haven't changed [[https://www.jwz.org/doc/worse-
is-better.html](https://www.jwz.org/doc/worse-is-better.html)]

"The Art of Doing Science and Engineering: Learning to learn" (1996) - because
the core principles that drive innovation haven't changed
[[https://www.youtube.com/playlist?list=PL2FF649D0C4407B30](https://www.youtube.com/playlist?list=PL2FF649D0C4407B30)]
[[https://www.amazon.com/Art-Doing-Science-Engineering-
Learnin...](https://www.amazon.com/Art-Doing-Science-Engineering-
Learning/dp/9056995006)]

"xv6" (an x86 version of Lion's Commentary, 1996) - because core OS concepts
haven't changed
[[https://pdos.csail.mit.edu/6.828/2011/xv6/xv6-rev6.pdf](https://pdos.csail.mit.edu/6.828/2011/xv6/xv6-rev6.pdf)]
[[https://pdos.csail.mit.edu/6.828/2014/xv6/book-
rev8.pdf](https://pdos.csail.mit.edu/6.828/2014/xv6/book-rev8.pdf)]

------
plaguna
Smashing The Stack For Fun And Profit by Aleph One -
[http://phrack.org/issues/49/14.html](http://phrack.org/issues/49/14.html)

------
georgecalm
Structured design by W.P. Stevens, G.J. Myers, and L.L. Constantine

------
galfarragem
On politics and management:

'The prince' \- Machiavelli (early 16th century)

~~~
charlysl
Best book I know to understand how the world really works. Here is a link to
an abridged version:
[http://sqapo.com/machiavelli.htm](http://sqapo.com/machiavelli.htm)

------
m4lvin
Edmund L. Gettier: Is Justified True Belief Knowledge? (1963)

[http://www.ditext.com/gettier/gettier.html](http://www.ditext.com/gettier/gettier.html)

[https://doi.org/10.1093/analys/23.6.121](https://doi.org/10.1093/analys/23.6.121)

------
martinlaz
Alan Turing's "Computing Machinery and Intelligence" (1950). Describes the
"Imitation Game", aka Turing test.

[https://en.wikipedia.org/wiki/Computing_Machinery_and_Intell...](https://en.wikipedia.org/wiki/Computing_Machinery_and_Intelligence)

------
spindle
L.J. Savage, Foundations of Statistical Inference, 1962

and (if this counts as old) Berger and Wolpert, The Likelihood Principle, 1984

------
OJFord
Turing _On computable numbers, with an application to the
Entscheidungsproblem_ (1936)

Sipser's _Intro to the theory of computation_ (1996; 3e in print)

Aho, Sethi, & Ullman's _Compilers: principles, techniques, and tools_ - 'the
dragon book' \- (1986; 2e in print)

Various authors' _Handbook of theoretical CS_ (2 volumes, 1990-1)

------
m0rc
Hamming, Richard R. Art of doing science and engineering: Learning to learn.
CRC Press, 2014.

...and for papers, I like the curated list in Fermat's Library:
[https://fermatslibrary.com/journal_club](https://fermatslibrary.com/journal_club)

------
graycat
Evar D. Nering, _Linear Algebra and Matrix_ Linear Algebra and Matrix Theory*

Kenneth Hoffmann And Ray Kunze. _Linear Algebra_ , 2nd Edition, Prentice-Hall,
Englewood Cliffs, New Jersey, 1971.

[https://www.zuj.edu.jo/download/linear-algebra-2nd-
edition-k...](https://www.zuj.edu.jo/download/linear-algebra-2nd-edition-
kenneth-hoffmann-and-ray-kunze-pdf/)

Halmos, _Finite Dimensional Vector Spaces_

George E. Forsythe and Cleve B. Moler, _Computer Solution of Linear Algebraic
Systems_

Paul R. Halmos, _Naive Set Theory_ , Van Nostrand, Princeton, NJ, 1960.

More has been done since this book, but this book is a gorgeous introduction
to _axiomatic set theory_. So, even people who want to dig into the latest
work would do well to have this as the first book. And for people wanting to
read any of the more advanced material here, knowledge of this book will be
from good to have to important.

[https://piazza-
resources.s3.amazonaws.com/is25bi6c6o1oh/isv1...](https://piazza-
resources.s3.amazonaws.com/is25bi6c6o1oh/isv14pknyni2z3/Halmos_NaiveSetTheory.pdf?X-Amz-
Algorithm=AWS4-HMAC-SHA256&X-Amz-
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Walter Rudin, _Principles of Mathematical Analysis_

The third edition is a lot better than the first two.

H. L. Royden, _Real Analysis: Second Edition_

Beautifully written, elegant, but maybe don't work way too hard on the
exercises about upper/lower semi-continuity, and there is a better summary
than Littlewood's three principles.

Bernard R. Gelbaum and John M. H. Olmsted, _Counterexamples in Analysis_

John C. Oxtoby, _Measure and Category: A Survey of the Analogies between
Topological and Measure Spaces_

Walter Rudin, _Real and Complex Analysis_

Walter Rudin, _Functional Analysis_

Leo Breiman, _Probability_

Kai Lai Chung, _A Course in Probability Theory, Second Edition_

Jacques Neveu, _Mathematical Foundations of the Calculus of Probability_

Erhan Cinlar, _Introduction to Stochastic Processes_

J. L. Doob, _Stochastic Processes_

I. I. Gihman and A. V. Skorohod, _The Theory of Stochastic Processes I, II_

Donald E. Knuth, _The TeX book_

Donald E. Knuth, _The Art of Computer Programming,_ Second Edition

Leo Breiman, "Statistical Modeling: The Two Cultures," _Statistical Science_ ,
Vol. 16, No. 3, 199–231, 2001.

Paul R. Halmos, "The Theory of Unbiased Estimation", _Annals of Mathematical
Statistics_ , Volume 17, Number 1, pages 34-43, 1946.

Paul R. Halmos and L. J. Savage, "Application of the Radon-Nikodym Theorem to
the Theory of Sufficient Statistics", _The Annals of Mathematical Statistics_
, Volume 20, Number 2 (1949), 225-241.

[https://projecteuclid.org/download/pdf_1/euclid.aoms/1177730...](https://projecteuclid.org/download/pdf_1/euclid.aoms/1177730032)

~~~
graycat
Here are URLs of PDFs of two of the references above:

Leo Breiman, "Statistical Modeling: The Two Cultures," _Statistical Science_ ,
Vol. 16, No. 3, 199–231, 2001.

[http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?vi...](http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ss/1009213726)

Paul R. Halmos, "The Theory of Unbiased Estimation", Annals of Mathematical
Statistics, Volume 17, Number 1, pages 34-43, 1946.

[https://projecteuclid.org/download/pdf_1/euclid.aoms/1177731...](https://projecteuclid.org/download/pdf_1/euclid.aoms/1177731020)

~~~
nextos
_Finite Dimensional Vector Spaces_ is a jewel. But I wish the typesetting was
updated to something more modern. Same applies to Rudin.

I find well typeset TeX a joy to read. Whereas FDVS is a bit cramped and looks
antique.

~~~
graycat
FDVS was written in 1942 when Halmos had just gotten his Ph.D. from J. Doob,
author of _Stochastic Processes_ in my list, at U. Illinois, and was an
assistant to John von Neumann at the Institute of Advanced Study in Princeton.

IIRC _Hilbert space_ was a von Neumann idea: It is first, just a definition --
complete inner product ( _dot_ product in much of physics and engineering)
space. But the good stuff is (1) importance of the examples and (2) the
theorems that show the consequences, e.g., in Fourier theory.

Well, the vector spaces of most interest in linear algebra are actually (don't
tell anyone) finite dimensional Hilbert spaces. So, one role of FDVS is to
provide a text on linear algebra that is also an introduction to Hilbert
space, that is, that tries to use ideas that work in any Hilbert space to get
the basic results in linear algebra.

The treatment of self-adjoint transformations and spectral theory are likely
the most influenced by this role.

This role is accomplished so well that sometimes physics students starting on
quantum mechanics are advised to get at least the start they need on Hilbert
space from FDVS.

Sure, a better start is the one chapter on Hilbert space in Rudin's _Real and
Complex Analysis_. The chapter there on the Fourier transform is also good,
short, all theorems nicely proved, the main, early results made clear.

Also a good start on the basic results of self-adjoint matrices are the
inverse and implicit function theorems given as nice exercises in the third
edition of Rudin's _Principles ..._. And spectral theory is in Rudin's
_Functional Analysis_. Also get a bonus of a nice treatment of distributions,
that is, replace the Dirac delta function usage in quantum mechanics.

For how to get the eigen value and orthogonal eigen vector results for self-
adjoint matrices from the inverse and implicit (these two go together like ice
cream and cake) function theorems is in Fleming, _Functions of Several
Variables_. Then you will be off and running on factor analysis, principle
components, the polar decomposition, the singular value decomposition, and
more.

------
nprateem
Tao te Ching. If you like that there's also the Art of War and Book of Five
Rings.

------
alok-g
I once read original works of Sir William Rowan Hamilton and was amazed at the
clarity of thought he demonstrated, a truly open mind to understanding nature.

Books by Max Born (Atomic Physics, and Theory of Relativity) are absolute
awesomness.

------
Crontab
"The Unix Programming Environment" would be my choice. Love it.

------
huffmsa
I didn't "get" calculus until I went and read the Principia.

In other fields, the Standardized Barbers Manual (for barbers) and The Modern
Tailor Outfitter And Clothier (tailoring) are still extremely relevant

------
oceanghost
General Chemistry by Linus Pauling.

Zen and the Art of Motorcycle Maintenance (Philosophy).

~~~
The_suffocated
Several reviewers at Amazon said that General Chemistry is unsuitable for
beginners or self-learners. Is that true?

------
usgroup
It’s funny , I get the feeling that 50% of the contributors on this thread are
would-be philosophers :)

Gettier cases and the life and times of a bat are far less interesting to
“civilians” ;)

------
pmalynin
Differential geometry of curves and surfaces by Do Carmo

------
casper345
"Computable numbers with an application to the Entscheidungsproblem" \- Alan
Turing

------
tigerlily
Gravitation, by Charles W. Misner, Kip S. Thorne, and John Archibald

------
JDWolf
The Works of Archimedes by Sir Thomas Heath

------
YeGoblynQueenne
A couple of papers on my reading list:

From information theory:

    
    
      A mathematical theory of communication (information theory, Claude E. Shannon) [1]
      Three approaches to the quantitative definition of information (A. N. Kolmogorov) [2]
    

And from inductive inference and computational learning theory:

    
    
      A formal theory of inductive inference (Ray Solomonoff, 1964) [3]
      Language identification in the limit (Mark E. Gold, 1967) [4]
      Inductive Inference of formal languages from positive data (Dana Angluin, 1980) [5]
      A theory of the learnable (PAC learning, Leslie Valiant, 1984) [6]
      Occam's Razor (Blumer et al, 1987) [7]
    

Bonus: a deep learning paper

    
    
      Long Short-Term Memory (Hochreiter and Schmidhuber, 1997)
    

The first two papers - well, one launched information theory and the other is
Kolmogorov's paper where he introduced the idea of Kolmogorov complexity.

The second batch of papers start with Solomonoff's inductive inference papers,
kinda important if you want to learn things from other things. Mark Gold's
paper proves that it is impossible to learn a non-finite automaton from
examples. Dana Angluin's follow up extends this with learnability results
about various classes of CFG. Any time someone claims that their deep neural
net has learned a CFG, point them to these two papers.

Valiant's paper is the theroy of machine learning as we know it today. It
basically relaxes the assumptions made in inductive inference and introduces
the notion of error. If you can't learn some concept perfectly, what degree of
error is likely from some set of training data? Blumer's paper discusses a
further bound on that amount of error that follows an Occamist bias (simplest
truths are better) and is a basis for understanding overfitting (error
increases as the hypothesis space does).

These two sets of papers probably look disconnected - but, learning is
compression. Compression, with generalisation, I guess. Anyway, no, they're
not unrelated.

The final paper is the one that introduced LSTMs and the, er, "constant error
carousel" (the solution to vanishing gradients, which this paper is worth
reading for).

These are papers that one must read if they're interested in machine learning.
Carefully so. They're not even "old" papers- more like, essential ones.

I'm totally omitting a whole bunch of others, obviously.

___________

Online pdfs (not all free):

[1]
[http://www.math.harvard.edu/~ctm/home/text/others/shannon/en...](http://www.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf)

[2] [http://alexander.shen.free.fr/library/Kolmogorov65_Three-
App...](http://alexander.shen.free.fr/library/Kolmogorov65_Three-Approaches-
to-Information.pdf)

[3.1]
[https://www.sciencedirect.com/science/article/pii/S001999586...](https://www.sciencedirect.com/science/article/pii/S0019995864902232)
(Part 1)

[3.2]
[https://www.sciencedirect.com/science/article/pii/S001999586...](https://www.sciencedirect.com/science/article/pii/S0019995864901317)

[4]
[https://www.sciencedirect.com/science/article/pii/S001999586...](https://www.sciencedirect.com/science/article/pii/S0019995867911655)

[6] [http://www-personal.umich.edu/~yinw/papers/Angluin80.pdf](http://www-
personal.umich.edu/~yinw/papers/Angluin80.pdf)

[7]
[https://www.sciencedirect.com/science/article/pii/0020019087...](https://www.sciencedirect.com/science/article/pii/0020019087901141)

------
nso95
Calculus made easy

------
franze
K&R

