17.649 history of 20C mathematics

From: Humanist Discussion Group (by way of Willard McCarty willard.mccarty@kcl.ac.uk)
Date: Mon Feb 16 2004 - 03:51:15 EST

               Humanist Discussion Group, Vol. 17, No. 649.
       Centre for Computing in the Humanities, King's College London
                     Submit to: humanist@princeton.edu

   [1] From: "Friedrich Heberlein" <friedrich.heberlein@ku- (18)
         Subject: Re: History of Mathematics

   [2] From: "Jim Marchand" <marchand@ux1.cso.uiuc.edu> (26)
         Subject: 20th C. Math

   [3] From: "Luigi M Bianchi" <lbianchi@yorku.ca> (55)
         Subject: Re: 17.647 history of 20C mathematics?

   [4] From: Matt Kirschenbaum <mk235@umail.umd.edu> (6)
         Subject: Re: 17.647 history of 20C mathematics?

   [5] From: "S.A.Rae" <S.A.Rae@open.ac.uk> (39)
         Subject: RE: 17.647 history of 20C mathematics?

         Date: Mon, 16 Feb 2004 08:43:50 +0000
         From: "Friedrich Heberlein" <friedrich.heberlein@ku-eichstaett.de>
         Subject: Re: History of Mathematics

A colleague of mine suggests:

"From Dedekind to Gödel: Essays on the Development of the Foundations
of Mathematics", Jaako Hintikka, ed., 1995

"The Limits of Mathematics", Gregory J. Chaitin, 1998

"Companion Encyclopedia of the History and Philosophy of the
Mathematicals Sciences", 2 Vols., Ivor Grattan-Guinness, ed, 1994

"Moderne-Sprache-Mathematik", Herbert Mehrtens, 1990

"Gödel, Escher, Bach: An eternal golden braid", Douglas R.
Hofstadter, 1979

"Mathematical thought from ancient to modern times", Morris Kline,


Fritz Heberlein

Dr. Friedrich Heberlein, Akad. Direktor
Seminar für Klassische Philologie,  KU Eichstaett-Ingolstadt
Universitaetsallee 1
D-85071 Eichstaett / Bayern

--[2]------------------------------------------------------------------ Date: Mon, 16 Feb 2004 08:44:18 +0000 From: "Jim Marchand" <marchand@ux1.cso.uiuc.edu> Subject: 20th C. Math

Everything, as is always is true in history, is quite out of date, Willard, but I would start with:

1. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, ed. Ivor Grattan-Guinness. 2 vols. (London: Routledge, 1994).

2. A somewhat shorter history, by the same author: The Norton History of the Mathematical Sciences: the rainbow of mathematics (NY: Norton, 1998). 817 pp.

3. Also good: Carl B. Boyer, A History of Mathematics, 2d ed. (NY: Wiley, 1989). 762 pp.

If these are not suitable, there is a good deal available through the internet:

1. http://archives.math.utk.edu from the University of Tennessee is very useful and has a section on the history of math.

2. http://www.sub.uni-goettingen.de/ssgfi/math/singleindex.html from Goettingen is also good, and you can search it by using the American Math Society's subject classification.

These will lead you to various databases, though there are printed collections which are perhaps better. My (and everybody's) favorite is James R. Newman, ed., The World of Mathematics. 4 vols. (NY: Simon and Schuster, 1956). Turing is found 2099-2123, surrounded by von Neumann and Shannon. One often found the computer called a Turing machine, though I would think Shannon would have a better call on being called its inventor.

If anyone wants early and medieval math, he will need to look also at Smith, Heath, et al.

--[3]------------------------------------------------------------------ Date: Mon, 16 Feb 2004 08:44:38 +0000 From: "Luigi M Bianchi" <lbianchi@yorku.ca> Subject: Re: 17.647 history of 20C mathematics?

Dear Willard,

as a very modest starting point, you may want to look at

"From Hollerith to Turing" <http://www.yorku.ca/sasit/sts/nats1700/lecture09.html>


"The Turning Point" <http://www.yorku.ca/sasit/sts/sts3700b/lecture14a.html>

These are two lectures I prepared for a couple of courses I teach: "Computers, Information and Society" and "History of Computing and Information Technology," respectively. They are simple outlines, but I hope they may be of some use.

Best regards,

Luigi M Bianchi

Luigi M Bianchi Science and Technology Studies Room 2048 TEL Building York University, 4700 Keele St, Toronto, Ontario, Canada M3J-1P3 phone: +1 (416) 736-2100 x-30104 fax: +1 (416) 736-5188 mail: lbianchi at yorku dot ca http://www.yorku.ca/sasit/sts/

--[4]------------------------------------------------------------------ Date: Mon, 16 Feb 2004 08:45:11 +0000 From: Matt Kirschenbaum <mk235@umail.umd.edu> Subject: Re: 17.647 history of 20C mathematics?


I'm sure you know Douglas R. Hofstadter's majestic Gödel, Escher, Bach (which I'm currently in the thick of); for a somewhat lighter touch try Martin Davis, The Universal Computer. Matt

Matthew G. Kirschenbaum_____________________________ _______________________http://www.otal.umd.edu/~mgk/

--[5]------------------------------------------------------------------ Date: Mon, 16 Feb 2004 08:45:49 +0000 From: "S.A.Rae" <S.A.Rae@open.ac.uk> Subject: RE: 17.647 history of 20C mathematics?

Willard, you requests that "it would also be useful to read about how Mr Turing's machine (as Richard Feynman calls it) has affected mathematics since. I'm interested in a philosophical view of this history, but it's important to me to get the facts straight, e.g. which important papers were published when."

While doing some work last year in our Maths & Computing faculty I was kindly given a copy of one of a set of four volumes - the Collected Works of A. M. Turing - by the editor of the third in the series: "Mechanical Intelligence". With the other titles in the series: Pure Mathematics; Mathematical Logic; and Morphogenesis, this collection sought to bring together all of Turing's 'mature scientific work' with some brief editorial comments. The books were published by North-Holland, Elsevier Science Publishers in 1992.

The Collected Works of A. M. Turing (4 volumes): Pure Mathematics - edited by J. L. Britton Mathematical Logic - edited by R. O. Gandy and C. E. M. Yates Mechanical Intelligence - edited by D. C. Ince, ISBN 0-444-88058-5 Morphogenesis - edited by P. T. Saunders North-Holland, Elsevier Science Publishers 1992.

The Mechanical Intelligence volume that I have includes Turing's paper "Computing Machinery and Intelligence" (originally published in MIND - a quarterly review of Psychology and Philosophy, October 1950, Vol. LIX, No.236) that contains a description of what has become known as the Turing Test of Machine Intelligence - a method of answering the question "can machines think?".

They might be of some help in your quest.


Simon Rae Programme on Learner Use of Media (PLUM), IET, The Open University MILTON KEYNES, MK7 6AA. UK 01908 654650 mailto:s.a.rae@open.ac.uk <mailto:s.a.rae@open.ac.uk> http://iet.open.ac.uk/pp/s.a.rae/personal.html <http://iet.open.ac.uk/pp/s.a.rae/personal.html>

Experimental BLOG page: http://plums-of-iet.blogspot.com/ <http://plums-of-iet.blogspot.com/> </x-flowed>

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