Great and Inspirational Math books?
Charles Neveu
I am collecting math books for my daughters and I would like to hear
people's stories about math books, games or other toys that inspired
them to study mathematics. I'm not looking for merely good books about
one subject or another, but great books, books that changed your life.
Charles Neveu
ne...@milo.berkeley.edu
Allan Adler
I was turned on to mathematics by experiences, not by books. Once experiences
had kindled my interest, I looked at all the books that were available to
me. Of those, a few actually taught me something at the time. One was my
father's college algebra book (that he read in college), another was Jerome
S. Meyer's Fun With Mathematics (whose influence is reflected in its inclusion
as a reference in my recent article in Mathematical Intelligencer),
another was the puzzle book of Geoffrey Mott-Smith (which led me to start
experimenting with Pell's equation) and another was Davenport's
Higher Arithmetic. Some book whose name I can't remember explained to me
Hilbert's idea of treating mathematical statements as strings and looking
for some pattern in thestrings that were theorems, so that one could
know something was a theorem without having to prove it. And the book
Fantasia Mathematica was lots of fun, as were Gamow's 1,2,3,infinity
and the nice books of Lillian Lieber (T.C.MITS).
That is some of what I found to read in and before high school. I'll leave
it at that.
Allan Adler
a...@altdorf.ai.mit.edu
Carter Bennett
In article <7...@capmkt.COM> cha...@capmkt.COM (Charles Neveu) writes:
> ... and I would like to hear
>people's stories about math books, games or other toys that inspired
>them to study mathematics.
While I was growing up, I spent HOURS poring over my dad's college texts
(Pop is a physicist). One book in his collection I still have on hand
right here - "One, Two, Three... Infinity!" by George Gamow. Dover Press
is probably still publishing it. Yes - Go get a copy of this book TODAY!
Don't wait until tomorrow. You'll probably have to special-order it, unless
you have a really super bookstore nearby.
Do I even need to mention "G:odel, Escher, Bach: an Eternal Golden
Braid" by Douglas Hofstadter? No, probably not. You'll probably be
inundated with suggestions for that one. It would probably supplant even
Gamow if I was starting again.
I should point this out, though. Gamow and others wouldn't have been
enough for me. My appreciation for math and science is largely from the
personal interaction with my father and a couple of *very* special teachers.
Yes, get the books! But your daughters will probably get the best impression
of math from your use of it and your introduction of it (as you seem to
be doing). :-)
Carter R. Bennett, Jr. - Scientist No matter where you go...
car...@scilab.lonestar.org ...tty!
KI5SR
Chris Koenigsberg
I had a high school math teacher, in an alternative "hippie school" in
the 1970's, and the textbook he used was "Mathematics: A Human
Endeavour" which I found quite inspiring (I eventually majored in pure
math in college).
In college, I found the words and notes of Professors Walter Noll and
Juan Jorge Schaeffer, at Carnegie Mellon University, to be quite
inspiring. Walter Noll's unusual treatment of the calculus, using his
own notation, and his constant comments like "dx, dx, what is that, it
makes no sense" and "If you understand calculus the way they taught it
to you in high school, then you must be STUPID!" inspired me (they
didn't even teach calculus in MY high school :-)...
------------------------------------------------------------------------
Christopher K. Koenigsberg : ck...@mills.edu,ck...@andrew.cmu.edu
(510) 482-2311 : Graduate student in Electronic Music
P.O.Box 9785 : Mills College Music Dept.
Oakland, CA. 94613 : former Carnegie-Mellon systems programmer etc.
Chris Koenigsberg
I was also quite inspired, after finishing a B.S. in Math, by reading
Morris Kline's books, starting with "Mathematics: the Loss of
Certainty", Rudy Rucker's "Infinity and the Mind", and an article
which an inspirational math teacher Saj-Nicole Joni copied for me,
author unknown to me (Joni claimed to be a radical separatist lesbian,
yet she taught for a year at mostly-male Carnegie Mellon before
returning to Boston :-), entitled "The Unreasonable Effectiveness of
Mathematics".
Thomas Colthurst
_Godel, Escher, Bach_, Douglas Hofstadter
_The Mathematical Experience_, Phillip Davis
_Men of Mathematics_, E.T. Bell
[Though don't let your daughters get the impression that
mathematics is only for men!]
-Thomas C
P.S. Also, any of the Gardiner books, though I had the
misfortune of discovering them after I was converted.
Timothy Y. Chow
>"dx, dx, what is that, it makes no sense"
This seems to be a common view---that "dx" on its own is not meaningful.
Why is this? Even without recourse to differential forms, it is easy to
construct a set of formal rules to manipulate the entity "dx" so that it
becomes just as legitimate an entity as a formal power series.
--
Tim Chow tyc...@math.mit.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons. ---Popular Mechanics, March 1949
Alex Lopez-Ortiz
> Sorry about the schmaltzy subject line.
> books that changed your life.
This is not a book for children but three of my friends were convinced
to study mathematics (as opposed to actuary) by this (excellent) book:
Mathematician's Apology, G.H. Hardy.
I should add that I prefaced the copies of the book with a quote taken
from *Aspects of Science* by John William Navin Sullivan (also quoted in
volume 3 of _The_World_of_Mathematics_ by James Newman). Here is the
excerpt for everybody's enjoyment.
Mathematics is of profound significance in the universe, not
because it exhibits principles that we obey, but because it
exhibits principles that we impose. It shows us the laws of our
own being and the necessary conditions of experience. And is it
not true that the other arts do something similar in those regions
of experience which are not of the intellect alone? May it not be
that meaning Beethoven declared his music to posses is that,
although man seems to live in an alien universe, yet it is true
of the whole of experience as well as of that part of it which is
the subject of science that what man finds is what he created, and
that the spirit of man is indeed free, eternally subject only to
its own decrees? But however this may be it is certain that the
real function of art is to increase our self-conciousness; to make
us more aware of what we are and therefore of what the universe in
which we live really is. And since mathematics, in its own way,
also performs this function, it is not only aesthetically charming
but profoundly significant. It is an art, and a great art. It is
on this, besides its usefulness in practical life, that its claim
to esteem are based.
Alex
--
Alex Lopez-Ortiz alop...@maytag.UWaterloo.ca
Deparment of Computer Science University of Waterloo
Waterloo, Ontario Canada
Dana Paxson
>In article <7...@capmkt.COM> cha...@capmkt.COM (Charles Neveu) writes:
>> ... and I would like to hear
>>people's stories about math books, games or other toys that inspired
>>them to study mathematics.
>
> While I was growing up, I spent HOURS poring over my dad's college texts
>(Pop is a physicist). One book in his collection I still have on hand
>right here - "One, Two, Three... Infinity!" by George Gamow.
>Carter R. Bennett, Jr. - Scientist No matter where you go...
>car...@scilab.lonestar.org ...tty!
>KI5SR
Gamow's book was my friend when I was a teenager (in the late '50s!).
Later I discovered his Mr. Tompkins series, which is currently (again!)
in print. Delightful, if dated. In one of the Mr. Tompkins stories
he quotes Gilbert and Sullivan while a game of quantum pool is going
on: "On a cloth untrue, with a twisted cue, and elliptical billiard
balls."
Then there was Edwin Abbott's book, Flatland -- still available.
When I was about ten, I was curious about nuclear physics, and sent
away to General Electric for a wall chart entitled "The Chart of the
Nuclides" -- all the elements, all their isotopes, and all the modes
of radioactive decay. Not math directly, but reinforcing.
At about fifteen (or somewhere along there) I remember my issue of
Scientific American with the article on making flexagons. That one
really got me going with topology.
It's only too bad a vicious collision with a math professor during
my sophomore year in college drove me away from math for so many
years afterwards. My loss -- math is beautiful.
Dana Paxson
Network Applications Systems Group, Northern Telecom
97 Humboldt Street, Rochester, New York 14609
1 716 654-2588
Disclaimer: The opinions expressed above are mine personally,
and do not necessarily reflect the views of my
employer. This should be obvious.
Mark Brader
> At about fifteen (or somewhere along there) I remember my issue of
> Scientific American with the article on making flexagons. That one
> really got me going with topology.
It may be noted that that was the *first* of Martin Gardner's monthly
writings for them. If I recall correctly, the flexagons piece appeared
as a regular article, and the next month, without fanfare, his column
"Mathematical Games" was there. (I'm not quite old enough to have
read these issues when they appeared, but I looked them up once out of
curiosity to see what they said when they started the column. Nothing.)
--
Mark Brader, Toronto "Why, I make more money than Calvin Coolidge,
utzoo!sq!msb, m...@sq.com put together!" -- SINGIN' IN THE RAIN
This article is in the public domain.
Mcinnes B T (Dr)
them NOT to make the fatal choice to become mathematicians? Any
inspirational books about surgeons, lawyers, orthodontists, etc?
Michael Zeleny
Chris Koenigsberg <ck...@andrew.cmu.edu> writes:
>I was also quite inspired, after finishing a B.S. in Math, by reading
>Morris Kline's books, starting with "Mathematics: the Loss of
>Certainty", Rudy Rucker's "Infinity and the Mind", and an article
>which an inspirational math teacher Saj-Nicole Joni copied for me,
>author unknown to me (Joni claimed to be a radical separatist lesbian,
>yet she taught for a year at mostly-male Carnegie Mellon before
>returning to Boston :-), entitled "The Unreasonable Effectiveness of
>Mathematics".
The author is the famous physicist Eugene Wigner; the article is reprinted
in his paper collection whose English title I am too lazy to look up in my
disarrayed library. Highly recommended. Nicholas Goodman had an amusing
article on this subject in the JSL a few years back; look it up in the
index.
best wishes,
mikhail zel...@husc.harvard.edu
"Un de mes plus grands plaisirs est de jurer Dieu quand je bande."
D.A.F. de Sade
David C. Chorlian
and the Imagination". I fell in love with the realm of mathematical
ideas. I read it over and over. I can't remember any other book
that I read at such an early age that had such a profound effect.
When I was a senior in high school I won a copy of Klein's
"Elementary Mathematics from an Advanced Standpoint". I've
carried it around with me ever since, always enjoying the
wealth of detail.
Many years later, when I became a high school math teacher, I
looked for books that would provide some sense of purpose. I
found Polya, W.W. Sawyer, and the best of all, W. K. Clifford's
"The Common Sense of the Exact Sciences". I think it is a gem.
The lucidity of the presentation dazzled me, and I tried to
let it influence my teaching.
David B. Chorlian
Neurodyamics Lab SUNY/HSCB
Allan Adler
them from becoming mathematicians. How about my autobiography? :-)
(Now in progress...)
I really liked to read about all sciences when I was a kid, so merely
pointing someone in a different direction doesn't necessarily dissuade
someone.
One of the things that tended to reinforce my involvement with math was
the fact that when the family was driving hundreds of miles in the
car, I could do math without any other equipment. If I had been
provided with greater access to laboratories and with
encouragement in doing experiments, I might have developed differently.
Ditto for nature walks...
Allan Adler
a...@altdorf.ai.mit.edu
Tal Kubo
One that hasn't been mentioned yet...
Mathematics for the Million, by Lancelot Hogben
Christopher P Menzel
>
>I was also quite inspired, after finishing a B.S. in Math, by reading
>Morris Kline's books, starting with "Mathematics: the Loss of
Kline's book is great fun, but the chapter on foundations, at least
contains a few rather serious errors, and reads as though hastily
written. For instance, after an informal paragraph on Zermelo's
axiomatization, Kline notes that his system "was improved some years
later (1922) by Abraham A. Fraenkel (1891-1965). Zermelo had failed
to distinguish the property of a set and the set itself. These were
used synonymously. The distinction was made by Fraenkel in 1922."
Note the choppy style and the redundancy. More seriously, according
to Kline, Zermelo's confusion rested on a failure to distinguish "the
property of a set (?!) and the set itself." Whatever this might mean,
it doesn't seem clearly to have anything to do with the issues that
led Fraenkel to revise Zermelo's system: first, the need for the axiom
of replacement (in order to prove, e.g., the existence of
\aleph_{\omega}), and the need to replace Zermelo's notion of a
"definite property" in the axiom of separation (and replacement, which
subsumes it) with a tighter notion, viz., essentially, that of a
first-order formula. Zermelo of course immediately acknowledged the
former revision, but was strongly against the latter, feeling that FOL
was far too limited a language for the expressive needs of set theory,
and desiring instead what amounted to something like an infinitary
\omega-order logic. (See Gregory Moore's excellent book {\it
Zermelo's Axiom of Choice}.)
Anyway, Kline sins further in his statement of what he calls the ZF
axioms. First, he omits replacement and states only separation,
though his version of it to my eyes looks to be exactly the old
inconsistent comprehension axiom that caused all the ruckus in the
first place: "Any property that can be formalized in the language of
the theory can be used to define a set." x \not\in x, for instance? :-)
Finally, he includes a weak version of foundation, which neither Z nor
F proposed; Mirimanoff toyed with it c. 1918, and I believe von
Neumann added it to his system later in the 20s. Z accepted it in
print first in his 1930 (31?) paper on the cumulative hierarchy. The
weak version Kline gives is simply x \not\in x, which doesn't rule
out, e.g., noncyclic infinite descending membership chains.
All the same, it's a good read.
--Chris Menzel
Philosophy Department
Andrej Panjkov, La Trobe Maths
>
> _Men of Mathematics_, E.T. Bell
>
That book pissed me off. I found it was written in a sneering and arrogant
tone. I agree that the lives and achievements of the greatest
mathematicians are worth reading about, but I'd try another book.
Other "inspirational" books, good for young ones:
_How to Solve It_, G. Polya
_Chaos_, J. Gleick (lots of applications, which I think impress young
ones.)
Dover has a nice book, I forget its name, which is a catalogue of
curves in the plane.
--
Also, you can find nice stuff in non-mathematical books:
Magic books (the ones that have cute 'guess the number' tricks)
Collections of M.C. Escher art
Atlases which have pages explaining the projections used
--
Andrej Panjkov, ma...@lure.latrobe.edu.au
Dept. of Mathematics,
La Trobe University, "I've got a goddamned PLAN!"
Melbourne, Victoria, 3083, Australia
Stan Isaacs
> When I was ~10, my father gave me Kasner & Newman's "Mathematics
> and the Imagination". I fell in love with the realm of mathematical
> ideas. I read it over and over. I can't remember any other book
> that I read at such an early age that had such a profound effect.
>
Yep, that's the one that got me too, when I was in high school. The
other book that really stood out for me was Nagel and Newman's "Godels
Proof".
-- Stan Isaacs
Allan Adler
hypothesis and nonmeasurable sets.
Allan Adler
a...@altdorf.ai.mit.edu
Christopher J. Henrich
and for a while I would read every one that I could find.
Some good ones:
_Mathematical Recreations_ by M. Kraitchik (available from Dover)
_Mathematical Recreations and Essays_ originally by W.W.R.Ball,
recent editions revised by H. S. Coxeter. (available from Dover)
For visual mathematics, the graphic art of Maurits C. Escher.
_Mathematical Snapshots_ by Hugo Steinhaus.
At a later age (and continuing to the present day) _Regular
Polytopes_ by H. S. M. Coxeter (available from Dover.
_What is Mathematics?_ by Courant & Robbins
_Mathematical Models_ by Cundt & Rollett - lots of interesting
things to make.
_How to Solve It_ and _Patterns of Plausible Inference_ by Polya.
Regards,
Chris Henrich
Paul Leyland
...
Other "inspirational" books, good for young ones:
_How to Solve It_, G. Polya
I came across this one recently. Nice.
_Chaos_, J. Gleick (lots of applications, which I think impress young
ones.)
A Xmas present 18 months ago. Very average, I thought.
A book that I *really* liked when younger was _Mathematical Models_,
by Cundy&Rollet. It was on almost permanent loan to me from the
library. Long out of print, I fear, but I managed to pick up a copy
last year for 10p at a school fete! Contains lots of good stuff about
plane and solid geometry in particular. I still have my collection of
hand-plotted curves; the cardboard polyhedra didn't survive house
moving; but my 4-d wireframe polytopes are still in existence, though
the hypercube is coming unsoldered.
Another excellent book, already mentioned in this thread, is Hofstadter's
GEB, an EGB.
Paul
--
Paul Leyland <p...@oxford.ac.uk> | Hanging on in quiet desperation is
Oxford University Computing Service | the English way.
13 Banbury Road, Oxford, OX2 6NN, UK | The time is come, the song is over.
Tel: +44-865-273200 Fax: +44-865-273275 | Thought I'd something more to say.
N.P.Smart
For pre O-Level (Under 16 Years Old) I didn't use books at all.
For A-Level (16-18) eg Calculus etc one cannot beat the books by
Dakin and Porter (Elementary Analysis etc)
These are very old fashioned but that means they actually teach you
something.
After that well as an undergrad we were discouraged from reading books
as its much better to work things out for yourself.
On a general level how about
Philosophy Of Mathematics by B. Russell
or History Of Maths books
(Note the book Numbers by J. Mcleish I think is very bad.
What do people think on the least great/non-inspirational Math books?)
Nigel
Thomas Clarke
The Education of T. C Mits.
by Lillian Lieber with drawings by Hugh Lieber
(T.C.Mits = The Celebrated Man in the street)
The drawings are cute, and she puts MATH at the top of her
tower of knowledge!
--
Thomas Clarke
Institute for Simulation and Training, University of Central FL
12424 Research Parkway, Suite 300, Orlando, FL 32826
(407)658-5030, FAX: (407)658-5059, cla...@acme.ucf.edu
Jon Jacky
Fantasia Mathematica and the Mathematical Mag\Pi. They are collections of
fiction and miscellania about math and mathematicians. Sort of a lighter
weight version of James R. Newman's The World of Mathematics. I remember
enjoying them; I have no idea whether they are still available. They weren't
hard to find in libraries.
- Jon Jacky, j...@radonc.washington.edu, University of Washington, Seattle
David Rusin
> ... and I would like to hear
>people's stories about math books, games or other toys that inspired
>them to study mathematics.
Gee, no one has mentioned "Mathematics Made Difficult". As I was only a
young teen I didn't think to record author and so on, but I was
delighted with the arcane. The author presented Lagrange interpolation
in order to prove that the next term of the sequence 1,2,4,8,16 was 31.
The solution to a cubic ax^3+bx^2+cx+d=0 was written out in full (note
b <> 0). That sort of thing.
Also appealing to a nerdy high-schooler were other, more serious, books
which had oodles of elegant formulas. Uspensky's "Theory of Equations"
and Hall and Knight's "Higher Algebra" landed my way, for example, and
occupied me for hours.
Not a book, but made of paper: that IBM-produced TimeLine of Mathematics,
showing when some math greats lived and what they worked on. Dated, now,
but I'm sure you can still find these hanging on office walls.
dave ru...@math.niu.edu
Charles Blair
Mathematics Its Magic and Mystery - Martin Gardner
Assorted magic tricks with mathematical basis
Mathematics Its Magic and Mastery - Aaron Bakst
Popular presentation of various math things, not too advanced. I
remember the enthusiastic description of logarithms ``Napier's escape
from drudgery... Nobody knew how to compute a fifth root, but here
you just divide by 5.'' [this paraphrase belittles the book, but I
liked it at the time.]
I learned algebra from TAKE A NUMBER by Lillian Leiber
Don Goldberg
> people's stories about math books, games or other toys that inspired
> one subject or another, but great books, books that changed your life.
The book I recall from about 6th grade was called "Mathematics" in the
Time-Life Science Library. I don't kn ow if it still available.
For the same age, I'd also try Lancelot Hogben, Mathematics in the Making.
--
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
Don Goldberg Occidental College
Department of Mathematics Los Angeles, CA 90041
d...@oxy.edu [NeXT mail accepted]
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-
C.E. Thompson
|> tho...@ricci.geom.umn.edu (Thomas Colthurst) writes:
|> >
|> > _Men of Mathematics_, E.T. Bell
|>
|> tone. I agree that the lives and achievements of the greatest
|> mathematicians are worth reading about, but I'd try another book.
Does anyone else have this reaction? Bell has his strong opinions, and is
(of course) very far from being PC, but I am slightly amazed at quite so
negative a report.
Chris Thompson
JANET: ce...@uk.ac.cam.phx
Internet: ce...@phx.cam.ac.uk
Jeremy Wilson
I can't find any record of who originally posted this question, but for my
money the books that inspired me to take up maths as a career were those
of W.W.Sawyer. Two books in particular impressed me:-
Prelude to Mathematics, published in Pelican
and
A Concrete Approach to Abstract Algebra, (Sorry I can't remember the publisher
but if anyone is interested I'll check at home.) The latter book is
an introduction to Galois theory for someone who has nothing beyond the most
elementary algbera (i.e. solving simple and quadratic equations.) Really quite
an achievement.
One of the problems about high school maths (well in Britain anyway)
is that it gives no flavour of what "serious" maths is about.
In fact for many who use it professionally, mathematics remains a
computational tool. Remarkably few people have the opportunity to
see the real beauty in the subject. For me anyway, Prelude to Mathematics
did that.
+---------------------------------+----------------------------------------+
! Jeremy Wilson ! email: jc...@fmg.bt.co.uk !
! Room 3-07 ! Telephone: 0473-227822 !
! BT Development and Procurement ! International: +44 473-227822 !
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+---------------------------------+----------------------------------------+
Adam M. Logan
Yes.
Adam
Mark Corscadden
>I am collecting math books for my daughters
>I'm not looking for merely good books about
>one subject or another, but great books, books that changed your life.
>
How old are your daughters? I'm a little embarrassed to share this
because the other articles on this thread all refer to much more
sophisticated books, but maybe your talking about the 7-9 year old range?
Your qualification "books that changed your life" fits, so I'll overcome
my embarrassment because your daughters might be young enough to like this
book as much as I did.
When I was pretty young my parents gave me "The Golden Book of Mathematics".
It's fair to say that it changed my life. This is not an advanced book,
for example complex numbers are mentioned but the process for multiplying
two complex numbers is not described in detail (not that I recall). What
I remember are the *images* this book left me with, though. Many, many
topics come back to mind now when I think about it, and yet it's been
about 30 years since I read this book!
Fibonacci series, with pictures of leaves spaced around the stem
of a plant, each leaf rotated around the stem by a fraction of a
turn which is the ratio of two consecutive Fibonacci numbers, so as
to block the light for the leaf below as little as possible. Rabbits
who breed for two generations and then stop, creating a live Fibonacci
series of descendant bunnies, also illustrated.
The golden ratio, illustrated by a gold-colored rectangle inscribed with
a straight-edge and compass construction. An overlay of this rectangle on
a picture of a Greek structure and mention of how the Greeks considered this
ratio "most beautiful". And finally a mysterious connection: the fact that
the ratio of consecutive terms of the Fibonacci series approaches this
golden ratio (all new to me).
Rectangular arrays of checker pieces (rectangle numbers) and the
numbers called "prime numbers" (first I'd heard of them) which you
can't arrange into rectangles. The sieve of Erostophenes (sp?), illustrated
by a stack of shelves, with holes on each shelf except at the positions
corresponding to the multiples of the number being held back by that
shelf, with numbered blocks falling through the holes. "The first
number held back on each shelf is a prime", with the higher primes all
shown zipping on downwards past the last shelf. Triangle numbers too,
with two copies of the checker-pattern for a triangle number put together
to make a rectangle, illustrating how one can quickly determine how
many checkers there are in a given triangle. I can't remember for sure,
but I don't think that a formula like n*(n+1)/2 would be mentioned,
pictures were favored.
Probability, with toothpicks turning and then falling at random across
(or not across) evenly spaced cracks on a floor. Mysterious partial
information being given: "the percentage of times a toothpick crosses
a crack depends on PI, because the toothpick turns in a circle as it
falls". Of course, circles and PI had been properly introduced earlier
in the book.
Pascal's triangle, illustrated by a literal triangular array of numbers
but also by a pinball type of arrangement, with a falling ball about
to randomly navigate a path down into an array of slots, each slot already
filled with just the expected number of balls, except for one slot that
was still one ball short. Naturally you could guess where the last falling
ball was headed!
And my favorite, complex numbers! This was at a time when my homework
consisted of multiplying sets of 2-digit numbers, and I'd annoy my mother
by spending time finding equivalent problems so I'd only have to do
one of them, instead of "just doing the *&^&*^*& things".
Complex numbers were the most mysterious of all. Numbers not on a
line, you see, but on a *plane*. And when you multiply them, they
perform a "trapeze-like swing" across the plane. It chokes me
up a bit just to remember this. I wanted *very* much to know how to
multiply numbers that could do this! I think this is when I first quit
waiting to learn things in school and started to teach myself.
This book "The Golden Book of Mathematics" had other good stuff too
I'm sure, and yet it wasn't more than 3/4 of an inch thick. If there's
anything that can make mathematics seem magical to a young reader I
think it's this book.
Mark Corscadden
ma...@smsc.sony.com
work: (408)944-4086
Steven Smith
> ma...@lure.latrobe.edu.au (Andrej Panjkov, La Trobe Maths) writes:
> |> tho...@ricci.geom.umn.edu (Thomas Colthurst) writes:
> |> >
> |> > _Men of Mathematics_, E.T. Bell
> |>
> |> That book pissed me off. I found it was written in a sneering and
> |> arrogant tone. I agree that the lives and achievements of the
> |> greatest mathematicians are worth reading about, but I'd try
> |> another book.
>
> Does anyone else have this reaction? Bell has his strong opinions, and is
> (of course) very far from being PC, but I am slightly amazed at quite so
> negative a report.
From Spivak, Vol. II, p. 132:
Even for those who can only plod through German, this [Dedekind's
biography of Riemann] is preferable to the account of E. T. Bell's
_Men of Mathematics_, which is hardly more than a translation of
Dedekind, written in a racy style and interladen with supercilious
remarks of questionable taste.
This judgment strikes at the heart of why I enjoyed reading this book
as a teenager.
Steven Smith
Peter Gogolek
In his biographical essay on Bateman, Clifford Truesdell gives the
following account of Bell:
The only course Bell taught was abstract algebra; while he
did little to excite the students in that subject, he was
admired for his science fiction and his _Men_of_Mathematics_.
I was shocked when, just a few years later, Walter Pitts
told me the latter was nothing but a string of Hollywood
scenarios; my own subsequent study of the sources has
shown me that Pitts was right, and I now find the contents
of that still popular book to be little more than rehashes
enlivened by nasty gossip and banal or indecent fancy.
[from Genius and the establishment at a polite standstill in
the modern university: Bateman, in An Idiot's Fugitive Essays
on Science, 1984, pages 423-424]
I find Truesdell's writing most envigorating, but a little
advanced for pre-university. But obviously not for those who
dislike strongly expressed opinions.
Peter Gogolek
Kingston, Ontario
Colin Mclarty
In a previous article, ce...@cl.cam.ac.uk (C.E. Thompson) says:
>In article <1992Aug6...@lure.latrobe.edu.au>,
>ma...@lure.latrobe.edu.au (Andrej Panjkov, La Trobe Maths) writes:
>|> In article <1992Aug4.1...@news2.cis.umn.edu>,
>|> tho...@ricci.geom.umn.edu (Thomas Colthurst) writes:
>|> >
>|> > _Men of Mathematics_, E.T. Bell
>|>
>|> That book pissed me off. I found it was written in a sneering and arrogant
>|> tone. I agree that the lives and achievements of the greatest
>|> mathematicians are worth reading about, but I'd try another book.
>
>Does anyone else have this reaction? Bell has his strong opinions, and is
>(of course) very far from being PC, but I am slightly amazed at quite so
>negative a report.
>
Conversations over the years led me to believe many people have
this reaction. The least you could say is that Bell never lets facts get
in the way of a good story--and his idea of a good story is smug
xenophobic and sexist. The book is not an accurate reference nor is it
meant to be. It is meant to be engaging and edifying. I can't consider it
edifying, and I don't think it a good bet to engage the original poster's
daughters.
Colin McLarty
Colin Bell
It covers quite a lot of 'basic' number theory, from an elementary and
recreational basis. Warnings: 1. it's reasonably hard in places: I wouldn't
recommend it to people (unless reasonably gifted) under the age of about
16 (but then on the flip side, it would be of interest to most
undergraduates and many mathematicians not working in number theory (who
would find it trivial))
2. It's somewhat out of date in some respects: despite being reprinted
recently, the tables of (for example) what is known about the factorisation
of Mersenne numbers are something like 25 years out of date.
--
-
Colin Bell, CR...@CUS.CAM.UK.AC
Department of Pure Mathematics, University of Cambridge.
Robert Langridge
...
>A book that I *really* liked when younger was _Mathematical Models_,
>by Cundy&Rollet. It was on almost permanent loan to me from the
>library. Long out of print, I fear, but I managed to pick up a copy
>last year for 10p at a school fete! Contains lots of good stuff about
>plane and solid geometry in particular. I still have my collection of
>hand-plotted curves; the cardboard polyhedra didn't survive house
>moving; but my 4-d wireframe polytopes are still in existence, though
>the hypercube is coming unsoldered.
I agree about Cundy and Rollett. In view of another thread in this group
on Freeman Dyson, I might note that on the first text page of the book
there is a footnote:
"There is a beautiful collection of polyhedral models in wire and cardboard
at Winchester College. These were made by three boys, F.J.Dyson, M.S. and
H.C.Longuet-Higgins, two of whom have later become university professors."
[Winchester College is, in US parlance, a private prep school. Unlike the
better known Eton and Harrow, it has obviously produced some first class
scientists and mathematicians]
The first paragraph of the Preface to the First Edition of Mathematical
Models reads:
"'I have often been surprised that Mathematics, the quintessence of Truth,
should have found admirers few and so languid. Frequent consideration
and minute scrutiny have at length unravelled the cause; viz. that
although Reason is feasted, Imagination is starved; whilst Reason is
luxuriating in its proper Paradise, Imagination is wearily travelling
on a dreary desert...'"
The author quoted is Samuel Taylor Coleridge in a letter to his brother
in 1791 (of course, he was only a poet :-)
Robert Langridge Phone: +1 415 476-2630, -1540, -5128
Computer Graphics Laboratory FAX: +1 415 476-0688
926 Medical Sciences
University of California E-Mail: r...@cgl.ucsf.edu
San Francisco CA 94143-0446
Steven Smith
Modern Mathematics_ (Princeton University Press, 1981), which is a
wonderful compendium of history, biographies, and elementary
descriptions of intermediate to advanced topics. This book is
directed at interested adults.
Steven Smith
Michael Zeleny
cme...@tamsun.tamu.edu (Christopher P Menzel ) writes:
>In article <92220.0931...@QUCDN.QueensU.CA>
>Peter Gogolek <GOGO...@QUCDN.QueensU.CA> writes:
PG:
>> In his biographical essay on Bateman, Clifford Truesdell gives the
>>following account of Bell:
>> The only course Bell taught was abstract algebra; while he
>> did little to excite the students in that subject, he was
>> admired for his science fiction and his _Men_of_Mathematics_.
>> I was shocked when, just a few years later, Walter Pitts
>> told me the latter was nothing but a string of Hollywood
>> scenarios; my own subsequent study of the sources has
>> shown me that Pitts was right, and I now find the contents
>> of that still popular book to be little more than rehashes
>> enlivened by nasty gossip and banal or indecent fancy.
CPM:
>In his excellent study of Cantor, Joseph Dauben also points out the
>serious inaccuracies of Bell's account of set theory's founder:
>
> In his own day, Cantor was regarded as an eccentric, if exciting,
> man, who apparently stimulated interest wherever he went,
> particularly among younger mathematicians. But it was the
> mathematician and historian E.T. Bell who popularized the portrait of
> a man whose problems and insecurities stemmed from Freudian
> antagonisms with his father and whose relationship with his archrival
> Leopold Kronecker was exacerbated because both men were Jewish. In
> fact, Cantor was not Jewish. He was born and baptized a Lutheran and
> was a devout Christian during his entire life....Equally unreliable
> are Bell's assertions about Cantor's mental illness... (Dauben,
> {\it Georg Cantor: His Mathematics and Philosophy of the Infinite},
> p. 1}
>
>Dauben also goes on to show in the final chapter of his book that
>Cantor's relationship with his father was marked by mutual admiration
>and affection.
Umm, not to contradict you, Chris, but the prevalent German conception of
Jewishness, later codified in the Nuremberg Laws, made Cantor very much a
Jew. (Recall the Groucho Marx joke: two friends, of which one is
erectively challenged, are walking past a synagogue. One looks at the
building, and remarks: "You know, I used to be a Jew." The other replies:
"Yes, and I used to be a hunchback.") As for Cantor's (very real; see
Dauben, Chapter 12) mental breakdowns, they seemed to fit in with the
prevailing fashion among the contemporaty German intelligentsia: think of
the span between the mental health of a Max Weber, and that of a Friedrich
Nietzsche. Finally, you may recall Russell's chatty characterization of
Einstein, G\"odel, and Pauli (congregating in the vicinity of the Princeton
I.A.S. in 1944) as "Jews and exiles, and, in intention, cosmopolitans",
which elicited an abortive rebuttal from G\"odel. I can't help wondering
whether, on the strength of this evidence, you would denounce dear old
Bertie as an antisemite.
>--Chris Menzel
> Philosophy Department
> Texas A&M University
ObMath: the Phallogocentric Cabal meets at 7pm each Thursday in front of
the Harvard University Science Center. Next week: Michael Glanzberg is
talking about constructibility and V=L. Coming up: Tal Kubo on infinite
combinatorics. New speakers and auditors are always welcome.
cordially,
mikhail zel...@husc.harvard.edu
Christopher P Menzel
>following account of Bell:
> The only course Bell taught was abstract algebra; while he
> did little to excite the students in that subject, he was
> admired for his science fiction and his _Men_of_Mathematics_.
> I was shocked when, just a few years later, Walter Pitts
> told me the latter was nothing but a string of Hollywood
> scenarios; my own subsequent study of the sources has
> shown me that Pitts was right, and I now find the contents
> of that still popular book to be little more than rehashes
> enlivened by nasty gossip and banal or indecent fancy.
In his excellent study of Cantor, Joseph Dauben also points out the
serious inaccuracies of Bell's account of set theory's founder:
In his own day, Cantor was regarded as an eccentric, if exciting,
man, who apparently stimulated interest wherever he went,
particularly among younger mathematicians. But it was the
mathematician and historian E.T. Bell who popularized the portrait of
a man whose problems and insecurities stemmed from Freudian
antagonisms with his father and whose relationship with his archrival
Leopold Kronecker was exacerbated because both men were Jewish. In
fact, Cantor was not Jewish. He was born and baptized a Lutheran and
was a devout Christian during his entire life....Equally unreliable
are Bell's assertions about Cantor's mental illness... (Dauben,
{\it Georg Cantor: His Mathematics and Philosophy of the Infinite},
p. 1}
Dauben also goes on to show in the final chapter of his book that
Cantor's relationship with his father was marked by mutual admiration
and affection.
--Chris Menzel
Christopher P Menzel
>In article <1992Aug7.1...@tamsun.tamu.edu>
>cme...@tamsun.tamu.edu (Christopher P Menzel ) writes:
>>In his excellent study of Cantor, Joseph Dauben also points out the
>>serious inaccuracies of Bell's account of set theory's founder:
>>
>> In his own day, Cantor was regarded as an eccentric, if exciting,
>> man, who apparently stimulated interest wherever he went,
>> particularly among younger mathematicians. But it was the
>> mathematician and historian E.T. Bell who popularized the portrait of
>> a man whose problems and insecurities stemmed from Freudian
>> antagonisms with his father and whose relationship with his archrival
>> Leopold Kronecker was exacerbated because both men were Jewish. In
>> fact, Cantor was not Jewish. He was born and baptized a Lutheran and
>> was a devout Christian during his entire life....Equally unreliable
>> are Bell's assertions about Cantor's mental illness... (Dauben,
>> {\it Georg Cantor: His Mathematics and Philosophy of the Infinite},
>> p. 1}
>>
>>Dauben also goes on to show in the final chapter of his book that
>>Cantor's relationship with his father was marked by mutual admiration
>>and affection.
>
>Umm, not to contradict you, Chris, but the prevalent German conception of
>Jewishness, later codified in the Nuremberg Laws, made Cantor very much a
>Einstein, G\"odel, and Pauli (congregating in the vicinity of the Princeton
>I.A.S. in 1944) as "Jews and exiles, and, in intention, cosmopolitans",
>which elicited an abortive rebuttal from G\"odel. I can't help wondering
>whether, on the strength of this evidence, you would denounce dear old
>Bertie as an antisemite.
According to Dauben, Cantor's family history is rather cloudy,
and he mentions only his grandfather's living in Copenhagen, from
which they moved to St. Petersburg after the English bombardment of
1807, his father's upbringing in a Lutheran mission, and his mother's
birth and baptism in the RC church in St. Petersburg. What is the
source of your claim, Mikhail? (Not that this is a matter of any more
than historical interest.)
As for the reference to antisemiticism (discussion of which I continue
on the net with great trepidation--I do so here as it concerns a well
known work in the history of mathematics), I was alluding to Dauben's
remark that the rivalry between Cantor and Kronecker was aggravated by
the fact that the two were Jewish, as if that had anything to do with
it. Dauben no doubt had the following passage from Bell in mind:
Rightly or wrongly, Cantor blamed Kronecker for his failure to
obtain the coveted position at Berlin. The aggressive clannishness of
Jews has often been remarked, sometimes as an argument against
employing them in academic work, but it has not been so generally
observed that there is no more vicious academic hatred than that of one
Jew for another when they disagree on purely scientific matters or
when one is jealous or afraid of another. Gentiles either laugh these
hatreds off (!!) or go at them in an efficient, underhand way which
often enables them to accomplish their spiteful ends under the guise
of sincere friendship. When two intellectual Jews fall out they
disagree all over, throw reserve to the dogs, and do everything in
their power to cut one anothers' throats or stab one another in the
back.
I'm not sure I see quite the same spirit in Bertie's remark.
Juhana Kouhia
In article <1992Aug6.2...@cl.cam.ac.uk> ce...@cl.cam.ac.uk
(C.E. Thompson) writes:
>
>|> > _Men of Mathematics_, E.T. Bell
>|>
>|> That book pissed me off. I found it was written in a sneering and arrogant
>|> tone. I agree that the lives and achievements of the greatest
>|> mathematicians are worth reading about, but I'd try another book.
>
>Does anyone else have this reaction? Bell has his strong opinions, and is
>(of course) very far from being PC, but I am slightly amazed at quite so
>negative a report.
This is what I remember from it and I would like to get an answer,
so that I can forget the whole book ;-)
Were Gauss who invented the closed form for arithmetic series?
The story in the book goes like this:
Gauss teacher draws a arithmetic serie on the board. Quite soon
Gauss have the answer. And Bell tells how Gauss invented the
closed form equation at moment described above.
I was able to calculate (in my head) the series in a couple of
minutes without knowledge about arithmetic series; so, I wonder,
because Gauss surely was better than I (ever? :-), did he calculate
the sum similarly than I but more faster?
If somebody has the book, please type the serie in.
Juhana Kouhia
Andrew Purshottam
Popular math books of: Martin Gardner, Doug Hofstadler (not sure of sp), Rudy Rucker
Rudy's math SF: _Mathnauts_ (anthology), _White Light_, _Spacetime Donuts_ (PG-13)
Stan Ulam: _Adventures of a Mathematician_
Marc Kac's autobiography
Weird little russian book: _Stories About Sets_
H Steinhaus: _Mathematical Snapshots_
Martin Gardner, ed, _The Annotated Alice_ (_Alice In Wonderland_)
Flat books: E. Abbot, _Flatland_; _Sphereland_; K. Dewney: _The Planiverse_
(More technical)
The "little books" of Paul Halmos: _Finite Dinesion Vector Spaces_, _Naive Set Theory_,
(and about one Boolean Algebras?)
D. Hilbert: _Geometry and the Imagination_
D. I. Solov: _How to Read and Do Proofs_
--
-
Andrew V. Purshottam /\ | an...@autodesk.com ...!fernwood!acad!andy
Autodesk, Inc. //\\ | (415)332-2344x2161 FAX (415) 331-8093
2320 Marinship Way ///\\\ | Sausalito CA 94965
"The views expressed are those of the speaker."
Michael Zeleny
CPM:
>According to Dauben, Cantor's family history is rather cloudy,
>and he mentions only his grandfather's living in Copenhagen, from
>which they moved to St. Petersburg after the English bombardment of
>1807, his father's upbringing in a Lutheran mission, and his mother's
>birth and baptism in the RC church in St. Petersburg. What is the
>source of your claim, Mikhail? (Not that this is a matter of any more
>than historical interest.)
The selfsame Dauben will readily attest to Cantor's references to his
_israelitische_ grandparents; this alone would suffice to render him a Jew
from the standpoint of the racial laws. I hasten to add that the
interpretation of Jewishness as a racially determined trait antedates the
Nazi regime, and corresponds to the general secularization of the European
society in the course of the XIXth century.
CPM:
>As for the reference to antisemiticism (discussion of which I continue
>on the net with great trepidation--I do so here as it concerns a well
>known work in the history of mathematics), I was alluding to Dauben's
>remark that the rivalry between Cantor and Kronecker was aggravated by
>the fact that the two were Jewish, as if that had anything to do with
>it. Dauben no doubt had the following passage from Bell in mind:
>
> Rightly or wrongly, Cantor blamed Kronecker for his failure to
> obtain the coveted position at Berlin. The aggressive clannishness of
> Jews has often been remarked, sometimes as an argument against
> employing them in academic work, but it has not been so generally
> observed that there is no more vicious academic hatred than that of one
> Jew for another when they disagree on purely scientific matters or
> when one is jealous or afraid of another. Gentiles either laugh these
> hatreds off (!!) or go at them in an efficient, underhand way which
> often enables them to accomplish their spiteful ends under the guise
> of sincere friendship. When two intellectual Jews fall out they
> disagree all over, throw reserve to the dogs, and do everything in
> their power to cut one anothers' throats or stab one another in the
> back.
The way I read this passage, it seems equally contemptuous of the allegedly
hypocritical gentile ways of settling personal scores, as it is of the open
animosity attributed to the Jews. In any case, historical manifestations
of this prejudice are well known -- consider the fact that, at the time
they hired Lionel Trilling, the Columbia university administrators turned
away Clifton Fadiman, explaining that their English department had room
only for one Jew. I'll go as far as saying that I am grateful to Bell for
putting it so bluntly, and making it a matter of record.
CPM:
>I'm not sure I see quite the same spirit in Bertie's remark.
The difference seems to be that of degree, rather than that of kind.
Furthermore, possessed as I am of a big mouth and a nasty temper, I am in
no position to deny the claims of Jewish obstreperousness. Besides, all
these rumors of internal struggle are really spread by the Elders of Zion,
anxious to produce a smokescreen for their efforts to dominate the IMF via
the Trilateral Commission. Or something like that.
>--Chris Menzel
> Philosophy Department
> Texas A&M University
cordially,
mikhail zel...@husc.harvard.edu
Mcinnes B T (Dr)
Peter Gogolek
B T (Dr)) says:
>
>"indecent fancy"?! For example?
I think you shall have to ask Truesdell for particular examples, if he
is still alive. I might suggest the Weierstrass-Kovalevska article as
an example.
Peter Gogolek
Kingston, Ontario, Canada
G.J. McCaughan
> Were Gauss who invented the closed form for arithmetic series?
> The story in the book goes like this:
>
> Gauss teacher draws a arithmetic serie on the board. Quite soon
> Gauss have the answer. And Bell tells how Gauss invented the
> closed form equation at moment described above.
>
> I was able to calculate (in my head) the series in a couple of
> minutes without knowledge about arithmetic series; so, I wonder,
> because Gauss surely was better than I (ever? :-), did he calculate
> the sum similarly than I but more faster?
>
> If somebody has the book, please type the serie in.
I haven't got the book, but the story as usually told goes like this:
Gauss's class in school was asked to calculate 1+2+...+100 (probably
just to shut them up while the teacher did something more interesting),
but Gauss had the answer very quickly (surely quicker than "a couple
of minutes"!), as follows:
1 + 2 + 3 + ..... + 100
100 + 99 + 98 + + 1
----------------------------------
101 + 101 + 101 + ..... + 101 (100 terms)
is 10100, and that's twice the sum we wanted. So 1+...+100 = 5050.
I don't know whether it's true that Gauss thought this up on the spot;
it's possible that he might have spotted it on another occasion. Not that
that makes it any more striking -- he was, er, quite young when this
happened.
Incidentally; yes, Gauss was very very good at mental arithmetic too.
Juhana Kouhia
In article <1992Aug8.1...@infodev.cam.ac.uk>
gj...@cus.cam.ac.uk (G.J. McCaughan) writes:
>
>I haven't got the book, but the story as usually told goes like this:
>Gauss's class in school was asked to calculate 1+2+...+100
No, the series was more difficult; I recall the first term was number
with 5 or 6 digits; I may recall incorrectly but it was not that easy
serie in the Bell's book.
Juhana Kouhia
John Mount
[ quoting E.T Bell ]
|> Rightly or wrongly, Cantor blamed Kronecker for his failure to
|> obtain the coveted position at Berlin. The aggressive clannishness of
|> Jews has often been remarked, sometimes as an argument against
|> employing them in academic work, but it has not been so generally
|> observed that there is no more vicious academic hatred than that of one
|> Jew for another when they disagree on purely scientific matters or
|> when one is jealous or afraid of another. Gentiles either laugh these
|> hatreds off (!!) or go at them in an efficient, underhand way which
|> often enables them to accomplish their spiteful ends under the guise
|> of sincere friendship. When two intellectual Jews fall out they
|> disagree all over, throw reserve to the dogs, and do everything in
|> their power to cut one anothers' throats or stab one another in the
|> back.
|>
|> I'm not sure I see quite the same spirit in Bertie's remark.
|>
|> --Chris Menzel
|> Philosophy Department
|> Texas A&M University
I don't like Bell either, but you cut the quotation off at a very key point.
It goes on to say:
Perhaps after all this is a more decent way of fighting- if men must
fight- than the sanctimonious hypocrisy of the other.
E.T. Bell, "Men of Mathematics", Simon and Schuster, seventh paperback
printing, p. 563.
--
--- It is kind of strange being in CS theory, given computers really do exist.
John Mount: jmo...@cs.cmu.edu (412)268-6247
School of Computer Science, Carnegie Mellon University,
5000 Forbes Ave., Pittsburgh PA 15213-3890
Tom Harding
>>|> tho...@ricci.geom.umn.edu (Thomas Colthurst) writes:
>>|> >
>>|> > _Men of Mathematics_, E.T. Bell
>>|>
>>|> That book pissed me off. I found it was written in a sneering and arrogant
>>|> tone. I agree that the lives and achievements of the greatest
>>|> mathematicians are worth reading about, but I'd try another book.
>>
>>Does anyone else have this reaction? Bell has his strong opinions, and is
>>(of course) very far from being PC, but I am slightly amazed at quite so
>>negative a report.
Not being a mathematician, I had thought I might not be in a
position to pass judgement; however, I had the same reaction to Bell's
book.
I was reminded of the notorious statement (made in another context) that some
people are more concerned with being clever and paradoxical than with
being right.
I have gained some indirect pleasure from _Men of Mathematics_, though.
It was there that I learned of Fermat's Theorem (not FLT), which is:
(n^p - n) mod p = 0 , where p = any prime, n = any whole.
Bell says of this theorem:
It is within the grasp of any normal fourteen-year-old, but it is safe
to wager that out of a million human beings of normal intelligence
of any or all ages, less than ten of those who had had no more
mathematics than grammar-grade arithmetic would succeed in finding
a proof within a reasonable time--say a year.
What self-respecting reader could resist such a gauntlet? I have been
working on this on and off for six months, so I guess my time is half up!
Hints, anyone?
-T
Mark Brader
> > Gauss's class in school was asked to calculate 1+2+...+100
>
> No, the series was more difficult; I recall the first term was number
> with 5 or 6 digits; I may recall incorrectly but it was not that easy
> serie in the Bell's book.
The story is "usually" told in one of two ways. In Bell's book[1] it says:
The problem was *of the following sort*, 81927 + 81495 + 81693
+ ... + 100899, where the step from one number to the next is
the same all along (here 198), and a given number of terms
(here 100) are to be added. ...
[Gauss writes down the answer at once, while everyone else
works for an hour ...]
To the end of his days Gauss loved to tell how the one number
he had written was the correct answer and how all the others
were wrong. Gauss had not been shown the trick for doing such
problems rapidly. It is very ordinary once it is shown, but
for a boy of ten to find it by himself is not so ordinary.
My emphasis added: notice that Bell doesn't say that that *was* the series.
The other "usual" telling of the story is as first quoted above, that the
series consisted of the integers from 1 to 100. I always assumed that the
"1 to 100" version of the story had been dumbed-down for innumerate readers,
and that nobody actually remembered what numbers were involved. But now
it occurs to me that "1 to 100" might instead be the true version, and that
Bell might have substituted larger numbers to make the problem seem more
difficult and dramatic.
If Gauss really loved to tell the story to the end of his days, then it
ought to be in print in *his* words somewhere, at least in German.
Has anyone seen such an account? If so, what does he say?
[1] I don't have a copy of it, but I do have a copy of the anthology
"The World of Mathematics" edited by James R. Newman, where the above
passage appears. And by the way, *that's* a notable math book...
--
Mark Brader, SoftQuad Inc., Toronto, utzoo!sq!msb, m...@sq.com
"Have you ever heard [my honesty] questioned?"
"I never even heard it mentioned." -- Every Day's a Holiday
This article is in the public domain.
Andrej Panjkov, La Trobe Maths
Time/Life did a series of books on the various sciences. One of them was
"Mathematics". This book really got me going. It made me pester my cousin
about Pythagorus' theorem.
--
Andrej Panjkov, ma...@lure.latrobe.edu.au
Dept. of Mathematics,
La Trobe University, "I've got a goddamned PLAN!"
Melbourne, Victoria, 3083, Australia
Christopher J. Henrich
>> > I haven't got the book, but the story as usually told goes like this:
>
>
> The problem was *of the following sort*, 81927 + 81495 + 81693
> + ... + 100899, where the step from one number to the next is
> the same all along (here 198), and a given number of terms
> (here 100) are to be added. ...
>
> [Gauss writes down the answer at once, while everyone else
> works for an hour ...]
>
> To the end of his days Gauss loved to tell how the one number
> he had written was the correct answer and how all the others
> were wrong. Gauss had not been shown the trick for doing such
> problems rapidly. It is very ordinary once it is shown, but
> for a boy of ten to find it by himself is not so ordinary.
>
>My emphasis added: notice that Bell doesn't say that that *was* the series.
>The other "usual" telling of the story is as first quoted above, that the
>series consisted of the integers from 1 to 100.
If this is what really happened, then Gauss had to recognize "at a
glance" that the numbers were in arithmetic progression. Moreover,
this arithmetic progression had to be what the schoolmaster intended.
As an example of the difference between intent and performance, note
that Mr. Brader has mistyped the first number in the sequence
(he meant to type 81297, I presume). BTW I did not notice the typo
on my first reading of Mr. Brader's post; why not? Because I knew
what I was *expected* to see and that's what I saw.
So the story with the big messy numbers in it has an added intrinsic
source of improbability. The schoolmaster would have had to be very
careful.
Regards,
Chris Henrich
Robert E George
According to some accounts (e.g., Bell as reprinted in Newman's
"The World of Mathematics", Vol. I) the arithmetic series formula
was well-known, and indeed known by Buettner (Gauss' schoolmaster).
Yet other accounts (mainly verbal ones from acquaintances) have creditted
Gauss as the *first* person to notice the formula. Comments?
Robert George
(speaking only for myself)
Mark Brader
> > + ... + 100899, where the step from one number to the next is
> > the same all along (here 198), and a given number of terms
> > (here 100) are to be added. ...
> As an example of the difference between intent and performance, note
> that Mr. Brader has mistyped the first number in the sequence
> (he meant to type 81297, I presume).
I did indeed miscopy. And it's quite an annoying error, because I *did*
go to the trouble of checking my *source* for misprints, i.e. verifying
that the other numbers really are the 2nd, 3rd, and 100th terms of an
A.P. starting at 81297 with a constant difference of 198. And the first
time the verification failed, because I copied the number 81927 from my
draft text instead of 81297 from the book. When I saw this, I then
proceeded to assume that I had typed it wrong the *second* time and
failed to recheck my own text... sigh.
> So the story with the big messy numbers in it has an added intrinsic
> source of improbability. The schoolmaster would have had to be very
> careful.
Well, I took the intent of the story to be that the schoolteacher *said*
that it was an A.P. (perhaps not using that terminology), not that he
wrote 100 numbers on the blackboard. Even if he had, I'm sure that Gauss
at age 10 could recognize an A.P. with constant difference of 198 about as
easily as most of us can recognize one with a constant difference of 5.
--
Mark Brader, SoftQuad Inc., Toronto, utzoo!sq!msb, m...@sq.com
"I'm a little worried about the bug-eater," she said. "We're embedded
in bugs, have you noticed?" -- Niven, "The Integral Trees"
Tord Malmgren
>>The story is "usually" told in one of two ways. In Bell's book[1] it says:
>> The problem was *of the following sort*, 81927 + 81495 + 81693
>> + ... + 100899, where the step from one number to the next is
>> the same all along (here 198), and a given number of terms
>> (here 100) are to be added. ...
>> [Gauss writes down the answer at once, while everyone else
>> works for an hour ...]
>> To the end of his days Gauss loved to tell how the one number
>> he had written was the correct answer and how all the others
>> were wrong. Gauss had not been shown the trick for doing such
>> problems rapidly. It is very ordinary once it is shown, but
>> for a boy of ten to find it by himself is not so ordinary.
>>My emphasis added: notice that Bell doesn't say that that *was* the series.
>>The other "usual" telling of the story is as first quoted above, that the
>>series consisted of the integers from 1 to 100.
as I read it in a volume called "Sigma", which is about 6 books about the
mathematical history, the teacher asked the children to add the numbers
from 1 to 100, and Gauss wrote the answer down, and handed it to his teacher
and said "da liegt es!". imagine a teacher going about to ask his children
to get the sum of 81927... I can see people are trying to make a monster
out off Gauss as people has done with, for example, Mozart
---------------+--------------------------------
Tord Malmgren | InterNet: To...@VanD.PhySto.SE | These opinions are my own,
| BITNet : TordM@SESUF51 | and NOT of this department!
---------------+--------------------------------
Department of Physics, University of Stockholm
Miguel Bamberger
|> >>The story is "usually" told in one of two ways. In Bell's book[1] it says:
|>
|> >> The problem was *of the following sort*, 81927 + 81495 + 81693
W.K. Buehler: "Gauss, A Biographical Study" Springer Verlag 1981. makes
almost no mention of the story. The author says (p. 7): "He [Gauss] was
unusually lucky ... for his teacher, Buettner, seems to have been
competent and concerned. He took a personal interest in the boy, trying
to help and encourage him". Later on there's an endnote in reference to
Gauss' precociousness: "The statements in this and the preceding
sentence are part of the "Gauss folklore" and probably go back to Gauss
himself". The story is mentioned in passing in another endnote: "one of
the childhood stories ends with the pronouncement (in the local dialect)
"Dar licht se" with which the young Gauss handed in his solution of a
mathematical assignment. Buehler's biography is very thorough...seems
he did not feel he had enough evidence to include the story.
--
Miguel Bamberger | Mr Cooper's Law: "If you do not understand a particular
Austin Tech Pubs | word in a piece of technical writing, ignore it.
| The piece will make perfect sense without it."
Jan Willem Nienhuys
>
> as I read it in a volume called "Sigma", which is about 6 books about the
>mathematical history, the teacher asked the children to add the numbers
>from 1 to 100, and Gauss wrote the answer down, and handed it to his teacher
>and said "da liegt es!".
"Ligget sie" (in his dialect). The story goes on that the slate had to be
put face down, and all the others piled on top in order of arrival.
All the time little Gauss was sitting quietly waiting intil the last
pupil was ready. In those days it seems, corporal punishment was quite
common for boys who had the answer wrong, and acted as smart alecks.
So as all the slates were turned one by one (with many wrong answers),
the tension must have mounting . . .
The story, by the way, used to be told by Gauss himself, no written records
by witnesses exist.
JWM
Gregory McColm
>ma...@lure.latrobe.edu.au (Andrej Panjkov, La Trobe Maths) writes:
>|> tho...@ricci.geom.umn.edu (Thomas Colthurst) writes:
>|> >
>|> > _Men of Mathematics_, E.T. Bell
>|>
>|> That book pissed me off. I found it was written in a sneering and arrogant
>|> tone. I agree that the lives and achievements of the greatest
>|> mathematicians are worth reading about, but I'd try another book.
>
>Does anyone else have this reaction? Bell has his strong opinions, and is
>(of course) very far from being PC, but I am slightly amazed at quite so
>negative a report.
>
>
Eric Temple Bell is what you might call a member of the
mathematical left (very pure and supports abstraction),
while Morris Kline was what you might call a member
of the mathematical right (very applied and opposed
to abstraction). Both have written interesting books
on the history of mathematics, and these books have
been criticised for being opinionated and error-infested.
In particular, Bell despises all politicians (he's not
alone in this), and has a tendency to think that good
mathematics is a mark of good character. He also
repeats gossip incautiously.
I don't know of a conventional, responsible, moderate
book containing short biographies of mathematicians.
As for histories of mathematics, Carl Boyer is a very
good conventional, responsible, and moderate writer
of mathematical history; his book is quite reasonable.
Edna Kramer's is more ahistorical. Other nominations?
-----Greg McColm
Jan Willem Nienhuys
>In particular, Bell despises all politicians (he's not
>alone in this), and has a tendency to think that good
>mathematics is a mark of good character. He also
>repeats gossip incautiously.
You can't trust anything in Bell, unless it's backed up
by somebody else. Better read the somebody else.
>
>I don't know of a conventional, responsible, moderate
>book containing short biographies of mathematicians.
>As for histories of mathematics, Carl Boyer is a very
>good conventional, responsible, and moderate writer
>of mathematical history; his book is quite reasonable.
>Edna Kramer's is more ahistorical. Other nominations?
D.M. Burton, The history of mathematics. An Introduction.
Allyn and Bacon, Boston etc., 1985.
It's a bit expensive, and not as encyclopedic as Boyer.
But it tends to give more non-mathematical historic background.
JWN
>
>-----Greg McColm
Charles Yeomans
>In article <1992Aug13....@ariel.ec.usf.edu> mcc...@darwin.math.usf.edu. (Gregory McColm) writes:
[discussion of math history books and their shortcomings]
The book I found most exciting as a high-schooler was my
CRC handbook of math. Was I not properly politicized?
Charles Yeomans
cyeo...@ms.uky.edu
yeo...@austin.onu.edu