Mathematical Culture Quiz
Paul R. Chernoff
With whom are the following quotations associated?
(Answers next week.)
1. "Let no one ignorant of Geometry enter here."
2. "Give me a lever long enough, and a place to stand upon,
and I will move the world."
3. "A point is that which has position, but not extension."
4. "The book of Nature is written in the language of Mathematics."
5. "Few, but ripe."
6. "I have no time."
7. "God created the integers; all the rest is the work of Man."
8. "We must know, and we shall know."
9. "A good mathematical joke is better, and better mathematics, than
a dozen mediocre papers."
-------------------------------------------------------------------------
--
# Paul R. Chernoff cher...@math.berkeley.edu #
# Department of Mathematics #
# University of California "Against stupidity, the gods themselves #
# Berkeley, CA 94720 struggle in vain." -- Schiller #
David Madore
Paul R. Chernoff wrote:
>
> 1. "Let no one ignorant of Geometry enter here."
Plato is supposed to have written this at the entrance of the Akademia.
It might be apocryphal, though.
>
> 2. "Give me a lever long enough, and a place to stand upon,
> and I will move the world."
Archimedes is supposed to have said that. Same comment.
>
> 3. "A point is that which has position, but not extension."
Euclid wrote that. At least, it is in the "Elements" (he might not have
been the first to write it...)
>
> 4. "The book of Nature is written in the language of Mathematics."
Galileo Galilei (except I though it was "Geometry" rather than
"Mathematics"; of course, the *meaning* is "Mathematics).
>
> 5. "Few, but ripe."
Dunno.
>
> 6. "I have no time."
\'Evariste Galois.
>
> 7. "God created the integers; all the rest is the work of Man."
Leopold Kronecker.
>
> 8. "We must know, and we shall know."
David Hilbert.
>
> 9. "A good mathematical joke is better, and better mathematics, than
> a dozen mediocre papers."
That's a good one. But I don't know the answer.
How about these (not in chronological order):
10. "From this paradise which Cantor created for us, shall we
never be driven away."
11. "I beg to introduce myself..."
12. "I do not know what I may appear to the world. But to myself,
I seem to have been like a child, playing on the seashore... while
the great ocean of truth lay all undiscovered before my eyes."
[I'm quoting this from memory, so I may have altered a few words.]
13. "You can tell the Lion by its claw."
14. "He founded a religion..." [Unfortunately, I can't remember
what comes after that.]
15. "Another of these monstrosities!"
16. "One of the central problems posed to the human mind is that of
the succession of shapes."
David A. Madore
(david....@ens.fr,
http://www.eleves.ens.fr:8080/home/madore/index.html.en)
Chris McManus
Solutions to some of M. Madore's and P. Chernoff's queries:
>>5. Few, but ripe. (Pauca sed matura) [Motto of Karl Gauss (1777-1855)]
>>9. A good mathematical joke is better, and better mathematics, than a dozen mediocre papers. [J.E. Littlewood, (1885-1977) in A M=
athematician's Miscellany, Methuen and Co. ltd., 1953.]
>>12. "I have been but a child playing upon the seashore. I have gathered a few pebbles here and there, but the great ocean lies b=
efore me unexplored." ... [Isaac Newton, summarizing his own life.]
>>13. I recognize the lion by his paw. [said by Bernoulli, Jacques (1654-1705), recognizing an anonymous solution to a problem a=
s Newton's handiwork, Quoted inn G. Simmons, Calculus Gems, New York: McGraw Hill, 1992, p. 136.]
>> 15. Another of these monstrosities! [Gauss' shortsighted remark in rejecting Niels Abel's work on quintic equations, Quoted in G.=
Simmons, Calculus Gems, New York: McGraw Hill, 1992]
--------------------------------------------------------------------
And now a few of my favorites. Who said:
17. Do not worry about your difficulties in mathematics, I assure you
that mine are greater.
18. He is like the fox, who effaces his tracks in the sand with his tail.
19. I have hardly ever known a mathematician who was capable of
reasoning.
20. I hope that posterity will judge me kindly, not only as to the things
which I have explained, but also to those which I have intentionally
omitted so as to leave to others the pleasure of discovery.
21. In mathematics you don't understand things. You just get used to
them.
22. Life is good for only two things, discovering mathematics and
teaching mathematics.
23. Mathematics is a game played according to certain simple rules with
meaningless marks on paper.
24. Mathematics is written for mathematicians.
25. Medicine makes people ill, mathematics make them sad and theology
makes them sinful.
26. omnia apud me mathematica fiunt. (With me everything turns into
mathematics.)
27. The different branches of Arithmetic -- Ambition, Distraction,
Uglification, and Derision.
28. [upon losing the use of his right eye] Now I will have less
distraction.
(Hint: the same genius is reputed to have said "Tell her to wait a
moment. I am almost done," when told his wife was dying. )
PS. David, thank you for the effort you put into your web page. It is
just the right blend of the useful and the whimsical. Regards, Chris
Zachary S Tseng
David Madore <mad...@clipper.ens.fr> asks:
>
>11. "I beg to introduce myself..."
>
That would be Srinivasa Ramanujan, in the beginning of his first letter
to G.H. Hardy.
Cheers,
Zach
David Eppstein
Here's a few more I saved from net.math years past...
"The *evident* character of this defective cognition of which mathematics is
proud, and on which it plumes itself before philosophy, rests solely on the
poverty of its purpose and the defectiveness of its stuff, and is therefore
of a kind that philosophy must spurn."
"What is algebra exactly? Is it those three-cornered things?"
"Mathematicians are a kind of Frenchmen. When you tell them something,
they translate it into their own language, and right away it is something
completely different."
"Those imposters, then, whom they call mathematicians, I consulted without
scruple, because they seemed to use no sacrifice, nor pray to any spirit
for their divinations."
"The good Christian should beware of mathematicians and all those who make
empty prophecies. The danger already exists that the mathematicians have
made a covenant with the Devil to darken the spirit and to confine man in
the bonds of Hell ..."
"In my opinion, a mathematician, in so far as he is a mathematician, need
not preoccupy himself with philosophy---an opinion, moreover, which has
been expressed by many philosophers."
"As far as the laws of mathematics refer to reality, they are not certain;
and as far as they are certain, they do not refer to reality."
"A mathematician's wife overhears her husband muttering the name 'Nancy'.
She wonders whether Nancy, the thing to which her husband referred, is
a woman or a Lie group."
"Thus mathematics may be defined as the subject in which we never know what
we are talking about, nor whether what we are saying is true."
"`Contrariwise,' continued Tweedledee, `if it was, it might be, and if it
were, it would be; but as it isn't, it ain't. That's logic.'"
"Can we deny that a warrior should have a knowledge of arithmetic?
Certainly he should, if he is to have the smallest understanding of military
tactics, or indeed, I should rather say, if he is to be a man at all."
"The question seems to be of such a character that if I should come to life
after my death and some mathematician were to tell me that it had been
definitely settled, I think I would immediately drop dead again."
--
David Eppstein UC Irvine Dept. of Information & Computer Science
epps...@ics.uci.edu http://www.ics.uci.edu/~eppstein/
Ulrich Lange
>> 8. "We must know, and we shall know."
>
>David Hilbert.
Wasn't that actually "Nescimus, sed sciemus" which is more precisely
translated by "We do not know, but we shall know"?
--
Ulrich Lange Dept. of Chemical Engineering
University of Alberta
la...@gpu.srv.ualberta.ca Edmonton, Alberta, T6G 2G6, Canada
Dick Jarvinen
>PS. David, thank you for the effort you put into your web page. It is
>just the right blend of the useful and the whimsical. Regards, Chris
>
Apologies, but I came into this thread rather late. Would you mind posting the
Web Site URL?
Thanks.
Xcott Craver
"I recoil with dismay and horror at this lamentable plague
of functions which do not have derivatives."
"When transcendental questions are under discussion be
transcendentally clear."
"It must have taken many ages to discover that a brace of pheasants
and a couple of days were both instances of the number two."
"There's a lot to be dissatisfied with about this problem,
and thus life in general."
...Actually, that very last one isn't a real math history quote, but
an offhand remark by Dr. Barnett Glickfeld, a CS professor here at NIU
with a curious knack for muttering the depressing-but-profound. A few
others, scribbled in my notes for posterity:
"Not disaster--'abstraction'!"
"Put a gun to myhead: 'think positively.' 'Nah, just shoot me.'"
[paraphrase] "This is called the `monkey and the banana' problem. So
obviously we know from the start that it involves ... a monkey ... and
a banana ... and thus *passion*, hunger, primal urges ... sweet
fruit...." "But it is a simplification of things, and so we'll get a
much different result than if we had a real flesh-and-blood monkey, a
real flesh-and-blood box, and a real flesh-and-blood banana."
,oooooooo8 o oo...@math.niu.edu -- http://www.math.niu.edu/~caj/
o888' `88 ,888. 888
888 ,8'`88. 888 You think this major will land you a
888o. ,oo ,8oooo88. 888 Cauchy desk job? Sure, pal, dRiemann!!
`888oooo88 o88o o888o 888
____________________8o888'_________________________________________________
Ilias Kastanas
In article <331FECCF...@clipper.ens.fr>,
David Madore <mad...@clipper.ens.fr> wrote:
>Paul R. Chernoff wrote:
>>
>> 1. "Let no one ignorant of Geometry enter here."
>
>Plato is supposed to have written this at the entrance of the Akademia.
>It might be apocryphal, though.
MHDEIS AGEWMETRHTOS EISITW
>> 2. "Give me a lever long enough, and a place to stand upon,
>> and I will move the world."
>
>Archimedes is supposed to have said that. Same comment.
DOS MOI PA STW, KAI TAN GAN KINHSW
>> 3. "A point is that which has position, but not extension."
>
>Euclid wrote that. At least, it is in the "Elements" (he might not have
>been the first to write it...)
SHMEION ESTIN OY MEROS OYDEN
>> 4. "The book of Nature is written in the language of Mathematics."
>
>Galileo Galilei (except I though it was "Geometry" rather than
>"Mathematics"; of course, the *meaning* is "Mathematics).
>
>>
>> 5. "Few, but ripe."
>
>Dunno.
PAUCA, SED MATURA (K. F. Gauss)
>> 6. "I have no time."
>
>\'Evariste Galois.
>
>>
>> 7. "God created the integers; all the rest is the work of Man."
>
>Leopold Kronecker.
>
>>
>> 8. "We must know, and we shall know."
>
>David Hilbert.
'In mathematics, there is no ignorabimus'... Well...
>> 9. "A good mathematical joke is better, and better mathematics, than
>> a dozen mediocre papers."
>
>That's a good one. But I don't know the answer.
I wish I knew myself.
>How about these (not in chronological order):
>
>10. "From this paradise which Cantor created for us, shall we
>never be driven away."
Hilbert
>11. "I beg to introduce myself..."
The Rolling Stones (Mick Jagger, "Sympathy for the Devil")
OK, not 'I beg' but 'Please allow me'.
>12. "I do not know what I may appear to the world. But to myself,
>I seem to have been like a child, playing on the seashore... while
>the great ocean of truth lay all undiscovered before my eyes."
>[I'm quoting this from memory, so I may have altered a few words.]
Newton
>13. "You can tell the Lion by its claw."
E3 ONYXOS TON LEONTA is kind of a cliche' ... who exactly
repeated it?
>14. "He founded a religion..." [Unfortunately, I can't remember
>what comes after that.]
>
>15. "Another of these monstrosities!"
Could it be Poincare, lamenting about constructions (maybe like
continuous nondifferentiable f) "meant to put at fault the reasonings
of our forefathers"...? Which they actually don't...
Ilias
Paul Bradley
>1. "Let no one ignorant of Geometry enter here."
Plato
>2. "Give me a lever long enough, and a place to stand upon,
>and I will move the world."
Archimedes
>3. "A point is that which has position, but not extension."
Euclid
>4. "The book of Nature is written in the language of Mathematics."
Dunno
>5. "Few, but ripe."
Again
>6. "I have no time."
Evariste Galois, on a scribbled page of theorems written the sometime
immediately before his death in a duel.
>7. "God created the integers; all the rest is the work of Man."
Sounds like a Hardy type comment to me, but I couldn`t be sure.
>8. "We must know, and we shall know."
dunno
>9. "A good mathematical joke is better, and better mathematics, than
>a dozen mediocre papers."
Erdos?
Datacomms Technologies web authoring and data security
Paul Bradley, Pa...@fatmans.demon.co.uk
Pa...@crypto.uk.eu.org, Pa...@cryptography.uk.eu.org
Http://www.cryptography.home.ml.org/
Email for PGP public key, ID: 5BBFAEB1
"Don`t forget to mount a scratch monkey"
Paul Bradley
>And now a few of my favorites. Who said:
>
>20. I hope that posterity will judge me kindly, not only as to the things
>which I have explained, but also to those which I have intentionally
>omitted so as to leave to others the pleasure of discovery.
Hardy in "A mathematicians apology"
> 23. Mathematics is a game played according to certain simple rules with
>meaningless marks on paper.
Turing?
Paul Bradley
>11. "I beg to introduce myself..."
Ramanujan?
>12. "I do not know what I may appear to the world. But to myself,
>I seem to have been like a child, playing on the seashore... while
>the great ocean of truth lay all undiscovered before my eyes."
>[I'm quoting this from memory, so I may have altered a few words.]
Newton
>15. "Another of these monstrosities!"
This had me for a minute, then I realised it was a Gauss quote,
incidentally there was another mathematician, the name of whom I
forget, who referred at one point to fractal geometry as a
"monstrosity" and that was what threw me, can anyone remember who it
was?
Norah Esty
In article <5fpjmh$l...@boursy.news.erols.com>,
Chris McManus <cmcm...@erols.com> wrote:
>And now a few of my favorites. Who said:
>
>17. Do not worry about your difficulties in mathematics, I assure you
>that mine are greater.
Einstein! :)
>
Some of my very favorites:
"The world would be a better place if every you student were given a
pocket calculator and encouraged to play with the logistic difference
equation."
"To call the study of chaos 'nonlinear science' was like calling zoology
'the study of non-elephant animals'."
:)
--
/--------------------------------\/---------------------------------\
| Norah Esty || "I would believe only |
| no...@math.montana.edu || in a god who could dance." |
| http://math.montana.edu/~norah || -Friedrich Nietzsche |
Paul R. Chernoff
In article <5fntn6$l...@agate.berkeley.edu>,
I <cher...@math.berkeley.edu> wrote:
>
>With whom are the following quotations associated?
>(Answers next week.)
>
Here are the answers (each of which was gotten by at least one
other poster to sci.math):
>1. "Let no one ignorant of Geometry enter here."
Plato (purportedly posted over the entrance to his Academy)
>2. "Give me a lever long enough, and a place to stand upon,
>and I will move the world."
Archimedes (attributed)
>
>3. "A point is that which has position, but not extension."
Euclid
>
>4. "The book of Nature is written in the language of Mathematics."
Galileo
>
>5. "Few, but ripe."
Gauss ("Pauca sed matura", his motto)
>
>6. "I have no time."
Galois (marginal note written on his long paper on
the solvability of polynomials; contrary to popular belief, Galois
did *not* write the paper itself in one night prior to his fatal duel.)
>
>7. "God created the integers; all the rest is the work of Man."
Leopold Kronecker
>
>8. "We must know, and we shall know."
David Hilbert
>
>9. "A good mathematical joke is better, and better mathematics, than
>a dozen mediocre papers."
John E. Littlewood
David Madore
The story so far...
The following quotes have been posted, and the following answers
have been given (I added several answers, and two extra quotes,
of my own, at the end):
1. "Let no one ignorant of Geometry enter here."
Plato is supposed to have written this at the entrance of the
Akademia.
It might be apocryphal, though.
2. "Give me a lever long enough, and a place to stand upon,
and I will move the world."
Archimedes is supposed to have said that. Same comment.
3. "A point is that which has position, but not extension."
Euclid wrote that. At least, it is in the "Elements" (he might not
have
been the first to write it...)
4. "The book of Nature is written in the language of Mathematics."
Galileo Galilei (except I though it was "Geometry" rather than
"Mathematics"; of course, the *meaning* is "Mathematics).
5. "Few, but ripe."
Motto of Karl Friedrich Gauss
6. "I have no time."
\'Evariste Galois.
7. "God created the integers; all the rest is the work of Man."
Leopold Kronecker.
8. "We must know, and we shall know."
David Hilbert, on his tombstone I believe (Wir mussen wissen,
Wir werden wissen)
9. "A good mathematical joke is better, and better mathematics, than
a dozen mediocre papers."
John Edensor Littlewood.
10. "From this paradise which Cantor created for us, shall we
never be driven away."
David Hilbert.
11. "I beg to introduce myself..."
Srinivasa Ramanujan, starting his first letter to Hardy.
12. "I do not know what I may appear to the world. But to myself,
I seem to have been like a child, playing on the seashore... while
the great ocean of truth lay all undiscovered before my eyes."
[I'm quoting this from memory, so I may have altered a few words.]
Isaac Newton, summarizing his own life.
13. "You can tell the Lion by its claw."
Jakob Bernoulli, in recognizing Newton to be the author of the
solution
to the problem of the brachystochrone.
14. "He founded a religion..." [Unfortunately, I can't remember
what comes after that.]
Bertrand Russell, about Pythagoras.
15. "Another of these monstrosities!"
Gauss, while rejecting Abel's work on the impossibility of solving the
quintic equation by means of radicals.
16. "One of the central problems posed to the human mind is that of
the succession of shapes."
Ren\'e Thom.
17. Do not worry about your difficulties in mathematics, I assure you
that mine are greater.
Albert Einstein.
18. He is like the fox, who effaces his tracks in the sand with his
tail.
19. I have hardly ever known a mathematician who was capable of
reasoning.
20. I hope that posterity will judge me kindly, not only as to the
things
which I have explained, but also to those which I have intentionally
omitted so as to leave to others the pleasure of discovery.
Geodfrey Harold Hardy.
21. In mathematics you don't understand things. You just get used to
them.
22. Life is good for only two things, discovering mathematics and
teaching mathematics.
23. Mathematics is a game played according to certain simple rules with
meaningless marks on paper.
24. Mathematics is written for mathematicians.
25. Medicine makes people ill, mathematics make them sad and theology
makes them sinful.
26. Omnia apud me mathematica fiunt. (With me everything turns into
mathematics.)
27. The different branches of Arithmetic -- Ambition, Distraction,
Uglification, and Derision.
28. [upon losing the use of his right eye] Now I will have less
distraction.
Leonhard Euler.
29. "The world would be a better place if every you student were given a
pocket calculator and encouraged to play with the logistic difference
equation."
30. "To call the study of chaos 'nonlinear science' was like calling
zoology
'the study of non-elephant animals'."
31. "The *evident* character of this defective cognition of which
mathematics is
proud, and on which it plumes itself before philosophy, rests solely on
the
poverty of its purpose and the defectiveness of its stuff, and is
therefore
of a kind that philosophy must spurn."
32. "What is algebra exactly? Is it those three-cornered things?"
33. "Mathematicians are a kind of Frenchmen. When you tell them
something,
they translate it into their own language, and right away it is
something
completely different."
Johann Wolfgang von Goethe [I think].
34. "Those imposters, then, whom they call mathematicians, I consulted
without
scruple, because they seemed to use no sacrifice, nor pray to any
spirit
for their divinations."
35. "The good Christian should beware of mathematicians and all those
who make
empty prophecies. The danger already exists that the mathematicians
have
made a covenant with the Devil to darken the spirit and to confine man
in
the bonds of Hell ..."
36. "In my opinion, a mathematician, in so far as he is a mathematician,
need
not preoccupy himself with philosophy---an opinion, moreover, which has
been expressed by many philosophers."
37. "As far as the laws of mathematics refer to reality, they are not
certain;
and as far as they are certain, they do not refer to reality."
38. "A mathematician's wife overhears her husband muttering the name
'Nancy'.
She wonders whether Nancy, the thing to which her husband referred, is
a woman or a Lie group."
39. "Thus mathematics may be defined as the subject in which we never
know what
we are talking about, nor whether what we are saying is true."
40. "`Contrariwise,' continued Tweedledee, `if it was, it might be, and
if it
were, it would be; but as it isn't, it ain't. That's logic.'"
Charles Dogdson (i.e. Lewis Caroll).
41. "Can we deny that a warrior should have a knowledge of arithmetic?
Certainly he should, if he is to have the smallest understanding of
military
tactics, or indeed, I should rather say, if he is to be a man at all."
42. "The question seems to be of such a character that if I should come
to life
after my death and some mathematician were to tell me that it had been
definitely settled, I think I would immediately drop dead again."
43. "I recoil with dismay and horror at this lamentable plague
of functions which do not have derivatives."
44. "When transcendental questions are under discussion be
transcendentally clear."
45. "It must have taken many ages to discover that a brace of pheasants
and a couple of days were both instances of the number two."
46. This treatise takes mathematics at its beginnings and gives complete
proofs. Its
reading does not, therefore, require any prior knowledge of
mathematics, but
only a certain habit of mathematical reasoning and a certain power of
abstraction.
47. Mathematics is a science in which one does not know what one is
talking about,
nor whether what one says is true.
[I'm posting this, but I really don't know the answer. Or rather, I've
seen this
quote attributed both to Russell and to Poincar\'e.]
rajib doogar
David Madore (mad...@clipper.ens.fr) wrote:
: 13. "You can tell the Lion by its claw."
might this concievably be "paw" instead of "claw"?
: 21. In mathematics you don't understand things. You just get used to
: them.
John von-Neumann?
--
Rajib Doogar http://www.nd.edu/~rdoogar
375 College of Business Administration
University of Notre Dame Ph: (219) 631 6499
Notre Dame, IN 46556-0339 Fax: (219) 631 5255
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
"Think as I think," said a man, "or you are abominably wicked: You are a
toad." And after I had thought of it, I said, "I will, then, be a toad."
-- Stephen Crane
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Estelle Souche
In article <33240A9F...@clipper.ens.fr>, David Madore <mad...@clipper.ens.fr> writes:
<many good quotes snipped>
>46. This treatise takes mathematics at its beginnings and gives complete
>proofs. Its
> reading does not, therefore, require any prior knowledge of
>mathematics, but
> only a certain habit of mathematical reasoning and a certain power of
>abstraction.
The great Nicolas B.? :-)
>47. Mathematics is a science in which one does not know what one is
>talking about,
> nor whether what one says is true.
>
> [I'm posting this, but I really don't know the answer. Or rather, I've
>seen this
> quote attributed both to Russell and to Poincar\'e.]
I've seen this quote attributed to Russell too...
Estelle (eso...@ens.ens-lyon.fr)
Robert Israel
Here are a few more. Have fun:
There is a divinity in odd numbers, either in nativity, chance or death.
Mathematics possesses not only truth, but supreme beauty - a beauty cold
and austere, like that of sculpture.
He uses statistics as a drunken man uses lamp-posts - for support rather
than illumination.
Lagrange is the lofty pyramid of the mathematical sciences.
The deep study of nature is the most fruitful source of mathematical
discovery.
I tell them that if they occupy themselves with the study of mathematics
they will find in it the best remedy for the lusts of the flesh.
Mathematical proofs, like diamonds, are hard as well as clear, and will
be touched with nothing but strict reasoning.
The beginner should not be discouraged if he finds that he does not have
the prerequisites for reading the prerequisites.
Robert Israel isr...@math.ubc.ca
Department of Mathematics (604) 822-3629
University of British Columbia fax 822-6074
Vancouver, BC, Canada V6T 1Y4
David Madore
Estelle Souche wrote:
` >46. This treatise takes mathematics at its beginnings and gives
complete
` >proofs. Its
` > reading does not, therefore, require any prior knowledge of
` >mathematics, but
` > only a certain habit of mathematical reasoning and a certain power
of
` >abstraction.
` The great Nicolas B.? :-)
That's right. The first two sentences of the "Elements of Mathematics"
of this famous former member of the Royal Polovtsian Academy of Science
(and professor of mathematics at the University of Nancago). :-)
`
` >47. Mathematics is a science in which one does not know what one is
` >talking about,
` > nor whether what one says is true.
` >
` > [I'm posting this, but I really don't know the answer. Or rather,
I've
` >seen this
` > quote attributed both to Russell and to Poincar\'e.]
`
` I've seen this quote attributed to Russell too...
Thanks. It *does* look more like his style.
David A. Madore
(david....@ens.fr,
http://www.eleves.ens.fr:8080/home/madore/index.html)
Robert Israel
And more:
In the thirties, under the demoralizing influence of quantum-theoretic
perturbation theory, the mathematics required of a theoretical physicist
was reduced to a rudimentary knowledge of the Latin and Greek alphabets.
One doesn't really understand a theorem until one regards its proof as
trivial.
The widely held belief that one cannot get something for nothing is a
superstition.
There is no permanent place in the world for ugly mathematics.
It saddens me that educated people don't even know that my
subject exists.
... it is now a well-established phenomenon that what is highly
abstract for a generation of mathematicians is just commonplace
for the next one.
Civilization advances by extending the number of important operations
which we can perform without thinking.
james dolan
chris mcmanus writes:
-15. Another of these monstrosities! [Gauss' shortsighted remark in
-rejecting Niels Abel's work on quintic equations, Quoted in G.=
-Simmons, Calculus Gems, New York: McGraw Hill, 1992]
does anyone know why gauss said this? in what way did some aspect of
abel's work appear to gauss to be a "monstrosity"?? on the face of it
it doesn't seem to make much sense.
Kesh Govinder
james dolan (jdo...@math.ucr.edu) wrote:
I believe that Gauss did not actually critically peruse the script but
just dismissed it as `another of these monstrosities'. It seemed that
everyone and their uncle were trying to find the general solution of the
quintic. I also think that it is generally believed that ahd Gauss actually
looked at the paper he would have realised that Abel was attempting the
opposite -- that no general solution existed.
--
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Kesh Govinder
Dept of Maths and App Maths, University of Natal -- Durban, South Africa
Tel: (+27) 31 260 3021
Fax: (+27) 31 260 1017
Email: govi...@lourie.und.ac.za |
govi...@ph.und.ac.za |
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