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QUOTES I enjoy reading books about the history of science, 1) Quote:
"Out of fifty mathematical papers presented in brief at such a
meeting, it is a rare mathematician indeed who really understands what more than
half a dozen are about." From:
Eric Temple Bell Source:
Mathematics: Queen and Servant of Science (p. 7) Context:
Meetings papers and who understands them. 2) Quote:
"By studying the masters, not their pupils." From:
N.H. Abel (Mathematician) Source:
Mathematics: Queen and Servant of Science (p. 12) Context:
On how he was so prolific w/his research output in such a short time. 3) Quote:
" 'Obvious' is the most dangerous word in mathematics." From:
Eric Temple Bell Source:
Mathematics: Queen and Servant of Science Context:
The use of obvious in mathematical proofs. 4) Quote:
"Hanging at dawn tends to focus the mind." From:
Johnson (unknown) Source:
Stephen Hawkings' mother in Movie A Brief History of Time. Context:
On why son became so productive after his disease was diagnosed. 5) Quote:
"An 'improperly posed' question." From:
Eric Temple Bell Source:
Mathematics: Queen and Servant of Science (p. 26) Context:
A question about the origin of the postulate much as postulate a
continuous function. If you don't like the calculus where the continuous function
came from is 'improperly posed' it's too late then!! 6) Quote:
"Common sense is nothing more than a deposit of prejudices laid down
in the mind before you reach eighteen." From:
Albert Einstein. Source:
Mathematics: Queen and Servant of Science & Readings in Philosophy of
Science "Why we should believe theories or something." Context:
Evident isn't it! 7) Quote:
"Nobody can say what a variable is." From:
H. Weyl Source:
Mathematics: Queen and Servant of Science Context:
Defining a variable 8) Quote:
"Fashion as King is sometimes a very stupid ruler." From:
Eric Temple Bell Source:
Mathematics: Queen and Servant of Science (p.146) 9) Quote:
…In particular, the axioms of plane geometry are true within the limits
of experiment on the surface of a plane sheet of paper, and yet we know that the
sheet is really covered with a number of small ridges and furrows upon which
(the total curvature being not zero) these axioms are not true. From:
W.K. Clifford. On the
Space-Theory of Matter Source:
Mathematics: Queen and Servant of Science (p. 204 - 205) Context:
Discussing metrics 10)
Quote: "Entities
shall not be multiplied beyond necessity." From:
W. Occam (razor: Occam's
razor) Source:
Mathematics: Queen and Servant of Science (p. 269) Context:
Abstraction vs. reality 11)
Quote: "Science
makes no pretension to eternal truth or absolute truth." From:
Eric Temple Bell Source:
Mathematics: Queen and Servant of Science (p. 291) 12)
Quote: "When
it doesn't rain I have no need to fix the hole in my roof and when it rains I
can't go outside to fix it." Source:
Unknown Context:
I heard in passing when someone was talking about the deficit (budget)
and it never being a good time to address it. 13)
Quote: In
a certain village a barber shaves all those, and only those, who do not shave
themselves. Does the barber shave himself? From:
Unknown (not quoted) Source:
Mathematics: Queen and Servant of Science (p. 403) Context:
Paradoxes in math 14)
Quote: …"As
for the knowledge of fact, it is originally sense and ever after, memory.
And for knowledge of consequence, which I have said before is called
science, it is not absolute but conditional." From:
Thomas Hobbes Source:
Leviathan Chapter VII Context:
Discussing what is knowledge and science 15)
Quote: "…It
is better not to look at than to look carelessly." From:
Henri Poincare' (French Mathematician) Source:
His book Science and Method "Introduction" 16)
Quote: "Science
is built up of facts, as a house is built up of stones, but an accumulation of
facts is no more science than a heap of stones is a house." From:
Henri Poincare' Source:
Reliable Knowledge (p. 142). 17)
Quote: "…Sociology
is the science w/ the greatest number of methods and the least results." From:
Henri Poincare' Source:
Science and Methods (p. 20) 18)
Quote: "But
what we must aim at is not so much to ascertain resemblances and differences, as
to discover similarities hidden under apparent discrepancies." From:
Henri Poincare' Source:
Science and Methods (p. 21) 19)
Quote: "…It
is not order only, but unexpected order, that has value." From:
Henri Poincare' Source:
Science and Methods (p. 32) 20)
Quote: "Chance
is only the measure of our ignorance." From:
Henri Poincare' Source:
Science and Methods (p. 65) 21)
Quote: "…intuition
cannot give us exactness, nor ever certainty, and this has been recognized more
and more." From"
Henri Poincare' Source:
Science and Methods (p. 123) Context:
Logic vs. intuition 22)
Quote: "They
have shown that there is no such thing as an "a prior" synthetic
judgment (The term employed by Kant to designate the judgments that can neither
be demonstrated analytically, nor reduced to an identity, not established
experimentally)…" From:
Henri Poincare' Source:
Science and Methods (p. 146) 23)
Quote: "I
don't know" From:
Lagrange Source:
Men of Mathematics E.T.
Bell (p. 9) 24)
Quote: "I
see I have made myself a slave to philosophy [science], but if I get free of Mr.
Lucas business [incessant, trivial and 'improperly posed' criticism of his
theory of optics by Mathematician Lucas], I will resolutely bid adieu to it
eternally, excepting what I do for my private satisfaction, or leave to come out
after me; for I see a man must either resolve to put out nothing new, or become
a slave to defend it." From:
Sir Isaac Newton Source:
Men of Mathematics E.T.
Bell (p. 107 -108) 25)
Quote: "If
I have seen a little farther than others it is because I have stood on the
shoulders of giants." From:
Sir Isaac Newton Source:
Men of Mathematics E.T.
Bell (p. 93) 26)
Quote: "Men
pass away but their deeds abide." From:
A. Cauchy (French Mathematician's last words) Source:
Men of Mathematics E.T. Bell (p. 293) 27)
Quote: "You
must always invert." From:
C.G.J. Jacobi's (German born mathematician) Source:
Men of Mathematics E.T. Bell (p. 323) Context:
When asked the secret of mathematical discoveries 28)
Quote: "Your
father would never have married and you wouldn't be here now, if he had insisted
on knowing all the girls in the world before marrying one." From:
C.G.J. Jacobi Source:
Men of Mathematics E.T.
Bell (p. 330) Context:
to a student who wanted to learn from other some more before offering his
own work. 29)
Quote: "…but
a philosopher like him [Fourier] should have known the sole end of science is
the honor of the human mind, and that under this title a question about number
is worth as much as a question about the system of the world." From:
C.G.J. Jacobi Source:
Men of Mathematics E.T.
Bell.. (p. 338) 30)
Quote: "May
not music be described as the mathematics of sense, mathematics as music of the
reason." From:
Sylvester, J.J. Source:
Men of Mathematics E.T.
Bell (p. 404) 31)
Quote: "To
publish an article of real merit every week - that is impossible." From:
Weierstrass on Poincare's deluge of papers Source:
Men of Mathematics E.T.
Bell (p. 428) 32)
Quote: "Time
makes fools of us all. Our only
comfort is that greater shall come after us." From:
E.T. Bell Source:
Men of Mathematics (p. 481) 33)
Quote: "All
of these dislikes and objections are of course themselves meaningless unless
they can be backed by a definite program to replace what is rejected." From:
E.T. Bell. Commenting on
Kronecher's objection to all mathematics based on anything but positive
integers. Source:
Men of Mathematics (p.
482) 34)
Quote: "Mathematical
discoveries, small or great…are never born of spontaneous generation. They always presuppose a soil seeded with preliminary
knowledge and well prepared by labor, both conscious and subconscious." From:
Swiss Mathematical periodical: L'Ensegnment Mathematique
1902 and 1904. Source:
Men of Mathematics (p.
548) (See also another example
Poincare': Science and Methods (p. 551)
in Men of Mathematics) 35)
Quote: "Intuition
(male, female or mathematical) has been greatly overrated.
Intuition is the root of all superstition." From:
E.T. Bell Source:
Men of Mathematics (p.
567) 36)
Quote: "There
can be no time without space." From:
Paul Davis Source:
The Mind of God (p.
49) 37)
Quote: "No
one who is closed off from mathematics can ever grasp the full significance of
the natural order that is woven so deeply into the fabric of physical
reality." From:
Paul Davis Source:
The Mind of God (p.
93) 38)
Quote: "Undecidable
propositions run through mathematics like threads of gristle that criss-cross a
steak in such a dense way that they cannot be cut out without the entire steak's
being estranged." From:
Douglas Hofstadter author of Alan Turing:
The Emgima in reference to Turing and the mere well know Godel's
theorem on self reference in mathematical logic, whereby by logic convults into
a do loop. for example see quote #
13. Source:
The Mind of God (p.
107) 39)
Quote: "The
popular image of mathematics as a collection of precise facts, linked together
by well-defined logical paths is revealed to be false.
There is randomness and hence uncertainty in mathematics, just as there
is in physics." From:
Paul Davis, discussing algorithmic information theory and Gregory Chaitin
development of the Diophantine equation Source:
The Mind of God (p.
132) 40)
Quote: "The
book of nature is written in mathematical language." From:
Galileo Source:
The Mind of God (p.
140) 41)
Quote: "So
much the worse for the experiment. The
theory is right!" From:
Albert Einstein, when asked what he would do if the experiment didn't
agree with the theory. Source:
The Mind of God (p.
175) 42)
Quote: "It
is more important to have beauty in one's equations than to have them fit the
experiment." From:
Paul Disae (Theoretical Physicist) Source:
The Mind of God (p.
176) 43)
Quote: "I
hate it when people try to be profound, sometimes the simplest words are
the most profound." Source:
Mellie E. Smith 44)
Quote: "…It
is pretentious to use mathematics when words will do and it is equally
pretentious to use "high brow" mathematics when more elementary
methods will do almost as well." From:
Frank Hahn Source:
(1990) "John Hicks the Theorist," Economic Journal vol. 100
June; 539-49. 45)
Quote: "Hypotheses
are tested in bundles." From:
Pierre Duhem Source:
Introductory Readings in the Philosophy of Science
(p. 67) 46)
Quote: "Where
Theories intersect, laws are usually hard to come by." From:
Nancy Cartwright Source:
Introductory Readings in the Philosophy of Science
(p. 45) 47)
Quote; "Philosophers
of science have learned a great deal about science, but the knowledge falls
short of any usable algorithm for scientific practice or theory choice." From:
Daniel M. Hausman Source:
The Philosophy of Economics: An
Anthology Introduction (p. 24) 48)
Quote: "When
an effect depends upon a concurrence of causes, those causes must be studied one
at a time, and their laws separately investigated, if we wish, through the
causes, to obtain the power of either predicting or controlling the
effect." From:
John S. Mill Source:
Philosophy of Economics (p.
53) 49)
Quote: "[The
pursuit of wealth] of all hypotheses equally simple, is nearest the truth." From:
J.S. Mill Source:
Philosophy of Economics (p. 54) 50)
Quote: "…those
who disavow theory cannot make one step without theorizing." From:
J.S. Mill Source:
Philosophy of Economics (p.
55) 51)
Quote: "The
conclusions of Political Economy, consequently, like those of geometry, are only
true,…,in the abstract…" From:
J.S. Mill Source:
Philosophy of Economics (p.
57) (cross reference w/ #9):
see last paragraph of p. 57 52)
Quote: "When
the principles of Political Economy are to be applied to a particular case, then
it is necessary to take into account all the individual circumstances of that
case; not only examining to which of the sets of circumstances contemplated by
the abstract science the circumstances of the case in question correspond, but
likewise what other circumstances may exist in that case, which not being common
to it with any large and strongly worded class of cases, have not fallen under
the cognizance of the science. These
circumstances have been called disturbing causes…
When the disturbing causes are known, the allowance for then in no way
distracts nor constitutes any deviations from the a priori method.. Like friction
in mechanics to which they have been compared,… in time many of them are
brought within the pale of the abstract science itself, and their effect is
found to admit of as accurate an estimation as those mere striking effects which
they modify.
The disturbing causes have their laws, as the cause which are thereby
disturbed have theirs…" From:
J.S. Mill Source:
Philosophy of Economics (p.
60 - 61) 53)
Quote: "…he
may be an excellent professor of abstract science; for a person may be of great
use who points out correctly what effects will follow from certain combinations
of possible circumstances,… If
however he does no more than this, he must rest contented to take no share in
practical politics; to have no opinion, or to hold it with extreme modesty, on
the applications which should be made of the existing circumstances." From:
J.S. Mill Source:
Philosophy of Economics (p.
63) 54)
Quote: "Each
undervalues that part of the materials of thought with which he is not
familiar." From:
J.S. Mill Source:
Philosophy of Economics (p.
64) 55)
Quote: "A
not unnatural consequence is that people think themselves competent to reason
about economic problems, however complex, without any such preparatory
scientific training as would be unwisely considered essential in other
departments of inquiry. This
temptation to discuss economic questions without adequate scientific training is
all the greater, because economic conditions exert so powerful an influence upon
men's material interest." From:
J. Neville Keynes Source:
Philosophy of Economics (p.
73) 56)
Quote; "…without
the aid of an extensive knowledge of facts, there is a danger of ascribing to
economic doctrines a much wider range of applications than really belongs to
them." From:
J. Neville Keynes Source:
Philosophy of Economics (p.
92) 57)
Quote: "…there
is a tendency to forget that the deductive method in its complete form consists
of three stages, only one of which is actually deductive, the two others being
the inductive determination of premises, and the inductive verification of
conclusions." From:
J. Neville Keynes Source:
Philosophy of Economics (p.
90) 58)
Quote:
"Models should be used, not believed." From:
Henri Theil Source:
Principles of Econometrics 59)
Quote: "Subjective
certainty is inversely proportional to objective certainty." From:
Bertrand Russell Source:
Reliable Knowledge (p. 22) 60)
Quote: "Indefinite
expression is the best exponent of imperfect knowledge." From:
Louis Pasteur Source:
Reliable Knowledge (p. 195) 61)
Quote: "With
such limited abilities as I possess, it is truly surprising that I should have
influenced to a considerable extent the belief of scientific men on some
important points." From:
Charles Darwin Source:
Introduction to Origin of Species
(p. 7) 62)
Quote: "So
profound is our ignorance, and so high our presumption, that we marvel when we
hear of the extinction of an organic being; and as we do not see the cause, we
invoke cataclysms to desolate the world, or invent laws on the duration of the
forms of life.: From:
Charles Darwin Source:
Introduction to Origin of Species
(p. 87) 63)
Quote: "Extinction
and natural selection go hand in hand." From:
Charles Darwin Source:
Introduction to Origin of Species
(p.179) 64)
Quote: "How
easily we can be mistaken in matters which concern us closely; and how much also
the judgments of our friends must be suspect when they are in our favor." From:
Rene' Descartes Source:
Discourse on Method and the Meditations 65)
Quote: "All
those who hold opinions quite opposed to ours are not on that account barbarians
or savages." From:
Rene' Descartes Source:
Discourse on Method and the Meditations 66)
Quote: "…One
cannot so well group a thing and make it one's own when it is learnt from
another person, as when one discovers it oneself." From:
Rene' Descartes Source:
Discourse on Method and the Meditations 67)
Quote: "For
the same thing that might, perhaps, with some reason, seem very imperfect if
quite alone, may be very perfect in its nature if it is looked upon as part of
the whole universe." From:
Rene' Descartes Source:
Discourse on Method and the Meditations, (p. 135)
4th meditation 68)
Quote: "It
is a fault which can be observed in most disputes, that, truth being midway
between two opinions that are held, each side departs the further from it the
greater his passion for contradiction." From:
Rene' Descartes Source:
Discourse on Method and the Meditations 69)
Quote: "Great
is the power of steady misrepresentation; but the history of science shows that
fortunately this power does not long endure." From:
Charles Darwin Source:
Introduction to Origin of Species
(p. 519) 70)
Quote: "Anyone
whose disposition leads him to attach more weight to unexplained difficulties
than to the explanation of a certain number of facts will certainly reject the
theory." From:
Charles Darwin Source:
Introduction to Origin of Species
(p.521) 71)
Quote: "The
rules for classifying will no doubt become simpler when we have a definite
object in view." From:
Charles Darwin Source:
Introduction to Origin of Species
(p.526) 72)
Quote: "I
know of nothing, in my education, to which I think myself more indebted for
whatever capacity of thinking I have attained [than logic]." From:
J.S. Mill Source:
Autobiography of J.S. Mill (p.
18) 73)
Quote: "A
pupil from whom nothing is ever demanded which he cannot do, never does all he
can." From:
J.S. Mill Source:
Autobiography of J.S. Mill (p.
26) 74)
Quote: "The
continuation of this article in the second number of the [Westminster] Review
was written by me under my father's eye, and (except as practice in composition,
in which respect it was, to me, more useful than anything else I ever wrote) was
of little or no value." From:
J.S. Mill Source:
Autobiography of J.S. Mill (p.
64) footnote [The inability to accurately access the consumers view of your own
work] 75)
Quote: "When
reason is against a man, a man will be against reason." From:
Thomas Hobbes Source:
Autobiography of J.S. Mill (p.
104) 76)
Quote: "…many
false opinions may be changed for true ones, without in the least altering the
habits of mind of which false opinions are the result." From:
J.S. Mill Source:
Autobiography of J.S. Mill (p.
153) 77)
Quote: "Men
are not more zealous for the truth than they often are for error." From:
J.S. Mill Source:
Liberty (p. 231) 78)
Quote: "No
one can be a great thinker who does not recognize, that as a thinker it is his
first duty to follow his intellect to whatever conclusions it may lead.
Truth gains more even by the errors of one who, with due study and
preparation, thinks for himself, than by the true opinions of those who only
hold them because they do not suffer themselves to think." From:
J.S. Mill Source:
Liberty (p. 236) 79)
Quote: "Tho'
purblind man sees but part of the chain, the nearest link, his eyes not carrying
to the equal beam; that poizes all above." From:
Benjamin Franklin Source:
The autobiography of Benjamin Franklin
(p. 79) **This is actually a
line from Dryden!!** 80)
Quote: "Like
a man traveling in foggy weather: Those
at some distance before him on the road he sees wrapt up in a fog, as well as
those behind him, and also the people in the fields on each side; but near him
all appears clear. Tho' in truth he
is as much in the fog as any of them." From:
Benjamin Franklin Source:
His autobiography (p. 153 -
154). 81)
Quote: "Theory
dominates the experimental work from its initial planning up to the finishing
touches in the laboratory." From:
Sir Karl Popper Source:
Logic of Scientific Discovery (p. 107) 82)
Quote: (Not
really a quote but a paraphrase) 'New
ideas pass through three phases of denial.
First, they are wrong, Second, they are against region.
Third, they are old news, trivial, common sense.' From:
J.S. Mill Source:
Fuzzy Thinking by Bent Kosko (p. 41) 83)
Quote: "[There
are 3 classes of problems in 'normal' science] - determination of significant
fact, matching facts w/ theory, and articulation of theory…" From:
Thomas Kuhn Source:
The Structure of Scientific Revolutions (p. 34) 84)
Quote: "…since
no paradigm ever solves all the problems it defines and since no two paradigms
leave all the same problems unsolved, paradigm debates always involve the
question: 'Which problem is it more significant to have solved?'" From:
Thomas Kuhn Source:
The Structure of Scientific Revolutions (p. 110) 85)
Quote: "The
competition between paradigms is not the sort of battle that can be resolved by
proofs." From:
Thomas Kuhn Source:
The Structure of Scientific Revolutions (p. 148) 86)
Quote: "Communication
across the revolutionary [different paradigms] divide is inevitably
partial." From:
Thomas Kuhn Source:
The Structure of Scientific Revolutions (p. 149) 87)
Quote: "…working
scientist are not going … to change their ways of thinking, in doing science,
ex more philosophic, because they have Popper and Fegerabend pontificating at
them like eighteenth-century divines…" From:
Margaret Masterman Source:
Criticism and the Growth of Knowledge (. 60) 88)
Quote: "There
is no falsification before the emergence of a better theory." From:
Imre Lakatos Source:
Criticisms and the Growth of Knowledge
(p. 119) 89)
Quote: "Success
in Science is the art of compromise." From:
George C. Davis 90)
Quote: "One
ounce of pretension is worth a pound of manure." From:
Steel Magnolias 91)
Quote: "Next
to the hunger to experience a thing, men have perhaps no stronger hunger than to
forget." From:
Herman Hesse Source:
The Journey East (p.
57) 92)
Quote: "This
enables us to regard all science as applied logic." From:
Nagel and Cohen Source:
Introduction to Logic and Scientific Method
(p. 191) 93)
Quote: "It
is a mark of scientific genius to be sensitive to difficulties where less gifted
people pass untroubled with doubt." From:
Nagel and Cohen Source:
Introduction to Logic and Scientific Method (p. 200) 94)
Quote: "Men
give themselves up to the first anticipation's of their minds." From:
John Locke Source:
Karl Popper Conjectures
and Refutations (p. 14) 95)
Quote: "Every
solution of a problem raises new unsolved problems; the more so the deeper the
original problem and the bolder its solution." From:
Karl Popper Source:
Karl Popper Conjectures and Refutations ( p. 28) 96)
Quote: "…The
role of deductive logical reasoning remains all-important for the critical
approach…because only by purely deductive reasoning is it possible for us to
discover what our theories imply, and thus to criticize them effectively." From:
Karl Popper Source:
Karl Popper Conjectures and Refutations ( p. 51) 97)
Quote: "A
false theory may be as great an achievement as a true one.
And many false theories have been more helpful in our search for truth
than some less interesting theories that are still accepted." From:
Karl Popper Source:
Karl Popper Conjectures and Refutations ( p. 141) 98)
Quote: "Properly
understood, a mathematical hypothesis does not claim that anything exists in
nature which corresponds to it - neither to the terms with which it operates,
nor the functional dependencies which it appears to assert. It erects, as it were a fictitious mathematical world behind
that of appearance, but without the claim that this world exists." From:
Berkeley Source:
Karl Popper Conjectures and Refutations ( p. 169) 99)
Quote: "Our
intellect does not draw its laws from nature, but imposes its laws upon
nature." From: |