QUotes
2001-11-10 by GAmoore@aol.com
Here are some other quotes for you:
o A collection of facts is no more a science than a heap of stones is a
house.
- Henri Poincare (1903)
o A mathematician, like a painter or poet, is a maker of patterns. If his
patterns are more permanent than theirs, it is because they are made with
ideas.
- Godfrey Hardy 1940
o There are things which seem incredible to most men who have not studied
mathematics.
- Archimedes (287 B.C.- 212 B.C.)
o I must study politics and war that my sons may have the liberty to
study mathematics and philosophy.
- John Adams (1780)
o Mathematics ... awakens the mind and purifies the intellect; she brings
light to our intrinsic ideas; she abolishes the oblivion and ignorance
which are ours by birth.
- Proclus (Fifth Century)
o In response to the statement that the number of publications by
Dirichlet was not so great, Gauss commented that the works of Dirichlet
are jewels and jewels are not weighed on a grocery scale.
o Mathematics, rightly viewed, posses not only truth, but extreme beauty.
- Bertrand Russell (1902)
o As is well known, physics becames a science only after the invention of
differential calculus.
-Bernhard Rieman 1882
o Many who have never had an opportunity of knowing any more about
mathematics confound it with arithmetic and consider it an arid science.
In reality, however, it is a science which requires a great amount of
imagination, and it is impossible to be a mathematician without being a
poet in soul. - Sonya Kovalevsky
o The essential bond between mathematics and the arts is found in the
fact that discovery in the mathematics is a not a matter of logic. It is
rather the result of mysterious powers which no one understands, and in
which unconscious recognition of beauty must play an important part.-
Marston Morse, 1959
o Creativity is the heart and soul of mathematics at all levels. The
collection of special skills and techniques is only the raw material out
of which the subject itself grows. To look at mathematics without the
creative side of it, is to look at a black and white photograph of a
Cezanne; outlines may be there, but everything that matters is missing. -
R.C. Buck, 1962
o My work has always tried to unite the true with the beautiful; but when
I had to choose one or the other, I usually chose the beautiful - Herman
Weyl
o What the imagination seizes as beauty must be truth - whether it
existed before or not. - Keats
o It is contact with the infinite that has been the dream of the sage as
seer, as pet, and as mathematician since the days when the world was
young, and this will endure until the world is old, for it is an
instinct of the race, the instinct that separates it from the brute. -
D.E. Smith
Traits of Mathematicians
o Mathematics is the one area of human enterprise where the motivation to
deceive has been practically eliminated. Not because mathematicians are
necessarily virtuous people, but because the nature of mathematical
ability is such that deception can be immediately determined by other
mathematicians. This requirement of honest soon affects the character of
the continuous student of mathematics.
- Howard Fehr, 1953
o I do not contend that the study of mathematics will automatically
produce intellectually honest people. Nevertheless, I do contend that
mathematics is the ideal subject in which to point out to the student the
virtues of intellectual honesty. In this age of the advertising man and
his more vicious cousin , the propaganda technician, is there any more
important function for education to perform?- Moses Richardson, 1952
o It is because the mathematician is expert in analyzing relations, in
distinguishing what is essential from what is superficial in the
statement of these relations, and in formulating broad and meaningful
problems, that he has come to be an important figure in industrial teams.
- Thornton C. Fry, 1956
o The desire to explore thus marks out the mathematician. This is one of
the forces making for the growth of mathematics. While the mathematician
enjoys what he already know, he is eager for new knowledge.
- W.W. Sawyer, 1957
o That mathematics is a difficult subject no one can deny. It demands,
among other things, accuracy of thought and statement, definite mental
concepts, connected thinking, a fair memory, quickness to recognize
relations between forms and numbers, power of generalization, a
willingness to work hard. The abstractness of much of the work renders it
difficult to most minds, and obnoxious to some...
These are some of the many characteristics that make mathematic hard.
Of course it is hardly necessary to say that many of these very
characteristics make it attractive and fascinating to some types of mind.
The fact that it is abstract and impersonal, that it requires effort and
compels concentration has made it a welcome refuge to minds distracted by
the perplexity of everyday life. Probably every one of us knows the joy
of losing ourselves and our cares completely in a problem that taxes our
minds. - Helen Merril, 1918
o My mother said that I was the stubbornest child she had ever known. I
would say that my stubbornness has been to a great extent responsible for
whatever success I have had in mathematics. But then it is a common trait
among mathematicians.
- Julia Robinson, 1986
o The peculiar charm of Mathematics lies partly in its precision of
thought and particularly in the fact that it is the only subject which
can be remade by each individual who touches it.... We are the only free
creatures in a world of slaves. In that spirit of independence we set off
in the world of reason, believing nothing because we are told it on good
authority, doubting, questioning in the name of truth, leaving no stone
unturned....
- J.L. Synge, 1957
The Unpolished Side of Mathematics
o It would appear that there is a private and public world of
mathematics. The private world is where struggle, failure,
incomprehension, intuition and creativity dominate... The public world is
where the results of the private struggle make their appearance in a
formal, conventional abstract formulation from which all evidence of
false trails, inadequate reasoning or misunderstandings have been
eliminated. Unfortunately for our pupils, the majority are given access
only to the public world - the pages of text books which present inert
knowledge as if it has always been just so.
- Leone Burton, 1986
o The only instruction which a professor can give, in my opinion, is to
think in front of his students.
- Henri Lebesgue, 1907 (French mathematician who discovered the Lebesgue
Integral)
o I lie on the sofa in the living room with my pencil and paper and think
and draw little pictures and try this thing and that thing. I'm
interested in how ideas fit together. Actually I'm very geometric in my
thinking. I'm not good at numbers at all. - Mary Ellen Rudin (famous
mathematician)
Eccentricities
o Einstein though that scientific greatness was primarily a question of
character, the determination not to compromise or to accept incomplete
answers. Let me mention the only occasion on which he said:"this would
make a good anecdote about me." We had finished the preparation of a
paper and we were looking for a paper clip. After opening a lot of
drawers we finally found one which turned out to be too badly bent for
use. So we were looking for a tool to straighten it. Opening a lot more
drawers we came on a whole box of unused paper clips, Einstein
immediately starting to shape one of them into a toll to straighten the
bent one. When I asked what he was doing, he said, "Once I am set on a
goal, it becomes difficult to deflect me."
-Ernst Straus, 1979 (Greg Moore's Professor at UCLA and writer of a
letter of recommendation)
o Now and then, teaching may approach poetry, and now and then it may
approach profanity. May I tell you a little story about the great
Einstein? I listened once to Einstein as he talked to a group of
physicists in a party. "Why have all the electrons the same charge"" said
he. "Well, why are all the little balls of goat dung of the same size?"
Why did Einstein say such things? Just to make some snob to raise their
eyebrows? He was not disinclined to do so, I think. Yet, probably, it
went deeper. I do not think this comment was casual. As Montaigne put it
: The truth is such a great thing that we should not disdain any means
that could lead to it. - George Polya, 1963
The Transcendence of Mathematics
o The mathematician believes that he will be able to slake his thirst at
the very sources of knowledge, convinced as he is that they will always
continue to pour forth, pure and abundant, while others have to have
recourse to the muddy streams of a sordid reality. If he be reproached
with the haughtiness of his attitude, if he be asked why he persist on
the high glaciers whither no one but his own kind can follow him, he will
answer, with Jacobi : For the honor of the human spirit. - Andre Weil,
1950 (Number Theorist)
o Pure mathematics is, in its way, the poetry of logical ideas. One seeks
the most general ideas of operation which will bring together in simple,
logical and unified form the largest possible circle of formal
relationships. In this effort toward logical beauty spiritual formulae
are discovered necessary for the deeper penetration into the laws of
nature. - Albert Einstein, 1935
o Abstract mathematics is a work of invention - a free creation of the
human spirit, as truly a work of art as the Moonlight Sonata or the
Sistine Madonna, but on a much vaster scale than the entire library of
great symphonies, the whole gallery of famous paintings, or, indeed, the
total assemblage of celebrated cathedrals. - F.L. Griffin, 1936
o Some proofs are merely convincing and to use a phrase of the famous
mathematical physicist, Lord Rayleigh, they "command assent". There are
other proofs "which woo and charm the intellect. They evoke delight and
an overpowering desire to say Amen. Amen." An elecgantly executed proof
is a poem in all but the form in which it is written. - Morris Kline, 1953
o Like many great temples of some religions, mathematics may be viewed
only from the outside by those uninitiated into its
mysteries...understanding its methods is reserved for those who devote
years to the study of mathematics. - Andrew Gleason 1964
o Whether his interest is focused on the golden cuboid or the
dodecahedron, or the logarithmic spiral or the genealogy of the drone
bee, he should realize that , in the act of appreciation, he is
re-enacting the creative act and , attracted by beauty, is experiencing
himself the job of creative activity. He is in fact, in Kepler's phrase
"thinking God's thoughts after Him." - H.E. Huntley, 1970
o Paul Erdos has the theory that God has a book containing all the
theorems of mathematics with their absolutely most beautiful proofs, and
when he want to express particular appreciation of a proof he exclaims,
"This is one from the book!" - Ross Honsberger, 1978
o No human investigation can be called true science without passing
through mathematical tests.
- Leonardo da Vinci
o When you can not measure it, when you can not express it in numbers,
you have scarcely in your thoughts advanced to the stage of science,
whatever the matter may be.- Lord Kelvin