## 1. MATHEMATICS

#### Subsections

- 1. mathematics - general
- 1.1 proofs
- 1.2 statistics and statisticians
- 1.3 mathematicians
- 1.4 mathematics poetry
- 1.5 mathematics quotes
- 1.6 mathematic puns
- 1.7 mathematical terms
- 1.8 mathematical exams
- 1.9 learning mathematics
- 1.10 mathematical tests to take
- 1.11 mathematical equations
- 1.12 topology
- 1.13 numbers
- 1.14 set theory
- 1.15 functions

### 1.5 MATHEMATICS QUOTES

Index | Comments and Contributions | previous page

mathematics
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    Special Category: Niels Abel
    Special Category: Karl F. Gauss

    From: http://math.furman.edu/~mwoodard/mquot.html
    Abel, Niels H. (1802 - 1829) [Norwegian Mathematician]

    [About Gauss' mathematical writing style]
    He is like the fox, who effaces his tracks in the sand with his tail.
    In G. F. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, p. 177.
    [Karl F. Gauss (1777-1855), German mathematician]

mathematics
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    Special Category: Jean le Rond d'Alembert
    From: http://math.furman.edu/~mwoodard/mquot.html
    D'Alembert, Jean Le Rond (1717-1783) [French mathematician and encyclopedist]
    The mathematician may be compared to a designer of garments, who is utterly
    oblivious of the creatures whom his garments may fit.  To be sure, his
    art originated in the necessity for clothing such creatures, but this
    was long ago; to this day a shape will occasionally appear which will
    fit into the garment as if the garment had been made for it.  Then there
    is no end of surprise and delight.

mathematics
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    Allen, Woody (1935-,American film director, writer,actor):
    Standard mathematics has recently been rendered obsolete by the discovery
    that for years we have been writing the numeral five backward. This has led
    to reevaluation of counting as a method of getting from one to
    ten. Students are taught advanced concepts of Boolean algebra, and formerly
    unsolvable equations are dealt with by threats of reprisals.

    In Howard Eves' Return to Mathematical Circles, Boston: Prindle, Weber, and
    Schmidt, 1988.

    Anglin, W.S.

mathematics
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    From: rww <richardw+@pitt.edu>
    "Like other occult techniques of divination, the statistical method has a
    private jargon deliberately contrived to obscure its methods from
    non-practitioners."    --   G. O. Ashley

mathematics
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    From: "tmw" <tmw@chariot.net.au>
    Although I am not stupid, the mathematical side of my brain is like dumb
    notes upon a damaged piano.

     ~ Margot Asquith 1864-1945, More or Less About Myself (1934)

mathematics
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    Special Category: St. Augustine de Hippo
    "The good Christian should beware of mathematicians and all those who
    make empty prophecies.  The danger already exists that mathematicians
    have made a covenant with the devil to darken the spirit and confine
    man in the bonds of Hell." -- St. Augustine (354-430)

    P.S. Augustine did really say that, but in his time there was no difference
    between mathematicans and astrologists. Astrologists told the future,
    which was diabolic.

mathematics
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    Special Category: St. Augustine de Hippo
    If I am given a formula, and I am ignorant of its meaning, it cannot teach
    me anything, but if I already know it what does the formula teach me?
    - St. Augustine (354-430), De Magistro ch X, 23.
    [Mircea Radu notified me that signum in this context should be translated
    as sign/symbol and not as formula and that this chapter has nothing to do
    with mathematics. ;-(]

mathematics
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    Special Category: Charles Babbage
    From: "Frank Bohan" <franbo@globalnet.co.uk>
    Babbage, Charles (1792-1871, English mathematician and inventor of computer)
    On two occasions I have been asked [by members of Parliament], 'Pray, Mr.
    Babbage, if you put into the machine wrong figures, will the right answers
    come out?' I am not able rightly to apprehend the kind of confusion of
    ideas that could provoke such a question.

mathematics
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    Special Category: Charles Babbage

    Babbage, Charles (1792-1871, English mathematician and inventor of computer)
    Every moment dies a man,
    Every moment 1 1/16 is born.
    (Parody of Tennyson's 'Vision of Sin' in an unpublished letter to the poet)

    Alfred, Lord Tennyson (1809-1892 English poet):
    Every moment dies a man,
    Every moment one is born
    In: Vision of Sin (1842)

mathematics
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    The cowboys have a way of trussing up a steer or a pugnacious bronce which
    fixes the brute so that it can neither move nor think. This is the
    hog-tie, and it is what Euclid did to geometry. -- Eric Temple Bell

mathematics
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    Bell, Eric Temple (1883-1960)
    "Obvious" is the most dangerous word in mathematics.

mathematics
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    From:         scotth9999@aol.com (ScottH9999)

    "Our paper became a monograph. When we had completed the details, we
    rewrote everything so that no one could tell how we came upon our ideas or
    why. This is the standard in mathematics."

     --David Berlinski, "Black Mischief" (1988).

mathematics
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    A mathematician's reputation rests on the number of bad proofs he has
    given.  - A.S. Besicovich, A Mathematicians miscellany, 1953

mathematics
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    Bolyai, Wolfgang (1775-1856)
    [To son János:]
    For God's sake, please give it up. Fear it no less than the sensual
    passion, because it, too, may take up all your time and deprive you of your
    health, peace of mind and happiness in life.
    [Bolyai's father urging him to give up work on non-Euclidian geometry.]
    In P. Davis and R. Hersh The Mathematical Experience , Boston: Houghton
    Mifflin Co., 1981, p. 220.

mathematics
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    Special Category: Definitions and terms
    "A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician."
       -- Brahmagupta

mathematics
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    Special Category: Nicolaus Copernicus

    From: http://math.furman.edu/~mwoodard/mquot.html
    Copernicus, Nicholaus  (1473-1543)
    Mathematics is written for mathematicians.

mathematics
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    Special Category: Charles Darwin
    Special Category: Definitions and terms
    From: ph2008@mail.bris.ac.uk (CJ. Bradfield)p
    hilosophy:

    "A mathematician is a blind man in a dark room looking for a black cat
    which isn't there" - Charles R. Darwin (1809-1882) [English biologist]

mathematics
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    From: "Havard Fosseng" <havardf@usit.uio.no>
    @A: R. Drabek
    @Q: Math is like love -- a simple idea but it can get complicated.

mathematics
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    Special Category: Arthur Eddington
    From: synapsid@hotmail.com (The Sanity Inspector)

    Proof is an idol before which the mathematician tortures himself.
    -- Sir Arthur Eddington

mathematics
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    Special Category: Albert Einstein
    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.
                    -- Albert Einstein  (1879-1955) [German physicist]

mathematics
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    From: synapsid@hotmail.com (The Sanity Inspector)
    Mathematicians are like lovers. Grant a mathematician the least
    principle, and he will draw from it a consequence which you must also
    grant him, and from this consequence another.
    -- Bernard Le Bovier Fontelle

mathematics
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    I've heard that the government wants to put a tax on the mathematically
    ignorant.  Funny, I thought that's what the lottery was!
                        -- Gallagher

mathematics
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    From: rww <richardw+@pitt.edu>
    "The laws of probability, so true in general, so fallacious in particular."
     -- Edward Gibbon (1737-1794) [British historian]

mathematics
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    Thomas Godfrey, a self-taught mathematician, great in his way . . .  knew
    little out of his way, and was not a pleasing companion; as, like most
    great mathematicians I have met with, he expected universal precision in
    everything said, or was forever denying or distinguishing upon trifles, to
    the disturbance of all conversation.
                            -- Benjamin Franklin (1706-1790), Autobiography

mathematics
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    Special Category: Karl F. Gauss

    From: http://math.furman.edu/~mwoodard/mquot.html
    Gauss, when asked how soon he expected to reach certain mathematical
    conclusions, that he had them long ago, all he was worrying about was
    how to reach them! [Karl F. Gauss (1777-1855), German mathematician]

mathematics
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    Special Category: Karl F. Gauss

    From:         kjwest4@shore.net (ken)

    "To avoid the clamor of the Boetians".
    C.F. Gauss, on why he did not immediately reveal his discovery of
    non-euclidean geometry.
    [Karl F. Gauss (1777-1855), German mathematician]

mathematics
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    Halmos, Paul R.
    I remember one occasion when I tried to add a little seasoning to a review,
    but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a
    perfectly sound contribution to abstract measure theory. The domains of the
    underlying measures were not sets but elements of more general Boolean
    algebras, and their range consisted not of positive numbers but of certain
    abstract equivalence classes. My proposed first sentence was:
    "The author discusses valueless measures in pointless spaces."
    In: I want to be a Mathematician, Washington: MAA Spectrum, 1985, p. 120.

mathematics
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    Anyone who cannot cope with mathematics is not fully human.  At best he
    is a tolerable subhuman who has learned to wear shoes, bathe and not
    make messes in the house. -- Lazarus Long, "Time Enough for Love", (Robert
    A. Heinlein (1907-19??) [US science-fiction writer] )

mathematics
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    Hempel, Carl G.
    ...to characterize the import of pure geometry, we might use the standard
    form of a movie-disclaimer: No portrayal of the characteristics of
    geometrical figures or of the spatial properties of relationships of actual
    bodies is intended, and any similarities between the primitive concepts and
    their customary geometrical connotations are purely coincidental.

    "Geometry and Empirical Science" in J. R. Newman (ed.) The World of
    Mathematics, New York: Simon and Schuster, 1956.

mathematics
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    Special Category: David Hilbert
    Special Category: Definitions and terms
    From: "Ed C" <zendam@snet.net>
    Hilbert, David (1862-1943)
    Mathematics is a game played according to certain simple rules with
    meaningless marks on paper.

mathematics
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    From: dougk <tz750@FlyingW.net>

    To understand this* for sense it is not required that a man should be a
    geometrician or a logician, but that he should be mad.
    	--Thomas Hobbes
    [*This is that the volume generated by revolving the region under 1/x
    from 1 to infinity has finite volume.]

mathematics
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    From: "Havard Fosseng" <havardf@usit.uio.no>
    @Q: All the limitative Theorems of metamathematics and the theory of
        computation suggest that once the ability to represent your own
        structure has reached a certain critical point, that is the kiss
        of death: it guarantees that you can never represent yourself
        totally. Godel's Incompleteness Theorem, Church's Undecidability
        Theorem, Turing's Halting Problem, Turski's Truth Theorem-- all
        have the flavour of some ancient fairy tale which warns you that
        `To seek self-knowledge is to embark on a journey which . . . will
        always be incomplete, cannot be charted on a map, will never halt,
        cannot be described.
    @A: Douglas R. Hofstadter

mathematics
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    The power of dealing with numbers is a kind of "detached lever" arrangement
    , which may be put into a mighty poor watch. I suppose it is as common as
    the power of moving ears voluntarily, which is a moderately rare endowment.
     -- Oliver Wendell Holmes (1809-1894) [US writer]

mathematics
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    From:         scotth9999@aol.com (ScottH9999)

    "Mathematics: A tentative agreement that two and two make four."
     --Elbert Hubbard (1859-1915; American writer)

mathematics
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    From: chollanamdo@mindspring.com (The Sanity Inspector)

    We have to come back to something like ordinary language after all when we
    want to talk _about_ mathematics!
    	--Sir Harold Jeffreys

mathematics
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    From: Joachim Verhagen
    Mathematics is the Queen of Science but she isn't very Pure; she keeps
    having babies by handsome young upstarts and various frog princes.
      --Donald Kingsbury (In "psychohistorical crisis", 2001)

mathematics
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    Kleinhenz, Robert J.
    When asked what it was like to set about proving something, the
    mathematician likened proving a theorem to seeing the peak of a mountain
    and trying to climb to the top. One establishes a base camp and begins
    scaling the mountain's sheer face, encountering obstacles at every turn,
    often retracing one's steps and struggling every foot of the
    journey. Finally when the top is reached, one stands examining the peak,
    taking in the view of the surrounding countrysideand then noting the
    automobile road up the other side!

mathematics
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    From: dylanh@minerva.cis.yale.edu (Dylan Howard)

    Stand firm in your refusal to remain conscious during algebra.  In real
    life, I assure you, there is no such thing as algebra"
      -- Fran Lebowitz (1946- ;American writer)

mathematics
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    Special Category: Lev Landau
    Wir Mathematiker sind alle ein biszchen meschugge.
    (We mathematicans are all a bit crazy).
      -- Landau

mathematics
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    From: "Frank Bohan" <franbo@globalnet.co.uk>
    Special Category: Lev Landau
    Landau, E.
    [Asked for a testimony to the effect that Emmy Noether was a great woman
    mathematician, he said:]
    I can testify that she is a great mathematician, but that she is a woman, I
    cannot swear.
    J.E. Littlewood, A Mathematician's Miscellany, Methuen and Co ltd., 1953.

mathematics
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    Littlewood, J. E. (1885 -1977)
    A good mathematical joke is better, and better mathematics, than a dozen
    mediocre papers.
    A Mathematician's Miscellany, Methuen and Co. ltd., 1953.

    (I do not know if Littlewood would have considered this list "good
    mathematical jokes", but I could not resist including this.)

mathematics
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    Special Category: Godfrey H. Hardy
    Littlewood, J. E. (1885 -1977)
    I read in the proof sheets of Hardy on Ramanujan: "As someone said, each of
    the positive integers was one of his personal friends." My reaction was, "I
    wonder who said that; I wish I had." In the next proof-sheets I read (what
    now stands), "It was Littlewood who said..."
    A Mathematician's Miscellany, Methuen Co. Ltd, 1953.

mathematics
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    From: "Frank Bohan" <franbo@globalnet.co.uk>
    Mathematics is inadequate to describe the universe, since mathematics is an
    abstraction from natural phenomena.  Also, mathematics may predict things
    which don't exist, or are impossible in nature.
     -- Ludovico delle Colombe Criticizing Galileo.

mathematics
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    Luther, Martin (1483-1546)
    Medicine makes people ill, mathematics make them sad and theology makes
    them sinful.

mathematics
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    From: "Christopher Brown" <cbrown@chem1.chem.dal.ca>
    The mathematician who pursues his studies without clear views of this
    matter, must often have the uncomfortable feeling that his paper and pencil
    surpass him in intelligence.

    - Mach, Ernst (1838-1916), in "The Economy of Science" in J. R. Newman
    (ed.) The World of Mathematics

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    From: Don Olivier <don@hsph.harvard.edu>
    Sweet Analytics, 'tis thou hast ravished me.
     -- Doctor Faustus according to Christopher Marlowe (British dramatist,
    1564-1593)

mathematics
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    From: Don Olivier <don@hsph.harvard.edu>
    Fast cars, fast women, fast algorithms... what more could a man want?
     -- Joe Mattis

mathematics
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    Special Category: James Clerk Maxwell

    From Science Week http://scienceweek.com
    Mathematicians my flatter themselves that they possess new ideas which mere
    human language is as yet unable to express. Let them make the effort to
    express these ideas in appropriate words without the aid of symbols, and if
    they succeed they will not only lay us laymen under a lasting obligation,
    but, we venture to say, they will find themselves very much enlightened
    during the process, and will even be doubtful whether the ideas as
    expressed in symbols had ever quite found their way out of the equations
    into their minds.
      -- James Clerk Maxwell (1831-1879) [Scottish physicist]

mathematics
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    Mathematics contains much that will neither hurt one if one does not know
    it nor help one if one does know it. - J.B. Mencken

mathematics
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    From: T.Moore@massey.ac.nz (Terry Moore)

    Imagine a person with a gift of ridicule [He might say] First that a
    negative quantity has no logarithm; secondly that a negative quantity has
    no square root; thirdly that the first non-existent is to the second as the
    circumference of a circle is to the diameter. - Augustus de Morgan

mathematics
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    Special Category: John von Neumann
    From: Hans de Vreught (J.P.M.deVreught@cs.tudelft.nl)

    Young man, in mathematics you don't understand things, you just get used to
    them.
      -- John von Neumann (1903-1957) [Hungarian/US mathematician and
    scientist]

mathematics
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    From: technochik@webtv.net (Marci Wolcott)

    "To speak algebraically, Mr. M.  is execrable, but Mr. G. is
    (x+1)ecrable."  --Edgar Alan Poe

mathematics
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    Special Category: Plato
    From: Don Olivier <don@hsph.harvard.edu>
    Mathematics is like checkers in being suitable for the young, not too
    difficult, amusing, and without peril to the state.
     -- Plato (c.428-347 B.C) [Greek philosopher]

mathematics
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    Special Category: Jules Henry Poincaré
    Special Category: Definitions and terms
    From: hcheng@gpu5.srv.ualberta.ca (Howard Cheng)

    Mathematics is the art of giving the same name to different things.
     -- Jules Henri Poincare (1854-1912) [French mathematician]

mathematics physics
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    Special Category: Jules Henry Poincaré
    On the Gaussian curve:
    Experimentalists think that it is a mathematical theorem while the
    mathematicians believe it to be an experimental fact.
     -- Jules Henri Poincare (1854-1912) [French mathematician]

mathematics
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    From: dougk <tz750@FlyingW.net>
    Special Category: Siméon Poisson
    Life is good for only two things, discovering mathematics and teaching
    mathematics.
    	--Siméon Poisson

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    Special Category: Definitions and terms

    Polyá, George (1887, 1985)
    Mathematics consists of proving the most obvious thing in the least obvious
    way.
    In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc.,
    1988.

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    Polyá, George (1887, 1985)
    The traditional mathematics professor of the popular legend is
    absentminded. He usually appears in public with a lost umbrella in each
    hand. He prefers to face the blackboard and to turn his back to the
    class. He writes a, he says b, he means c; but it should be d. Some of his
    sayings are handed down from generation to generation.

    "In order to solve this differential equation you look at it till a
    solution occurs to you."
    "This principle is so perfectly general that no particular application of
    it is possible."
    "Geometry is the science of correct reasoning on incorrect figures."
    "My method to overcome a difficulty is to go round it."
    "What is the difference between method and device? A method is a device
    which you used twice."

    How to Solve It. Princeton: Princeton University Press. 1945.

mathematics
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    Pordage, Matthew
    One of the endearing things about mathematicians is the extent to which
    they will go to avoid doing any real work.
    In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and
    Schmidt, 1988.

mathematics
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    From: "Ken Stevenson" <kenstevo@zip.com.au>
    If I feel unhappy, I do mathematics to become happy. If I am happy, I do
    mathematics to keep happy.

    P. Turan, "The Work of Alfred Renyi", Matematikai Lapok 21, 1970, pp 199-210

mathematics
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    From: "Havard Fosseng" <havardf@usit.uio.no>
    @A: M. C. Reed.
    @Q: Sex is the mathematics urge sublimated.

mathematics
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    From: Bill Thomas <liblanc1@nic.cerf.net>
    As long as algebra is taught in school, there will be prayer in school.
     - Cokie Roberts

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    Special Category: Bertrand (Arthur William) Russell

    Bertrand (Arthur William) Russell (1872-1970) [British philopher and
    mathematician]:
    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
     -- Bertrand Russell (Mysticism and Logic and Other Essays, 1918)

    From: jr3000@aol.com (JR3000)

    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.
    -Bertrand Russell, _Mysticism and Logic and Other Essays_, 1918

    As, for example:

    We may lay it down that, if there were no universe, _all_
    general propositions would be true;
    for the contradictory of a general proposition is a proposition asserting
    existence, and would therefore always be false if no universe existed.
    -Bertrand Russell, _An Introduction to Mathematical Philosophy_, 1919

    I have come to believe, though very reluctantly, that it [mathematics]
    consists of tautologies. I fear that to a mind of sufficient intellectual
    power, the whole of mathematics would appear trivial...
    I cannot any longer find any mystical satisfaction in the contemplation
    of mathematical truth.
    -Bertrand Russell,_My Philosophical Development_, 1959

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    It is a pleasant surprise to him [the pure mathematician] and an added
    problem if he finds that the arts can use his calculations, or that the
    senses can verify them, much as if a composer found that the sailors could
    heave better when singing his songs
    -- George Santayana (1863-1952) [US philosopher]

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    The summer '87 issue (#55) of The Whole Earth Review contains an article
    called "Let's Eliminate math From The Schools" by Roger Schank.

    "Many very smart people are lousy at mathematics and never quite get over
    their failure at something so important". - R. Schank

mathematics physics
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    From: http://math.furman.edu/~mwoodard/mquot.html
    De Sua, F. (1956)
    Suppose we loosely define a religion as any discipline whose foundations
    rest on an element of faith, irrespective of any element of reason which
    may be present. Quantum mechanics for example would be a religion under
    this definition. But mathematics would hold the unique position of being
    the only branch of theology possessing a rigorous demonstration of the fact
    that it should be so classified.

    In H. Eves,In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

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    McShane, E. J.
    There are in this world optimists who feel that any symbol that starts off
    with an integral sign must necessarily denote something that will have
    every property that they should like an integral to possess. This of course
    is quite annoying to us rigorous mathematicians; what is even more annoying
    is that by doing so they often come up with the right answer.

    Bulletin of the American Mathematical Society, v. 69, p. 611, 1963.

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    From: anthem@virginia.edu (dark star = Scott Herman)

    "Math was always my bad subject.  I couldn't convince my teachers that
    many of my answers were meant ironically."  -- writer Calvin Trillin

mathematics
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    From: Haim Guivon <guivon@netvision.net.il>, Ben Webster
    <bwebste@simons-rock.edu>, Martin Winkler <e9325827@student.tuwien.ac.at>,
    Stephen Montgomery-Smith <stephen@showme.missouri.edu>

    Special Category: Leopold Kronecker
    Leopold Kronecker [German mathematician, 1823-1891]:
    "God made the whole (natural) numbers. The others, were man-made" (approximate
    translation from German, from memory).
    (In Analysis I by Heuser, Kronecker is quoted to have said that)

    From: Alain Gottcheiner <agot@ulb.ac.be>
    I've seen Weierstrass [German mathematician Weierstrass (1815-1897)] quoted
    twice [this being no proof, of course] for having said that "God made the
    whole numbers. The rest of the mathematical works is man-made." , which is
    a stronger statement.

    Is it just possible that Weierstrass knew about Kronecker's utterance,
    and strengthened it ?

mathematics
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    From: synapsid@hotmail.com (The Sanity Inspector)
    God exists since mathematics is consistent, and the Devil exists since
    we cannot prove it.
    -- Andre Weil

mathematics
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    It is a safe rule to apply that, when a mathematical or philosophical
    author writes with a misty profundity, he is talking nonsense.
         -- Alfred North Whitehead, An Introduction to Mathematics, 1948.

mathematics
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    From: "Havard Fosseng" <havardf@usit.uio.no>
    @Q: I will not go so far as to say that to construct a history
        of thought without profound study of the mathematical ideas of
        successive epochs is like omitting Hamlet from the play which is
        named after him. . . But it is certainly analogous to cutting out
        the part of Ophelia. This simile is singularly exact. For Ophelia
        is quite essential to the play, she is very charming-- and a
        little mad.
    @A: Alfred North Whitehead (1861-1947) [English philosopher and mathematician]

mathematics
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    From: "Richard I. Pelletier" <bitbucket@home.com>
    "There are only two kinds of math books. Those you cannot read beyond
    the first sentence, and those you cannot read beyond the first page."
       C.N. Yang, about 1980 I think. (Nobel Prize in Physics, 1957.)

next page | Index | Comments and Contributions

#### Subsections

- 1. mathematics - general
- 1.1 proofs
- 1.2 statistics and statisticians
- 1.3 mathematicians
- 1.4 mathematics poetry
- 1.5 mathematics quotes
- 1.6 mathematic puns
- 1.7 mathematical terms
- 1.8 mathematical exams
- 1.9 learning mathematics
- 1.10 mathematical tests to take
- 1.11 mathematical equations
- 1.12 topology
- 1.13 numbers
- 1.14 set theory
- 1.15 functions

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