Adams, Douglas (1952 - 2001)
Numbers written on restaurant bills within the confines of restaurants do not follow
the same mathematical laws as numbers written on any other pieces of paper in any other
parts of the Universe.
This single statement took the scientific world by storm. It completely revolutionized it.
So many mathematical conferences got held in such good restaurants that many of the finest
minds of a generation died of obesity and heart failure and the science of math was put
back by years.
Life, the Universe and Everything. New York: Harmony Books, 1982.
Auden, W. H. (1907-1973)
Thou shalt not answer questionnaires
Or quizzes upon world affairs,
Nor with compliance
Take any test. Thou shalt not sit
with statisticians nor commit
A social science.
"Under which lyre" in Collected Poems of W H Auden, London: Faber and
Faber.
Bell, Eric Temple (1883-1960)
Wherever groups disclosed themselves, or could be introduced, simplicity crystallized
out of comparative chaos.
Mathematics, Queen and Servant of Science, New York, 1951, p 164.
Bentham, Jeremy (1748-1832)
O Logic: born gatekeeper to the Temple of Science, victim of capricious destiny:
doomed hitherto to be the drudge of pedants: come to the aid of thy master, Legislation.
In J. Browning (ed.) Works.
Chekov, Anton (1860 - 1904)
There is no national science just as there is no national multiplication table; what
is national is no longer science.
In V. P. Ponomarev Mysli o nauke Kishinev, 1973.
Comte, Auguste (1798-1857)
C'este donc par l'�ude des math�atiques, et seulement par elle, que l'on
peut se faire une id� juste et approfondie de ce que c'est qu'une science.
Quoted by T. H. Huxley in Fortnightly Review, Vol. II, N.S. 5.
De Morgan, Augustus (1806-1871)
Every science that has thriven has thriven upon its own symbols: logic, the only
science which is admitted to have made no improvements in century after century, is the
only one which has grown no symbols.
Transactions Cambridge Philosophical Society, vol. X, 1864, p. 184.
Diophantus
[His epitaph.]
This tomb hold Diophantus Ah, what a marvel! And the tomb tells scientifically the measure
of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a
twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage
after a seventh, and in the fifth year after his marriage He granted him a son. Alas!
late-begotten and miserable child, when he had reached the measure of half his father's
life, the chill grave took him. After consoling his grief by this science of numbers for
four years, he reached the end of his life.
In Ivor Thomas Greek Mathematics, in J. R. Newman (ed.) The World of Mathematics,
New York: Simon and Schuster, 1956.
Dirac, Paul Adrien Maurice (1902- )
In science one tries to tell people, in such a way as to be understood by everyone,
something that no one ever knew before. But in poetry, it's the exact opposite.
In H. Eves Mathematical Circles Adieu, Boston: Prindle, Weber and Schmidt, 1977.
Dubos, Ren�J.
Gauss replied, 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!
In Mechanisms of Discovery in I. S. Gordon and S. Sorkin (eds.) The Armchair
Science Reader, New York: Simon and Schuster, 1959.
Eddington, Sir Arthur (1882-1944)
I believe there are
15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,914,527,116,709,366,231,425,076,185,631,031,296
protons in the universe and the same number of electrons.
The Philosophy of Physical Science. Cambridge, 1939.
Einstein, Albert (1879-1955)
Imagination is more important than knowledge.
On Science.
Einstein, Albert (1879-1955)
The most beautiful thing we can experience is the mysterious. It is the source of all
true art and science.
What I Believe.
Einstein, Albert (1879-1955)
Most of the fundamental ideas of science are essentially simple, and may, as a rule,
be expressed in a language comprehensible to everyone.
The Evolution of Physics.
Einstein, Albert (1879-1955)
Science without religion is lame; religion without science is blind.
Reader's Digest, Nov. 1973.
Flaubert, Gustave (1821-1880)
Poetry is as exact a science as geometry.
Galilei, Galileo (1564 - 1642)
Measure what is measurable, and make measurable what is not so.
Quoted in H. Weyl "Mathematics and the Laws of Nature" in I Gordon and S. Sorkin
(eds.) The Armchair Science Reader, New York: Simon and Schuster, 1959.
Galton, Sir Francis (1822-1911)
[Statistics are] the only tools by which an opening can be cut through the formidable
thicket of difficulties that bars the path of those who pursue the Science of Man.
Pearson, The Life and Labours of Francis Galton, 1914.
Gauss, Karl Friedrich (1777-1855)
There are problems to whose solution I would attach an infinitely greater importance
than to those of mathematics, for example touching ethics, or our relation to God, or
concerning our destiny and our future; but their solution lies wholly beyond us and
completely outside the province of science.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
p. 314.
Glanvill, Joseph
And for mathematical science, he that doubts their certainty hath need of a dose of
hellebore.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956,
p. 548.
Goedel, Kurt
I don't believe in natural science.
[Said to physicist John Bahcall.]
Ed Regis, Who Got Einstein's Office? Addison Wesley, 1987.
Haldane, John Burdon Sanderson (1892-1964)
A time will however come (as I believe) when physiology will invade and destroy
mathematical physics, as the latter has destroyed geometry.
Daedalus, or Science and the Future, London: Kegan Paul, 1923.
Halmos, Paul R.
Mathematics is not a deductive science -- that's a cliche. When you try to prove a
theorem, you don't just list the hypotheses, and then start to reason. What you do is
trial and error, experimentation, guesswork.
I Want to be a Mathematician, Washington: MAA Spectrum, 1985.
Hardy, Godfrey H. (1877 - 1947)
A science is said to be useful of its development tends to accentuate the existing
inequalities in the distribution of wealth, or more directly promotes the destruction of
human life.
A Mathematician's Apology, London, Cambridge University Press, 1941.
Hempel, Carl G.
The most distinctive characteristic which differentiates mathematics from the various
branches of empirical science, and which accounts for its fame as the queen of the
sciences, is no doubt the peculiar certainty and necessity of its results.
"Geometry and Empirical Science" in J. R. Newman (ed.) The World of
Mathematics, New York: Simon and Schuster, 1956.
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.
Hilbert, David (1862-1943)
Before beginning I should put in three years of intensive study, and I haven't that
much time to squander on a probable failure.
[On why he didn't try to solve Fermat's last theorem]
Quoted in E.T. Bell Mathematics, Queen and Servant of Science, New York: McGraw
Hill Inc., 1951.
Hilbert, David (1862-1943)
Galileo was no idiot. Only an idiot could believe that science requires martyrdom -
that may be necessary in religion, but in time a scientific result will establish itself.
In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1971.
Hilbert, David (1862-1943)
How thoroughly it is ingrained in mathematical science that every real advance goes
hand in hand with the invention of sharper tools and simpler methods which, at the same
time, assist in understanding earlier theories and in casting aside some more complicated
developments.
Hilbert, David (1862-1943)
The further a mathematical theory is developed, the more harmoniously and uniformly
does its construction proceed, and unsuspected relations are disclosed between hitherto
separated branches of the science.
In N. Rose Mathematical Maxims and Minims, Raleigh NC: Rome Press Inc., 1988.
Hobbes, Thomas
Geometry, which is the only science that it hath pleased God hitherto to bestow on
mankind.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Hughes, Richard
Science, being human enquiry, can hear no answer except an answer couched somehow in
human tones. Primitive man stood in the mountains and shouted against a cliff; the echo
brought back his own voice, and he believed in a disembodied spirit. The scientist of
today stands counting out loud in the face of the unknown. Numbers come back to him - and
he believes in the Great Mathematician.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Huxley, Aldous
I admit that mathematical science is a good thing. But excessive devotion to it is a
bad thing.
Interview with J. W. N. Sullivan, Contemporary Mind, London, 1934.
Jacobi, Carl
It is true that Fourier had the opinion that the principal aim of mathematics was
public utility and explanation of natural phenomena; but a philosopher like him should
have known that the sole end of science is the honor of the human mind, and that under
this title a question about numbers is worth as much as a question about the system of the
world.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Jacobi, Carl
The real end of science is the honor of the human mind.
In H. Eves In Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.
Jacobi, Carl
Mathematics is the science of what is clear by itself.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Jeans, Sir James
The essential fact is that all the pictures which science now draws of nature, and
which alone seem capable of according with observational facts, are mathematical pictures.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Jefferson, Thomas
...the science of calculation also is indispensable as far as the extraction of the
square and cube roots: Algebra as far as the quadratic equation and the use of logarithms
are often of value in ordinary cases: but all beyond these is but a luxury; a delicious
luxury indeed; but not be in indulged in by one who is to have a profession to follow for
his subsistence.
In J. Robert Oppenheimer "The Encouragement of Science" in I. Gordon and S.
Sorkin (eds.) The Armchair Science Reader, New York: Simon and Schuster, 1959.
Jevons, William Stanley
It is clear that Economics, if it is to be a science at all, must be a mathematical
science.
Theory of Political Economy.
Jowett, Benjamin (1817 - 1893)
Logic is neither a science or an art, but a dodge.
In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
Kant, Emmanual (1724 - 1804)
The science of mathematics presents the most brilliant example of how pure reason may
successfully enlarge its domain without the aid of experience.
The Mathematical Intelligencer, v. 13, no. 1, Winter 1991.
Kasner, E. and Newman, J.
Mathematics is the science which uses easy words for hard ideas.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J.
Mathematics is often erroneously referred to as the science of common sense. Actually,
it may transcend common sense and go beyond either imagination or intuition. It has become
a very strange and perhaps frightening subject from the ordinary point of view, but anyone
who penetrates into it will find a veritable fairyland, a fairyland which is strange, but
makes sense, if not common sense.
Mathematics and the Imagination, New York: Simon and Schuster, 1940.
Kasner, E. and Newman, J. R.
The testament of science is so continually in a flux that the heresy of yesterday is
the gospel of today and the fundamentalism of tomorrow.
E. Kasner and J. R. Newman, Mathematics and the Imagination, Simon and Schuster,
1940.
La Touche, Mrs.
I do hate sums. There is no greater mistake than to call arithmetic an exact science.
There are permutations and aberrations discernible to minds entirely noble like mine;
subtle variations which ordinary accountants fail to discover; hidden laws of number which
it requires a mind like mine to perceive. For instance, if you add a sum from the bottom
up, and then from the top down, the result is always different.
Mathematical Gazette, v. 12.
de Laplace, Pierre-Simon (1749 - 1827)
Nature laughs at the difficulties of integration.
In J. W. Krutch "The Colloid and the Crystal", in I. Gordon and S. Sorkin (eds.)
The Armchair Science Reader, New York: Simon and Schuster, 1959.
da Vinci, Leonardo (1452-1519)
No human investigation can be called real science if it cannot be demonstrated
mathematically.
Mach, Ernst (1838-1916)
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.
"The Economy of Science" in J. R. Newman (ed.) The World of Mathematics,
New York: Simon and Schuster, 1956.
Maxwell, James Clerk (1813-1879)
... that, in a few years, all great physical constants will have been approximately
estimated, and that the only occupation which will be left to men of science will be to
carry these measurements to another place of decimals.
Scientific Papers 2, 244, October 1871.
Peirce, Benjamin (1809-1880)
Mathematics is the science which draws necessary conclusions.
Memoir read before the National Academy of Sciences in Washington, 1870.
Peirce, Charles Sanders (1839-1914)
The one [the logician] studies the science of drawing conclusions, the other [the
mathematician] the science which draws necessary conclusions.
"The Essence of Mathematics" in J. R. Newman (ed.) The World of Mathematics,
New York: Simon and Schuster, 1956.
Peirce, Charles Sanders (1839-1914)
...mathematics is distinguished from all other sciences except only ethics, in
standing in no need of ethics. Every other science, even logic, especially in its early
stages, is in danger of evaporating into airy nothingness, degenerating, as the Germans
say, into an arachnoid film, spun from the stuff that dreams are made of. There is no such
danger for pure mathematics; for that is precisely what mathematics ought to be.
"The Essence of Mathematics" in J. R. Newman (ed.) The World of Mathematics,
New York: Simon and Schuster, 1956.
Plutarch (ca 46-127)
[about Archimedes:]
... being perpetually charmed by his familiar siren, that is, by his geometry, he
neglected to eat and drink and took no care of his person; that he was often carried by
force to the baths, and when there he would trace geometrical figures in the ashes of the
fire, and with his finger draws lines upon his body when it was anointed with oil, being
in a state of great ecstasy and divinely possessed by his science.
In G. Simmons Calculus Gems, New York: McGraw Hill Inc., 1992.
Poincar� Jules Henri (1854-1912)
Science is built up with facts, as a house is with stones. But a collection of facts
is no more a science than a heap of stones is a house.
La Science et l'hypoth�e.
Poincar� Jules Henri (1854-1912)
Absolute space, that is to say, the mark to which it would be necessary to refer the
earth to know whether it really moves, has no objective existence.... The two
propositions: "The earth turns round" and "it is more convenient to suppose
the earth turns round" have the same meaning; there is nothing more in the one than
in the other.
La Science et l'hypoth�e.
Poincar� Jules Henri (1854-1912)
...by natural selection our mind has adapted itself to the conditions of the external
world. It has adopted the geometry most advantageous to the species or, in other words,
the most convenient. Geometry is not true, it is advantageous.
Science and Method.
Poly� 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.
Poly� George (1887, 1985)
Mathematics is the cheapest science. Unlike physics or chemistry, it does not require
any expensive equipment. All one needs for mathematics is a pencil and paper.
D. J. Albers and G. L. Alexanderson, Mathematical People, Boston: Birkh�ser,
1985.
Reid, Thomas
It is the invaluable merit of the great Basle mathematician Leonard Euler, to have
freed the analytical calculus from all geometric bounds, and thus to have established
analysis as an independent science, which from his time on has maintained an unchallenged
leadership in the field of mathematics.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Rosenblueth, A
[with Norbert Wiener]
The best material model of a cat is another, or preferably the same, cat.
Philosophy of Science 1945.
Russell, Bertrand (1872-1970)
Although this may seem a paradox, all exact science is dominated by the idea of
approximation.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York:
Viking Press, 1966.
Russell, Bertrand (1872-1970)
Aristotle maintained that women have fewer teeth than men; although he was twice
married, it never occurred to him to verify this statement by examining his wives' mouths.
The Impact of Science on Society, 1952.
Schopenhauer
Of all the intellectual faculties, judgment is the last to mature. A child under the
age of fifteen should confine its attention either to subjects like mathematics, in which
errors of judgment are impossible, or to subjects in which they are not very dangerous,
like languages, natural science, history, etc.
Smith, David Eugene
One merit of mathematics few will deny: it says more in fewer words than any other
science. The formula, e^iπ = -1 expressed a world of thought, of truth, of poetry,
and of the religious spirit "God eternally geometrizes."
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Somerville, Mary (1780-1872)
Nothing has afforded me so convincing a proof of the unity of the Deity as these
purely mental conceptions of numerical and mathematical science which have been by slow
degrees vouchsafed to man, and are still granted in these latter times by the Differential
Calculus, now superseded by the Higher Algebra, all of which must have existed in that
sublimely omniscient Mind from eternity.
Martha Somerville (ed.) Personal Recollections of Mary Somerville, Boston, 1874.
Steinmetz, Charles P.
Mathematics is the most exact science, and its conclusions are capable of absolute
proof. But this is so only because mathematics does not attempt to draw absolute
conclusions. All mathematical truths are relative, conditional.
In E. T. Bell Men of Mathematics, New York: Simona and Schuster, 1937.
Sullivan, John William Navin (1886 - 1937)
The mathematician is entirely free, within the limits of his imagination, to construct
what worlds he pleases. What he is to imagine is a matter for his own caprice; he is not
thereby discovering the fundamental principles of the universe nor becoming acquainted
with the ideas of God. If he can find, in experience, sets of entities which obey the same
logical scheme as his mathematical entities, then he has applied his mathematics to the
external world; he has created a branch of science.
Aspects of Science, 1925.
Sullivan, John William Navin (1886-1937)
Mathematics, as much as music or any other art, is one of the means by which we rise
to a complete self-consciousness. The significance of mathematics resides precisely in the
fact that it is an art; by informing us of the nature of our own minds it informs us of
much that depends on our minds.
Aspects of Science, 1925.
Thompson, D'Arcy Wentworth (1860-1948)
Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and
it is in obedience to the laws of physics that their particles have been moved, moulded
and conformed. They are no exceptions to the rule that God always geometrizes. Their
problems of form are in the first instance mathematical problems, their problems of growth
are essentially physical problems, and the morphologist is, ipso facto, a student
of physical science.
On Growth and Form, 1917.
Thoreau
He is not a true man of science who does not bring some sympathy to his studies, and
expect to learn something by behavior as well as by application. It is childish to rest in
the discovery of mere coincidences, or of partial and extraneous laws. The study of
geometry is a petty and idle exercise of the mind, if it is applied to no larger system
than the starry one. Mathematics should be mixed not only with physics but with ethics;
that is mixed mathematics. The fact which interests us most is the life of the naturalist.
The purest science is still biographical.
Veblen, Thorstein (1857-1929)
The outcome of any serious research can only be to make two questions grow where only
one grew before.
The Place of Science in Modern Civilization and Other Essays.
Weyl, Hermann (1885 - 1955)
... numbers have neither substance, nor meaning, nor qualities. They are nothing but
marks, and all that is in them we have put into them by the simple rule of straight
succession.
"Mathematics and the Laws of Nature" in The Armchair Science Reader, New
York: Simon and Schuster, 1959.
Whitehead, Alfred North (1861 - 1947)
The science of pure mathematics ... may claim to be the most original creation of the
human spirit.
Science and the Modern World.
Whitehead, Alfred North (1861 - 1947)
Mathematics as a science, commenced when first someone, probably a Greek, proved
propositions about "any" things or about "some" things, without
specifications of definite particular things.
Whitehead, Alfred North (1861 - 1947)
In modern times the belief that the ultimate explanation of all things was to be found
in Newtonian mechanics was an adumbration of the truth that all science, as it grows
towards perfection, becomes mathematical in its ideas.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Whitehead, Alfred North (1861 - 1947)
The progress of Science consists in observing interconnections and in showing with a
patient ingenuity that the events of this ever-shifting world are but examples of a few
general relations, called laws. To see what is general in what is particular, and what is
permanent in what is transitory, is the aim of scientific thought.
An Introduction to Mathematics.
Whitehead, Alfred North (1861 - 1947)
The study of mathematics is apt to commence in disappointment....We are told that by
its aid the stars are weighed and the billions of molecules in a drop of water are
counted. Yet, like the ghost of Hamlet's father, this greatest science eludes the efforts
of our mental weapons to grasp it.
An Introduction to Mathematics
Whitehead, Alfred North (1861 - 1947)
Familiar things happen, and mankind does not bother about them. It requires a very
unusual mind to undertake the analysis of the obvious.
Science and the Modern World.