No doubt but magic may do much in this;

For he that reads but mathematic rules

Shall find conclusions that avail to work

Wonders that pass the common sense of men.

Robert Greene, in Friar Bacon and Friar Bungay

Our Professor, which doth have tenure,

Feared be thy name.

Thy sets partition,

Thy maps commute,

In groups as in vector spaces.

Give us this day our daily notation,

And forgive us our obtuseness,

As we forgive tutors who canot help us.

Lead us not into Lye rings,

But deliver us from eigenvalues,

For thine is the logic, the notation,
and the accent,

That confuses us forever.

Amen.

An anonymous University of Toronto mathematics student.

"ARITHMETICUS" Virginia, Nevada. -- "If it would take a cannonball 3 1/8 seconds to travel four miles, and 3 3/8 seconds to travel the next four, and 3 5/8 to travel the next four, and if its rate of progress continued to diminish in the same ratio, how long would it take to go fifteen hundred million miles?"

I don't know.

Mark Twain [Sam Clemens] from Answers to Correspondents

In mathematics, you never understand things; you just get used to them.

John von Neumann

You burros have calculus in your blood.

Jaime Escalante

Minus times minus equals plus;

The reason for this we won't discuss.

Anonymous

Mathematics is the subject in which we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell

The elegance of a theorem is directly proportional to the number of ideas you can see in it and inversely proportional to the effort it take to see them.

George Polya

The mathematician's patterns, like the painter's or the poet's, must be *beautiful*; the ideas, like the colors or the words, must fit together in a harmonious way. ... There is no permanent place in the world for ugly mathematics.

G. H. Hardy

Detest it [a certain difficult mathematics problem] just as much as lewd intercourse; it can deprive you of all your leisure, your health, your rest, and the whole happiness of your life.

Wolfgang Bolyai (in a letter to his son Janos)

Mark all mathematical heads which be wholly and only bent on these sciences, how unfit to live with others, how unapt to serve the world.

Roger Ascham (1515-1568)

Mathematics is the science which draws necessary conclusions.

Benjamin Pierce

In mathematics he was greater

Than Tycho Brahe, or Erra Pater:

For he, by geometric scale,

Could take the size of pots of ale;

Resolve, by sines and tangents straight,

If bread or butter wanted weight;

And wisely tell what hour o' the day

The clock does strike, by Algebra.

Samuel Butler (1612-1680)

"Can you do addition?" the White Queen asked.

"What's one and one and one and one and one and one and one and one and one and one?"

"I don't know," said Alice, "I lost count."

Lewis Carroll [Charles Lutwidge Dodgson] (1832-1898)

"Why," said the Dodo, "the best way to explain it is to do it."

Lewis Carroll [Charles Lutwidge Dodgson] (1832-1898)

Mathemata mathematicis scribuntur.

[Mathematics is written for mathematicians.]

Nicolaus Copernicus (1473-1543)

A marvelous newtrality have these things mathematicall, and also a strange participation between things supernaturall, immortall, intellectuall, simple and indivisible, and things naturall, mortall, sensible, compounded and divisible.

John Dee (1527-1608)

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 Fontenelle (1657-1757)

Should I refuse a good dinner simply because I do not understand the processes of digestion?

Oliver Heaviside (1850-1925)

[On being criticized for using formal mathematical manipulations without understanding how they worked.]

Geometry enlightens the intellect and sets one's mind right. All its proofs are very clear and orderly. It is hardly possible for errors to enter into geometrical reasoning, because it is well arranged and orderly. Thus, the mind that constantly applies itself to geometry is not likely to fall into error. In this convenient way, the person who knows geometry acquires intelligence. It has been assumed that the following statement was written upon Plato's door: "No one who is not a geometrician may enter our house."

Ibn Khaldun (1332-1406)

He who can properly define and divide is to be considered a god.

Plato (429-347 B.C.)

Sir, I have found you an argument. I am not obliged to find you an understanding.

Samuel Johnson (1709-1784)

The Good Lord made all the integers; the rest is man's doing.

Leopold Kronecker (1823-1891)

Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover, this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.

Pierre Simon de Laplace (1749-1827)

Medicine makes people ill, mathematics makes them sad, and theology makes them sinful.

Martin Luther (1483-1546)

I tell them that if they will occupy themselves with the study of mathematics they will find in it the best remedy against the lusts of the flesh.

Thomas Mann (1875-1955), in The Magic Mountain

The habit of analysis has a tendency to wear away the feelings.

John Stuart Mill (1806-1873)

There are two ways to do great mathematics. The first way is to be smarter than everybody else. The second way is to be stupider than everybody else -- but persistent.

Raoul Bott

But the velocities of the velocities -- the second, third, fourth, and fifth velocities, etc. -- exceed, if I mistake not, all human understanding...

Bishop Berkeley, in The Analyst: A Discourse Addressed to an Infidel Mathematician (1734)

And what are these fluxions? The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities...?

Bishop Berkeley, in The Analyst: A Discourse Addressed to an Infidel Mathematician (1734)

Mathematics is the life of the gods.

Novalis [Friedrich von Hardenberg] (1772-1801)

I know not what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Isaac Newton (1642-1727)

He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side.

Plato (429-347 B.C.)

Do not imagine that mathematics is hard and crabbed, and repulsive to common sense. It is merely the etherialization of common sense.

William Thomson, Lord Kelvin (1824-1907)

You should help a man to take up a burden, but you should not help him put it back down.

Pythagoras [?]

How I need a drink -- alcoholic, of course -- after the heavy chapters involving quantum mechanics.

Anonymous

Structures are the weapons of the mathematician.

Nicholas Bourbaki

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 is of course quite annoying to us rigorous mathematicians; what is even more annoying is that by doing so they often come up with the right answer.

E. J. Mcshane

Sir, We must be aware of needless innovations, especially when guided by logic.

Sir Winston Churchill

An idea which can be used once is a trick. If it can be used more than once it becomes a method.

George Polya and Gabor Szego

Transcendental numbers occupy a position in the field of real or complex numbers much like that of insects in the kingdom of animals. Everybody knows they are, by a large margin, the most abundant class, but few know more than one or two of them by name.

Donald R. Newman

Mathematics consists in proving the most obvious thing in the least obvious way.

George Polya

I understand mathematics, I just can't do proofs.

Anonymous

Whoever despises the high wisdom of mathematics nourishes himself on delusion and will never still the sophistic sciences whose only product is an eternal uproar.

Leonardo da Vinci

It is an error to believe that rigor in a proof is an enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is, at the same time, the simpler and the more easily comprehended. The very effort for rigor forces us to find the simpler methods of proof.

David Hilbert

To think logically the logically thinkable -- that is the mathematician's aim.

C. J. Keyser

Some of the greatest advances in mathematics have been due to the invention of symbols, which it afterwards became necessary to explain; from the minus sign proceeded the whole theory of negative quantities.

Aldous Huxley

Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told that the young man had gone off to become a poet. Hilbert is reported to have remarked, "I never thought he had enough imagination to be a mathematician."

George Polya

What science can there be more noble, more excellent, more useful for men, more admirably high and demonstrative, than this of the mathematics?

Benjamin Franklin

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Felix Klein

Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.

Johann Wolfgang von Goethe

Mathematical proofs, like diamonds, are hard as well as clear, and will be touched with nothing but strict reasoning.

John Locke

No more fiction, for now we calculate; but that we may calculate, we had to make fiction first.

Friedrich Nietzsche

Stefan Bilaniuk

Department of Mathematics

Trent University

Maintained by Stefan Bilaniuk. Last updated 1997.08.28.