“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

“Mathematics is the art of giving the same name to different things.” -- J. H. Poincare

"Mathematics consists in proving the most obvious thing in the least obvious way." -- George Polya

"A tragedy of mathematics is a beautiful conjecture ruined by an ugly fact.”

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

“Mathematics is like love; a simple idea, but it can get complicated.”

"Obvious is the most dangerous word in mathematics." -- E.T. Bell"Mathematics is not a deductive science – that's a cliché. 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." -- Paul Halmos

"Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics."

An expert is a man who has made all the mistakes, which can be made, in a very narrow field.

Quoted in A L Mackay,

*Dictionary of Scientific Quotations*(London 1994)

I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.

Quoted in F Wilczek, B Devine,

*Longing for the Harmonies*

This result is too beautiful to be false; it is more important to have beauty in one's equations than to have them fit experiment.

The evolution of the Physicist's Picture of Nature

*Scientific American*

**208**(5) (1963)

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it... That is because I don't understand it. Nobody does.

*QED, The Strange Theory of Light and Matter*, (London, 1990) 9.

And the most important one:

God used beautiful mathematics in creating the world. Paul Dirac

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