[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with which I read that remarkable work, the first inspiration for so many mathematicians of my generation, and learnt for the first time as I read it what mathematics really meant.
G. H. Hardy
Mathematicians come to the solution of a problem by the simple arrangement of the data, and reducing the reasoning to such simple operations, to judgments so brief, that they never lose sight of the evidence that serves as their guide.
But what exceeds all wonders, I have discovered four new planets and observed their proper and particular motions, different among themselves and from the motions of all the other stars; and these new planets move about another very large star [Jupiter] like Venus and Mercury, and perchance the other known planets, move about the Sun. As soon as this tract, which I shall send to all the philosophers and mathematicians as an announcement, is finished, I shall send a copy to the Most Serene Grand Duke, together with an excellent spyglass, so that he can verify all these truths.
What is this frog and mouse battle among the mathematicians?
Oh these mathematicians make me tired! When you ask them to work out a sum they take a piece of paper, cover it with rows of A's, B's, and X's and Y's ... scatter a mess of flyspecks over them, and then give you an answer that's all wrong!
Thomas A. Edison
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
Nobody is publicly accepted as an expert on poetry unless he displays the sign of poet, mathematician, etc., but universal men want no sign and make hardly any distinction between the crafts of poet and embroiderer. Universal men are not called poets or mathematicians, etc. But they are all these things and judges of them too. No one could guess what they are, and they will talk about whatever was being talked about when they came in. One quality is not more noticeable in them than another, unless it becomes necessary to put it into practice, and then we remember it.
"Do you know," the Devil confided, "not even the best mathematicians on other planets - all far ahead of yours - have solved it? Why, there is a chap on Saturn - he looks something like a mushroom on stilts - who solves partial differential equations mentally; and even he's given up."
Sometimes a line of mathematical research extending through decades can be thought of as one long conversation in which many mathematicians take part. This is fortunately true at present.
Guided only by their feeling for symmetry, simplicity, and generality . . . creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.
Spending time with math people is a lot of fun. As a result of the play, I've had semi-drunken dinners with mathematicians all over the country. I recommend the experience.
There was a Russian cult of eunuchs known as the Skoptsy who were renowned for their proficiency as mathematicians, bankers, and moneylenders. Outsiders called them rapacious but this was simply their jealousy speaking - when one is freed from sexual desire, or sexual desire is transmuted into work, suddenly the world becomes engorged with possibilities.
I am a Christian which means that I believe in the deity of Christ, like Tycho de Brahe, Copernicus, Descartes, Newton, Leibnitz, Pascal… like all great astronomers mathematicians of the past.
People tend to think that mathematicians always work in sterile conditions, sitting around and staring at the screen of a computer, or at a ceiling, in a pristine office. But in fact, some of the best ideas come when you least expect them, possibly through annoying industrial noise.
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 de Fontenelle
Mathematicians care no more for logic than logicians for mathematics.
Augustus De Morgan