Hilbert once had a student in mathematics who stopped coming to his lectures, and he was finally told 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.'
Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.
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.
You know we all became mathematicians for the same reason: we were lazy.
A mathematician who can only generalise is like a monkey who can only climb up a tree, and a mathematician who can only specialise is like a monkey who can only climb down a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise.
One can always reason with reason.
The mathematician has reached the highest rung on the ladder of human thought.
There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician.
The way in which mathematicians and physicists and historians talk is quite different, and what a physicist means by physical intuition and what a mathematician means by beauty or elegance are things worth thinking about.
All these people that I used to know, they're an illusion to me now. Some are mathematicians, some are carpenters' wives.
It is obvious that mathematics needs both sorts of mathematicians, theory-builders and problem-solvers.
Among mathematicians, even in those days, the reputation of being a good Glass Bead Game player meant a great deal; it was equivalent to being a very good mathematician.
...the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know
It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation.
Biographical history, as taught in our public schools, is still largely a history of boneheads; ridiculous kings and queens, paranoid political leaders, compulsive voyagers, ignorant general the flotsam and jetsam of historical currents. The men who radically altered history, the great scientists and mathematicians, are seldom mentioned, if at all.
Mathematicians stand on each other's shoulders.
Some mathematician, I believe, has said that true pleasure lies not in the discovery of truth, but in the search for it.
A mathematician may say anything he pleases, but a physicist must be at least partially sane.
How happy the lot of the mathematician. He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve.
The mathematician's best work is art, a high perfect art, as daring as the most secret dreams of imagination, clear and limpid. Mathematical genius and artistic genius touch one another.
So-called professional mathematicians have, in their reliance on the relative incapacity of the rest of mankind, acquired for themselves a reputation for profundity very similar to the reputation for sanctity possessed by theologians.
Today, it is not only that our kings do not know mathematics, but our philosophers do not know mathematics and - to go a step further - our mathematicians do not know mathematics.
A mathematician who is not also something of a poet will never be a complete mathematician.
Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different.
The good Christian should beware the mathematician and all those who make empty prophecies. The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of hell.
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