The infinitely competent can be uncreative.
The concept of number is the obvious distinction between the beast and man. Thanks to number, the cry becomes a song, noise acquires rhythm, the spring is transformed into a dance, force becomes dynamic, and outlines figures.
Neither you nor I nor anybody else knows what makes a mathematician tick. It is not a question of cleverness. I know many mathematicians who are far abler than I am, but they have not been so lucky. An illustration may be given by considering two miners. One may be an expert geologist, but he does not find the golden nuggets that the ignorant miner does.
The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.
Our notion of symmetry is derived form the human face. Hence, we demand symmetry horizontally and in breadth only, not vertically nor in depth.
Let no one say that I have said nothing new... the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
Reverend Fathers, my letters did not usually follow each other at such close intervals, nor were they so long.... This one would not be so long had I but the leisure to make it shorter.
I feel engulfed in the infinite immensity of spaces whereof I know nothing, and which know nothing of me, I am terrified The eternal silence of these infinite spaces alarms me.
The mathematician, carried along on his flood of symbols, dealing apparently with purely formal truths, may still reach results of endless importance for our description of the physical universe.
... 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.
To speak algebraically, Mr. M. is execrable, but Mr. G. is (x + 1)- ecrable.
Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
To think I have spent my life on absolute muck.
It is a pleasant surprise to him (the pure mathematician) and an added problem if he finds that the arts can use his calculations, or that the senses can verify them, much as if a composer found that sailors could heave better when singing his songs.
I am ill at these numbers.
The control of large numbers is possible, and like unto that of small numbers, if we subdivide them.
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.
This paper gives wrong solutions to trivial problems. The basic error,however, is not new.
No Roman ever died in contemplation over a geometrical diagram.
Mathematics is one of the surest ways for a man to feel the power of thought and the magic of the spirit. Mathematics is one of the eternal truths and, as such, raises the spirit to the same level on which we feel the presence of God.
The only thing I am interested in using mathematics for is to have a good time and to help others do the same.
A typical mathematician does not actively try to be useful. Individual mathematicians are motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society, nevertheless, mathematics as a whole does benefit society.
Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
The product of mathematics is clarity and understanding. Not theorems, by themselves. ... In short, mathematics only exists in a living community of mathematicians that spreads understanding and breathes life into ideas both old and new.
Everything useful in mathematics has been devised for a purpose. Even if you don't know it, the guy who did it first, he knew what he was doing. Banach didn't just develop Banach spaces for the sake of it. He wanted to put many spaces under one heading. Without knowing the examples, the whole thing is pointless.
Follow AzQuotes on Facebook, Twitter and Google+. Every day we present the best quotes! Improve yourself, find your inspiration, share with friends
or simply: