500+ Sourced quotes
The study of mathematics would show... the necessity there is in reasoning, to separate all the distinct ideas, and to see the habitudes that all those concerned in the present inquiry have to one another, and to lay by those which relate not to the proposition in hand, and wholly to leave them out of the reckoning.
We tend to believe the premises because we can see that their consequences are true, instead of believing the consequences because we know the premises to be true. But the inferring of premises from consequences is the essence of induction; thus the method in investigating the principles of mathematics is really an inductive method, and is substantially the same as the method of discovering general laws in any other science.
As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.
Mathematics, trigonometry, chemistry, psychoanalysis, music, and what not have been related to cubism to give it an easier interpretation. All this has been pure literature, not to say nonsense, which brought bad results, blinding people with theories. Cubism has kept itself within the limits and limitations of painting, never pretending to go beyond it.
We have heard much about the poetry of mathematics, but very little of it has as yet been sung. The ancients had a juster notion of their poetic value than we. The most distinct and beautiful statements of any truth must take at last the mathematical form. We might so simplify the rules of moral philosophy, as well as of arithmetic, that one formula would express them both.
I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.
The word "Verse" is used here as the term most convenient for expressing, and without pedantry, all that is involved in the consideration of rhythm, rhyme, meter, and versification... the subject is exceedingly simple; one tenth of it, possibly, may be called ethical; nine tenths, however, appertains to the mathematics.
No one is without Christianity, if we agree on what we mean by that word. It is every individual's individual code of behavior by means of which he makes himself a better human being than his nature wants to be, if he followed his nature only. Whatever its symbol — cross or crescent or whatever — that symbol is man's reminder of his duty inside the human race. Its various allegories are the charts against which he measures himself and learns to know what he is. It cannot teach a man to be good as the textbook teaches him mathematics. It shows him how to discover himself, evolve for himself a moral codes and standard within his capacities and aspirations, by giving him a matchless example of suffering and sacrifice and the promise of hope.