I shall now address you on the subject of the present situation in research in the foundations of mathematics. Since there remain open questions in this field, I am not in a position to paint a definitive picture of it for you. But it must be pointed out that the situation is not so critical as one could think from listening to those who speak of a foundational crisis. From certain points of view, this expression can be justified; but it could give rise to the opinion that mathematical science is shaken at its roots.
Paul BernaysRelated topics
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With your spirit open and unconstricted, look at things from a high point of view. You must cultivate your wisdom and spirit. Polish your wisdom: learn public justice, distinguish between good and evil, study the Ways of different arts one by one. When you cannot be deceived by men you will have realised the wisdom of strategy.
The wisdom of strategy is different from other things. On the battlefield, even when you are hard-pressed, you should ceaselessly research the principles of strategy so that you can develop a steady spirit.
Miyamoto Musashi
While the Christian apostles preached their ideal in the open, the Talmud hides; and its two appendages, the Kahal and Freemasonry, are even more invisible. The three of them use, in order to remain in the dark, a scabrous and accursed means, namely the lie. In other words, the lie is the basis of the system used by Jews, to whom one can say.. 'You speak, therefore you be.' But the lie has a mortal enemy, namely the truth. For truth is the distinctive trait of Christianity.
Nicolae Paulescu
Your eyes, accustomed to semi-darkness, will soon open to more radiant visions of light. The shadows which we shall paint shall be more luminous than the high-lights of our predecessors, and our pictures, next to those of the museums, will shine like blinding daylight, compared with deepest night. We conclude that painting cannot exist today without divisionism... w:Divisionism - [ Paul Signac initiated divisionism slightly earlier, together with Seurat ] - for the modern painter, must be an innate complementariness which we declare to be essential and necessary.
Umberto Boccioni
Econometrics is the name for a field of science in which mathematical-economic and mathematical-statistical research are applied in combination. Econometrics, therefore, forms a borderland between two branches of science, with the advantages and disadvantages thereof; advantages, because new combinations are introduced which often open up new perspectives; disadvantages, because the work in this field requires skill in two domains, which either takes up too much time or leads to insufficient training of its students in one of the two respects.
Jan Tinbergen
We shall see that the mathematical treatment of the subject [of electricity] has been greatly developed by writers who express themselves in terms of the 'Two Fluids' theory. Their results, however, have been deduced entirely from data which can be proved by experiment, and which must therefore be true, whether we adopt the theory of two fluids or not. The experimental verification of the mathematical results therefore is no evidence for or against the peculiar doctrines of this theory.
James Clerk Maxwell
