I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods - but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.
Benoît MandelbrotRelated topics
certain close earth forever fresh ground hero hold mathematics mother mythology needs off order pure saw strength study touch inputRelated quotes
There are many pharisees in literature as well as in religion, wrapped up in the garments of self-idolatry, and making their very deficiencies the ground of their highest complacency. There are many blind wanderers through unbounded fields of instruction, who can discover nothing but nakedness-nothing but barrenness around them. Fertility itself offers no attractions to them-how much less can they understand the power of that benign principle which makes the waters gush forth, fresh, pure, and sparkling, from the very rocks of the desert.
John Bowring
The atoms in the philosophy of do not move merely by chance. Leucippus seems to have believed in complete determinism, since he is known to have said: "Naught happens for nothing, but everything from a ground and of necessity." The atomists did not give any reason for the original motion of the atoms, which just shows that they thought of a causal description of the atomic motion; causality can only explain later events by earlier events, but it can never explain the beginning.
Werner Heisenberg
Anyone who compares the bibliography with the reprinted papers will notice that mathematics and physics have not been given equal treatment. There is a strong bias in favor of mathematics. The bias arises from the fact that mathematical papers, provided that are correct and not trivial, have permanent value, whereas most papers in physics journals are ephemeral. For this reason, it is customary to publish complete collected works of mathematicians but only selected works of physicists.
Freeman Dyson
The psychical condition of men's minds may be compared with a set of bells close together, and so arranged that in the ordinary man a bell rings only when one beside it sounds, and the vibration lasts only a moment. In the genius, when a bell sounds it vibrates so strongly that it sets in action the whole series, and remains in action throughout life. The latter kind of movement often gives rise to extraordinary conditions and absurd impulses, that may last for weeks together and that form the basis of the supposed kinship of genius with insanity.
Otto Weininger
I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began work on extensions to notation that might serve. In particular, I adopted the matrix algebra used in my thesis work, the systematic use of matrices and higher-dimensional arrays (almost) learned in a course in Tensor Analysis rashly taken in my third year at Queen's, and (eventually) the notion of Operators in the sense introduced by Heaviside in his treatment of Maxwell's equations.
Kenneth E. Iverson