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- All the limitative Theorems of metamathematics and the theory of computation suggest that once the ability to represent your own structure has reached a certain critical point, that is the kiss of death: it guarantees that you can never represent yourself totally. Godel's Incompleteness Theorem, Church's Undecidability Theorem, Turing's Halting Problem, Turski's Truth Theorem-- all have the flavour of some ancient fairy tale which warns you that "To seek self- knowledge is to embark on a journey which . . . will always be incomplete, cannot be charted on a map, will never halt, cannot be described."
- Douglas R. Hofstadter
- Any impatient student of mathematics or science or engineering who is irked by having algebraic symbolism thrust upon him should try to get along without it for a week.
- Eric Temple Bell
- Mathematicians are like Frenchmen: whatever you say to them they translate into their own language, and forthwith it is something entirely different.
- Johann Wolfgang von Goethe (1749 - 1832)
- The subspace W inherits the other 8 properties of V. And there aren't even any property taxes.
- J. MacKay, Mathematics 134b
- [F]or academic men to be happy, the universe would have to take shape. All of philosophy has no other goal: it is a matter of giving a frock coat to what is, a mathematical frock coat. On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit.
- Battaille
- Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
- Henri Poincare (1854 - 1912)
- Beauty is the first test; there is no permanent place in the world for ugly mathematics.
- G.H. Hardy, in _A Mathematician's Apology_
- Mathematics has given economics rigor, but alas, also mortis.
- Robert Heilbroner
- As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
- Albert Einstein (1879 - 1955)
- It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics or chemistry.
- H. L. Mencken (1880 - 1956)
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