Friday, February 17, 2012
Of Standard Theories
Of Standard Theories L. Edgar Otto 02-17-12
"All revolutionary advances in science may consist less of sudden and dramatic revelations than a series of transformations, of which the revolutionary significance may not be seen (except afterwards, by historians) until the last great step. In many cases that full potentiality and force of a most radical step in such a sequence of transformations may not even be manifest to its author."
Bernard Cohen (1914-2003)
The Newtonian Revolution (1980) 162
"Non-standard analysis frequently simplifies substantially the proofs, not only of elementary theorems, but also of deep results.. This is true, e.g., also for the proof of the existence of invariant subspaces for compact operators, disregarding the improvement of the result; and it is true in an even higher degree in other cases. This state of affairs should prevent a rather common misinterpretation of non-standard analysis, namely the idea that it is some kind of extravagance or fad of mathematical logicians. Nothing could be further from the truth. Rather, there are good reasons to believe that non-standard analysis , in some version or other, will be the analysis of the future."
Kurt Godel (1906-1978)
Remark on Non-standard Analysis (1974) Collected Works Vol. I , 145
Synchronicity again... see the summary here of a fellow blogger.