gsmith@garnet.berkeley.edu (Gene W. Smith) (02/01/90)
In article <1076@sys.uea.ac.uk>, jrk@sys (Richard Kennaway) writes: >>Another Academic Legend? >I heard this story told at Oxford, where it was said to have happened at >Cambridge. At Cambridge, do they tell it of Oxford? This is definitely a Legend. I heard a version where the subject was ring theory. The thesis was about rings with certain conditions, about which many amazing theorems were proven by the PhD student in question. When asked for an example,it turned out that there weren't any. -- ucbvax!garnet!gsmith Gene Ward Smith/Brahms Gang/Berkeley CA 94720 ucbvax!bosco!gsmith Institute of Pi Research
alopez-ortiz@violet.waterloo.edu (Alex Lopez-Ortiz) (02/02/90)
In article <1990Feb1.084329.23934@agate.berkeley.edu> gsmith@garnet.berkeley.edu (Gene W. Smith) writes: > >>I heard this story told at Oxford, where it was said to have happened at >>Cambridge. At Cambridge, do they tell it of Oxford? > > This is definitely a Legend. Not at all, actually, a few years ago I was at a conference, and the lecturer was talking about some measurable spaces, and proving this and that, at the end of the lecture one of the attendants asked for an example of such a space, and the lecturer haven't one, later on that day it turned out that no such measurable space exists. Moral : Never attempt an induction without working out the first 4 values. Alex
fs@rex.cs.tulane.edu (Frank Silbermann) (02/03/90)
In article <20433@watdragon.waterloo.edu> alopez-ortiz@violet.waterloo.edu (Alex Lopez-Ortiz) writes: > > ...the lecturer was talking about some measurable spaces, > and proving this and that, ... later on that day it turned out > that no such measurable space exists. Moral: > > Never attempt an induction > without working out the first 4 values. Better Moral: A notation is but a language, and a proof theory merely a way of verifying one's hypotheses. The models are what make a theory interesting. Therefore, never get so caught up in a theory that you forget about the concrete problems which motivated the theory in the first place. Frank Silbermann fs@rex.cs.tulane.edu (just trying to inject a little controversy)
harper@oravax.UUCP (Douglas Harper) (02/03/90)
In article <2072@rex.cs.tulane.edu>, fs@rex.cs.tulane.edu (Frank Silbermann) writes: > A notation is but a language, and a proof theory ^^^^^^^^^^^^^^ > merely a way of verifying one's hypotheses. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ You can't have meant what I read this to mean, that proof theory is used solely to determine whether or not one's hypotheses hold in an intended model. Could you please restate this? -- Douglas Harper oravax!harper@cu-arpa.cs.cornell.edu "Gimme eat."..."Give *everybody* eat!" -- Major _____ de Coverley -- Joseph Heller, _CATCH-22_
aaron@grad2.cis.upenn.edu (Aaron Watters) (02/05/90)
In article <2072@rex.cs.tulane.edu> fs@rex.UUCP (Frank Silbermann) writes: >A notation is but a language, and a proof theory >merely a way of verifying one's hypotheses. >The models are what make a theory interesting. I like the spirit, but I have to object that `proof theories' are seldom used at all (except for trivial things like type checking and getting students to drop your class on symbolic logic). Proof theories are primarily an abstract object of mathematical discussion and not a used mathematical technique. -aaron
cjh@petsd.UUCP (Chris Henrich) (02/07/90)
In article <1990Feb1.084329.23934@agate.berkeley.edu> gsmith@garnet.berkeley.edu (Gene W. Smith) writes: >In article <1076@sys.uea.ac.uk>, jrk@sys (Richard Kennaway) writes: > >>>Another Academic Legend? > >>I heard this story told at Oxford, where it was said to have happened at >>Cambridge. At Cambridge, do they tell it of Oxford? > > This is definitely a Legend. I heard a version where the >subject was ring theory. The thesis was about rings with certain >conditions, about which many amazing theorems were proven by the >PhD student in question. When asked for an example,it turned out >that there weren't any. I heard a version of it in the first person, as reminiscence by a topologist. He reviewed a paper which proved that if a topological space X had property A then it also had property B. In his review he stated that if X had property A then it also had property not-B. What were A and B? He never said. I conjecture that they were mildly esoteric stuff in point-set topology, and the fact that no space has property A was not earth-shaking. Regards, Chris (201)758-7288 106 Apple Street, Tinton Falls,N.J. 07724