Do mathmatician ever prove that a theorem could not generalize into a much general theorem? Is there a historic mile-stone example refer to the above question?
Do mathmatician ever prove that a theorem could not generalize into a much general theorem? Is there a historic mile stone example?
3
$\begingroup$
math-history
proof-writing
-
0It's my feeling that any theorem can be generalized. There is also the old joke about a theorem so general it has no particular application. Examples are welcomed. – 2012-04-07
-
4[This](http://en.wikipedia.org/wiki/Abel-Ruffini_theorem) theorem is a nice example. – 2012-04-07
-
0I think this depends on what you put into the word generalize. There are often different ways to look upon things, one may for example try to generalize a statement within a universe, lift a statement into a larger universe or restrict a statement into a smaller universe. – 2012-04-07
-
1Why the two downvotes? Admittedly it's a rather open-ended question, but I do think there could be meaningful answers. – 2012-04-07
-
0Suppose you have to theorems, $T_1$ and $T_2$. Although they seem to have nothing common, one can ask whether it is true if both $T_1$ and $T_2$ holds, and that is more general than $T_1$ or $T_2$. If you continue this and take all known theorems and ask whether all of them holds, I get an application of Russell's paradox. – 2012-10-23