3 ms·

Well, why exactly would you think that a simple to state problem should have a simple solution? It is of course false, as demonstrated for example by the insolv

by stiff 13y ago

Well, why exactly would you think that a simple to state problem should have a simple solution? It is of course false, as demonstrated for example by the insolvability of equations of degree higher than 5 [1] and by countless other examples, but I don't see a reason why it would even be a reasonable heuristic. If you spent just a few hours trying to think of a proof of the Fermats theorem you would very quickly see a lot of good reasons why it is difficult and why an elementary solution most likely does not exist. E=mc^2 is just a statement of a relationship, it isn't a proof or a solution to a problem. Mathematical work in modern physics is in fact just as complicated and messy. [1] http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

Someone 13y ago
As others said, once you have sufficient terminology, the proof is simple. For the Ruffini theorem, http://math.stackexchange.com/questions/286927/why-cant-there-be-a-quintic-formula http://math.stackexchange.com/questions/286927/why-cant-ther... states: "The reason five is special is that the group A5 of all even permutations of 5 letters is the smallest non-abelian simple group". An example from computer science that some may understand better: A monad is just a monoid in the category of endofunctors. Both are short statements that one cannot grasp without prior knowledge, but that become simple once one has 'some' prior knowledge. And in some sense, it is turtles all the way down. Even the statement 1+1=2, when studied deeply enough, requires huge amounts of prior knowledge (about 380 pages, and that excludes the definition of 'addition' (http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations http://en.wikipedia.org/wiki/Principia_Mathematica#Quotation...) :-)) Some say that there are three kinds of theorems: false, trivial and not yet trivial.

by stiff 13y ago

Someone 13y ago

As others said, once you have sufficient terminology, the proof is simple. For the Ruffini theorem, http://math.stackexchange.com/questions/286927/why-cant-there-be-a-quintic-formula http://math.stackexchange.com/questions/286927/why-cant-ther... states: "The reason five is special is that the group A5 of all even permutations of 5 letters is the smallest non-abelian simple group". An example from computer science that some may understand better: A monad is just a monoid in the category of endofunctors. Both are short statements that one cannot grasp without prior knowledge, but that become simple once one has 'some' prior knowledge. And in some sense, it is turtles all the way down. Even the statement 1+1=2, when studied deeply enough, requires huge amounts of prior knowledge (about 380 pages, and that excludes the definition of 'addition' (http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations http://en.wikipedia.org/wiki/Principia_Mathematica#Quotation...) :-)) Some say that there are three kinds of theorems: false, trivial and not yet trivial.