The Important Theorems Are the Beautiful Ones  Dr. Gene Chase
guest blog author here again.  What makes a math theorem
important?  The usual answer is that it is either beautiful or
useful. If like me you think that being useful is a beautiful
thing, then important theorems are the beautiful ones.  But what
makes a theorem beautiful? For example, why is the Theorem of
Pythagoras widely regarded as beautiful: and a, b, and c are not
0 if and only if a, b, and c are the sides of a right triangle?
(OK, break into small groups and discuss this among yourselves!
An answer appears at the bottom of this post.)  But the theorem
1223334444 = 1223334443 + 1 is not beautiful, won’t you agree?
If the theorem is geometric, we can appeal to visual beauty. For
example, three circles pairwise tangent have a beautiful
property that is animated here.  But beautiful theorems do not
have to be geometric. Numbers are beautiful. For example,
Euclid’s theorem that there are an infinity of primes is
beautiful. No one has been able