User ann o'nimous - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T07:23:56Z http://mathoverflow.net/feeds/user/12351 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/51531/theorems-that-are-obvious-but-hard-to-prove/52602#52602 Answer by ann o'nimous for Theorems that are 'obvious' but hard to prove ann o'nimous 2011-01-20T11:12:30Z 2011-01-20T15:16:19Z <p>On an elementary level, the intermediate value theorem is surprisingly deep.</p> <p>On a less elementary level, the prime number theorem is "obvious" from $\sum_{p\leq x}1/p\sim \log\log x$ (that was noticed by Euler) and Dirichlet's theorem on primes in arithmetic progressions is "obvious" if you use the sieve of Erathostenes.</p>