Why are mathematical proofs that rely on computers controversial? There are many theorems in mathematics that have been proved with the assistance of computers, take the famous four color theorem for example. Such proofs are often controversial among some mathematicians. Why is it so?
I my opinion, shifting from manual proofs to computer-assisted proofs is a giant leap forward for mathematics. Other fields of science rely on it heavily. Physics experiments are simulated in computers. Chemical reactions are simulated in supercomputers. Even evolution can be simulated in an advanced enough computer. All of this can help us understand these phenomena better. 
But why are mathematicians so reluctant?

I think a computer-assisted or computer-generated proof can be less convincing if it consists of a lot of dense information that all has to be correct. A proof should have one important property: a person reading it must be convinced that the proof really proves the proposition it is supposed to prove. 
Now with most computer generated proofs that in fact is not the case. What often happens is that the proof is output of an algorithm that for instance checks all possibilities in a huge state space. And then we say the computer proved it since all states has been checked and they were all ok. 
An important question here is: can there be a simple, elegant proof if we have to check a million cases separately and cannot use an elegant form of induction or other technique to reduce the number of logical cases?
I would say no, so in this case it does not matter if the output is from a computer or not. However, most mathematicians would look for a more elegant solution where the number of distinct cases to check fits one page of paper, and would only consider a proof of that size a nice proof.
