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I would like to ask about examples where experimentation by computers have led to major mathematical advances.

##Motivation

I am aware about a few such cases and I think it will be useful to gather such examples together. I am partially motivated by the recent polymath5 which, at this stage, have become an interesting experimental mathematics project. So I am especially interested in examples of successful "mathematical data mining"; and cases which are close in spirit to the experimental nature of polymath5. My experience is that it can be, at times, very difficult to draw useful insights from computer data.

###Meta Question:

Is there a useful way to classify the various types of experimental mathematics?

I would like to ask about examples where experimentation by computers have led to major mathematical advances.

##Motivation

I am aware about a few such cases and I think it will be useful to gather such examples together. I am partially motivated by the recent polymath5 which, at this stage, have become an interesting experimental mathematics project. So I am especially interested in examples of successful "mathematical data mining"; and cases which are close in spirit to the experimental nature of polymath5. My experience is that it can be, at times, very difficult to draw useful insights from computer data.

###Meta Question:

Is there a useful way to classify the various types of experimental mathematics?

Bounty: many excellent answers so let's give the bounty to Gauss...

I would like to ask about examples where experimentation by computers have led to major mathematical advances.

##Motivation

I am aware about a few such cases and I think it will be useful to gather such examples together. I am partially motivated by the recent polymath5 which, at this stage, have become an interesting experimental mathematics project. So I am especially interested in examples of successful "mathematical data mining"; and cases which are close in spirit to the experimental nature of polymath5. My experience is that it can be, at times, very difficult to draw useful insights from computer data.

###Meta Question:

Is there a usefull way to classify the various types of experimental mathematics?

I would like to ask about examples where experimentation by computers have led to major mathematical advances.

##Motivation

I am aware about a few such cases and I think it will be useful to gather such examples together. I am partially motivated by the recent polymath5 which, at this stage, have become an interesting experimental mathematics project. So I am especially interested in examples of successful "mathematical data mining"; and cases which are close in spirit to the experimental nature of polymath5. My experience is that it can be, at times, very difficult to draw useful insights from computer data.

###Meta Question:

Is there a useful way to classify the various types of experimental mathematics?