[olivierduval]

IMHO, "creativity" is all about breaking existing rules, replacing them partially or totally with others. In math, it's a new axiom set, allowing/forbidding new inferences. And it's also using analogies with other domains to find new intuitions and new deductions.

However, the main problem with creativity is not reducing the knowledge base, it's finding new knowledges to extend the knowledge space consistently. Sometimes enumeration or automatic generation can help... but in that case, it's "only" a fixed set of meta-rules