Don't confuse interpolation with extrapolation. Curing cancer will require new ideas. IMO requires skill proficiency in tasks where the methods of solving are known.
Also, there's no reason to affirm that an eventual cure for cancer requires fundamentally new methods. Maybe the current methods are sufficient, it's just that nobody has been "smart" enough to put the pieces together. (disclaimer: not an expert at all)
Search is different from either of those things, it's when you have a target and a collection of other things, and are trying to find the target in that collection.
- Search allows exploration of the game tree, potentially finding novel strategies.
- Learning compresses the insights gained from search into a more efficient policy.
- This compressed policy then guides future searches more effectively.
Evolution is also a form of search, and it is open-ended. AlphaProof solved IMO problems, those are chosen to be out of distribution, simple imitation can't solve them. Scientists do (re)search, they find novel insights nobody else discovered before. What I want to say is that search is on a whole different level than what neural nets do, they can only interpolate their training data, search pushes outside of the known data distribution.
It's actually a combo of search+learning that is necessary, learning is just the little brother of search, it compresses novel insights into the model. You can think of training a neural net also as search - the best parameters that would fit the training set.