A kind of counter-example to your claim is the following: http://www.math.rutgers.edu/~zeilberg/GT.html It is an automated reasoning system for Euclidean geometry. Starting from literally nothing, it derived all of the geometric propositions in Euclid's Elements in a matter of seconds. Then it proceeded to produce a number of geometric theorems of human interest that were never noticed by any previous Euclidean geometers, classical or modern.

This is interesting.

It's hard for me to assess it from the outside. In particular, I don't have a good sense for the number of sequences of logical derivations one has to consider in order to arrive at the theorems that were proved if one were to proceed by brute force. I find it more interesting that it honed in on classical theorems on its own than that it was able to prove them (one can use coordinate geometry to reduce proofs to solving polynomial equations).

I think that it's significant that Euclidean geometry fell out of fashion a long time ago: the fraction of modern mathematicians who think about Euclidean geometry is negligible, and this may reflect an accurate assessment of the field as mathematically shallow. I didn't appreciate geometry until I learned about discrete groups of isometries acting on homogeneous Riemannian manifolds.

For those I think this paper is a good introduction to some state-of-the-art, machine-learning based techniques: http://arxiv.org/abs/1108.3446 One can see from the paper that there is plenty of room for machine learning techniques to be ported from fields like speech and vision.

Thanks for the reference

Progress in machine learning in vision and speech has recently been driven by the existence of huge training data-sets. It is only within the last few years that truly large databases of human-made proofs in things like set theory or group theory have been formalized. I think that future progress will come as these databases continue to grow.

How much future progress? :-)

Starting from literally nothing, it derived all of the geometric propositions in Euclid's Elements in a matter of seconds. Then it proceeded to produce a number of geometric theorems of human interest that were never noticed by any previous Euclidean geometers, classical or modern.

Where do you get these detailed claims about the program? I don't see anything like them in the book or here or here