[Math] How helpful is non-standard analysis

Question

So, I can understand how non-standard analysis is better than standard analysis in that some proofs become simplified, and infinitesimals are somehow more intuitive to grasp than epsilon-delta arguments (both these points are debatable).

However, although many theorems have been proven by non-standard analysis and transferred via the transfer principle, as far as I know all of these results were already known to be true. So, my question is:

Is there an example of a result that was first proved using non-standard analysis? To wit, is non-standard analysis actually useful for proving new theorems?

Edit: Due to overwhelming support of Francois' comment, I've changed the title of the question accordingly.

Answer 1

From the Wikipedia article:

the list of new applications in mathematics is still very small. One of these results is the theorem proven by Abraham Robinson and Allen Bernstein that every polynomially compact linear operator on a Hilbert space has an invariant subspace. Upon reading a preprint of the Bernstein-Robinson paper, Paul Halmos reinterpreted their proof using standard techniques. Both papers appeared back-to-back in the same issue of the Pacific Journal of Mathematics. Some of the ideas used in Halmos' proof reappeared many years later in Halmos' own work on quasi-triangular operators.