Carrying on from that thought, the various mathematician-employing agencies have now had over 60 years to study the problem of "how much can we use this critical information-revealing tool without exposing its existence?" If they can identify an upper bound on "sparingly", that's immensely valuable.
During WW2, the Allies would crack messages to locate submarines.
Now killing a submarine once you know where it is, is pretty easy. The problem is finding the submarine, and explaining how you were found. To handle that, the Allies used a form of parallel construction. They would send a spotting plane over the area, to spot the sub and give a plausible reason to have located the submarine.
That just moves the problem. Now the Germans start wondering how the spotting planes seem to be so damn good at being in the right place at the right time.
