There are two extremes to airport security. One is the full body cavity search of every single flier, an extreme which is so unpopular as to be unsustainable. The other is to search only those fliers who meet a particular profile, e.g., Middle Eastern man, age range 18-30, paying cash and purchasing only a one-way ticket. If this latter is used, the terorists will simply send someone who does not fit the profile.
The obvious conclusion is that an intermediate policy is needed. This is where the mathematician comes in. The mathematician can devise a middle ground between the two extermes, by devising a formula for random searches which nobody can predict. Parameters can be given to a computer, which will print out daily schedules for searches. The formula itself can be changed periodically, since apparently our government is no longer able to keep any secrets.
I say that anybody meeting the above profile should be searched 100% of the time. Little old ladies and young kids should be searched only a small fraction of the time. Those in between would be searched a certain percentage of the time based on the formula. The completeness of the search would also be randomized.