Didn't know the von Neumann story about his influence from poor Kurt.
For 'more mathematical', really should say from when! Right, not from von Neumann!
If pick when carefully, if only from yesterday, then since then the field has become more mathematical! Or pick from the start of Stanford Professor Ng's class on 'machine learning' which seems to borrow a lot from maximum likelihood estimation in statistics and steepest ascent optimization from mathematical programming or operations research. Or, CLRS -- they went to mathematical programming and borrowed linear programming. Once at IBM's Watson lab I saw some guys attacking load leveling via some carefully done work in stochastic optimal control. Design of distributed computer systems has long been one of the better applications of queuing theory. Once I needed to find nearest neighbors in R^n so started by doing essentially binary search on each axis (yes, after that need to do some tree backtracking with some cutting planes). I heard that there was such a thing, k-D trees, and, yup, found it in Sedgewick and later discovered that such work is called 'computational geometry'. And, for my last example (drum roll), finally there is some interest in the computer and network monitoring community in regarding monitoring as some continually applied statistical hypothesis tests, maybe! We will see if KPCB sends a copy of my paper to Endgame!
In the short run, to attack a field with math can be one heck of a publishing opportunity. So in the long run, if only from 'academic competitiveness', a field doesn't have much hope as 'science' but to 'mathematize'.