Wired Insider: Today, I read this and yesterday that.
And I think, it will be great to manipulate interactive systems without extra devices to get more insight or just have fun. With software that follows me where I go, on computer devices that do not even need a connection to a server - providing interaction in a very natural way by 3D gesture control.
Improvements can be expected in many fields including life sciences, engineering, design & arts, finance, ...
On a higher level (of education in math or better problem solving) I think of problem-model-methods organized orthogonally.
Manipulation of their combinations will help to to get insight in model and method traps, say, the application of an SDE, if a translation into a PDE was better or the application of lousy solvers for complex PDEs, ....
With back test and stress test environments ... We all should be aware that our model-method combinations are only as good as they back test and as robust as they behave under "stress conditions".
This is not only true in quantitative finance.
I confess, this is my "hobby horse": generalized model and method validation.
At the other hand a promise has been addressed: One day technology will become invisible and know what we want.
It will be so sophisticated that it will quietly create models, select solvers and compute results.
The improvements of interaction patterns are great, but the automation of the operational semantics of problem solving? Nobody says explicitly that this will happen in computational mathematics soon, but I hear the "grass growing".
I am a Mathematica evangelist driven by business success. Mathematica empowers us to do things better. And Leap Motion and Mathematica's dynamic visualization will be a fantastic combination.
But I have reservations with its automated algorithm selection, from the beginning. Not only, because it has a few intrinsic traps (missing the required regime switches - like if the convection term becomes dominant in a reaction-convection-diffusion PDE), but I believe human-machine interaction should have higher goals - like explorative, experimental and finally evolutionary learning.
As Aaron Brown highlights it in his great book Red-Blooded Risk Management - learn about risk from misconceptions ... IMO, also this is not only true in quant finance.
The worst type of derivative pricer is the one that gives you false comfort about its robustness (now, when market regimes can lead to negative interest rates, normally distributed, short rate models need to be reactivated), the worst kind of portfolio optimizer is the one that does not take in account, that correlations change with the market dynamics ...