(1) Economist understand quite well that basic research is a public good that we cannot expect to be funded by the private sector. Public research programs of government funded research in universities and institutes are essential. It is not that venture capitalists fail to understand the importance of basic research, it is that, of the large potential (social) returns to a research program, only a small and very uncertain share of (private) returns are appropriable by the investors.

(2) Concerning the “[...] lessons of the complex financial models involved in the current global financial crisis,” I would say that the flaw was not technical but conceptual: many did not seem to understand the limitations of the theories behind the mathematical models on which these software tools stood. Those theories were reasonable in smooth phases of the business cycle but useless during a recession; not to speak about a recession coupled with a banking crisis.

In physics, which I was primarily teaching, the students could “fake” thinking by memorizing their way through it, and could work problems as long as they had seen problems that required the same “algorithm”. But in computer programming, there is a much greater range of type of problems to tackle, and you have to be able to invent an algorithm for each situation.

I think most colleges have never found a break-through to this hurdle in C.Sc., and, consequently, C.Sc. depts. have “dumbed-down” the curriculum in order to produce graduates, many of which, still cannot invent an algorithm – hence a huge work force of lousy programmers.

One further thought about it: I also found (mainly in my 2 sons) that the “ability for algorithm invention” comes, if at all, with mental age. I am convinced that many high schoolers and underclassmen are not at that “age” until later – maybe 25 or 30 years old. But by then, the mold has been set, and they never try again. Our educational system doesn’t encourage that, especially in Europe, and possibly in India. In U.S., many go to college after being in the work force for years, and then they find they can do things mentally that never knew they could do before then. And it is simply because their “brains” have caught up with their “bodies”.

“The dream algorithm R&D tool would be similar to Matlab or Mathematica but could be compiled to fast, efficient binaries similar to ANSI C and would be available for all platforms.”

By the way, what you’re looking for exists already. I’ve been fiddling with building trading systems in it for the last year or so.
http://lush.sf.net

Others may prefer Common Lisp (I prefer CMU-CL to SBCL for lots of different reasons), but I don’t think there is enough numerics developed for CL to justify this assertion. Chicken ain’t bad either, though it has the same problem.

The article had a complete enough list to make the author’s point, and the author did make it well.

BTW: some of us have heard LISP aficionados sing its lisping praises for so long, we no longer believe it when someone claims such and such version of LIST “fits that bill”. Especially not when the manual is still a work in progress!

R.G. Vickson

You should note other free systems, like Sage and Fermat.

More importantly, I am surprised that you don’t mention encryption algorithms like RSA, which use more sophisticated mathematics, at the junior/senior undergraduate math major level. There are new encryption algorithms based on elliptic curves that use more advanced mathematics than that.

Also, I think you underestimate the kind of mathematics involved in GPS systems.

- Robert H. Lewis