Due to the continuous synergistic progress in algorithm development, computer technology, and computational science methodology, the scope of large-scale problems such as the one just mentioned can be continuously increased. Examples can be matched to the curve corresponding to the increase in computing power of Cray vector supercomputers.

At the time the Cray 1S emerged, codes forcasting the weather were accurate for no more than 12 hours. The Cray XMP raised that limit to 24 hours and plasma modeling in 2D became feasible. With the Cray 2 weather forcasting for 48 hours, modeling in chemical dynamics and estimate of the Higgs Boson Mass were addressed. The Cray YMP allowed 72 hour weather forcasting, and 2D nonlinear hydrodynamics. The C90 has made pharmaceutical design, and vehicle signature feasible.

Similarly, following the curve of Intel's massively parallel systems, there are examples of problems that could be addressed in an increasing scope as the has computing power increased. [2] In 1952 Hartree had recognized the importance of algorithm development. His vision was that:

"With the development of new kinds of equipment of greater capacity, and particularly of greater speed, it is almost certain that new methods will have to be developed in order to make the fullest use of this new equipment. It is necessary not only to design machines for the mathematics, but also to develop a new mathematics for the machines."