The fundamental laws governing physics and chemistry and many branches of engineering are clearly defined, but when they are applied to solving concrete practical and theoretical problems the required calculations are often too costly to be carried out at any desired accuracy. The common reason is the enormous gap between the fine (microscopic) scale at which these laws are given and the much larger (macroscopic) scales of the phenomena we wish to calculate. To address this challenge, first in the specific context of fluid dynamic problems, Weizmann Institute scientists devised in 1972 a new computational approach in which separate calculations are conducted at many intermediate scales (resolutions) of the problem, with various modes of transferring information from one scale to another. This produced huge reductions in the computer resources required to solve each flow problem. The multi-scale (or "multigrid") methodology has subsequently been generalized and extended to many other types of mathematical problems and areas of application, influencing almost every aspect of contemporary science and engineering. It also inspires current developments of multi-level algorithms in computer science, from large network analysis and data mining to machine vision, learning and recognition.