The years of the 1950s and ’60s were very exciting times to be a renal physiologist because of the upsurge of interest in a previously most resilient problem of urine concentration and dilution by the mammalian kidney which occurs according to the state of hydration of the organism. Active transport of water across membranes was a most unattractive hypothesis as the micro structure was unsuitable and the high energy requirements for it were not satisfied in the kidney. The first impulse towards solution originated from Werner Kuhn, a physical chemist in Basel. In 1942, he described an apparatus that could make concentrated solutions from dilute ones by a countercurrent model system. The basic principle is that two streams, moving in opposite directions, are so juxtaposed as to facilitate the mutual exchange of energy or substance through a membrane that separates them (Smith & Bull, 1959). Kuhn and Heinrich Wirz, a physiologist also in Basel, noted that in the mammalian renal medulla there are both tubular and vascular loops in countercurrent arrangements. Other renal physiologist, first cautiously then enthusiastically joined Kuhn’s inspired lead. Among Kuhn’s models the one that provided the best fit (Kuhn & Ramel, 1959) to the morphological and physiological reality of the kidney was published in 1959. In this model the membrane transported sodium. The differential equations described the model with variables including length of the loop, velocity of flow through the system and membrane transport activity. Paper and pencil calculations based on the model allowed an increasing number of researchers to seek a one-to-one correspondence between the model and physical reality. Soon a major discrepancy was discovered: While the model required that active sodium transport be continuous in the tubular loop throughout the entire region where concentration kept increasing, in reality, this was the case only in the outer medulla. In the inner medulla, in the thin-walled structures, cellular machinery appeared to be lacking for active sodium transport. Yet, in reality, solute concentration showed a steep continuous increase throughout the medulla to the papillary tip. The magic word on modeling is attributed to Einstein: “Make everything as simple as possible, but no simpler”. We thought that Kuhn’s model has been far too simplified. The model we developed (Pinter & Shohet, 1963; Shohet & Pinter, 1964) included both the tubular and the vascular loops, and also the feature that active transport of sodium was restricted to the loop segment in the outer medulla. A set of ordinary linear equations was developed which assumed that, except for the thick segment of the loop of Henle, membrane transport of sodium was proportional to the concentration difference across them. The mathematical description was rather messy. Fortunately, one of us (JLS) had access to an analog computer. The results were graphs showing that in this model there can be a continuous increase of sodium concentration in the inner medulla, in absence of active transport from the loop. Our model quickly generated criticism the essence of which was that we made two assumptions implicit in the model, each of which alone being fully justified, but used together contradicted each other. One of these was that diffusion of solute along the length of the loops could be neglected, as this longitudinal dimension is several hundred times greater than transverse distances. The second assumption was that discontinuities could not exist in solute concentration along the longitudinal axis without specifying whether the concentration should go up or down. As detailed analysis by the Mathematical Division of the NIH, led by John Stephenson, showed our model was over-determined. Now, 41 years after our initial effort, it seems that Einstein might have been right all along. In recent journals on mathematical biology we find new models that use more solutes, much more complex structural layout, and highly increased number of variables. And they use, of course, very powerful computers which make all this possible. It is, perhaps, not too presumptuous of us to try to complement Einstein’s rule by saying: Make models as complicated as necessary, but not more complicated.