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I think that there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. If Schroedinger had been more confident of his work, he could have published it some months earlier, and he could have published a more accurate equation. It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory.
Scientific American, May 1963
Loci: Convergence
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Extracting Square Roots Made Easy: A Little Known Medieval Method
Introduction
In 1901 the Swiss historian of mathematics and Arabist Heinrich Suter (1848-1922) published in the journal Bibliotheca mathematica the German translation of an Arabic mathematical treatise composed by (as the author himself wrote) “Master Abu Zakariya Muhammad ibn Abd Allah known under the name of el-Hassar,” in which we find the earliest known description of an iterative process for extracting square roots yielding closer and closer approximations to the real value. Although this ingenious yet basically simple way to calculate square roots – completely different from our method today – was taught later by the outstanding Italian mathematicians Luca Pacioli (ca. 1445-1517), Hieronimo Cardano (1501-1576), Nicolo Tartaglia (1499/1500-1557), and Pietro Antonio Cataldi (1548-1626), it is largely unknown today. But it is worthy of study, and we present it in this article.
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Katscher, Friedrich, "Extracting Square Roots Made Easy: A Little Known Medieval Method," Loci (June 2010), DOI: 10.4169/loci003494