Log24

    “Throughout Einstein’s five and a half years at the Luitpold Gymnasium, he was taught mathematics from one or another edition of the separately published parts of Sickenberger’s Textbook of Elementary Mathematics.  When it first appeared in 1888 the book constituted a major contribution to reform pedagogy.  Sickenberger based his book on twenty years of experience that in his view necessarily took precedence over ‘theoretical doubts and systematic scruples.’  At the same time Sickenberger made much use of the recent pedagogical literature, especially that published in the pages of Immanuel Carl Volkmar Hoffmann’s Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht, the leading pedagogical mathematics journal of the day.  Following in the tradition of the reform movement, he sought to present everything in the simplest, most intuitive way possible.  He opposed introducing scientific rigour and higher approaches in an elementary text.  He emphasised that he would follow neither the synthesis of Euclidean geometry nor the so-called analytical-genetic approach.  He opted for a great deal of freedom in the form of presentation because he believed that a textbook was no more than a crutch for oral instruction.  The spoken word, in Sickenberger’s view, could infuse life into the dead forms of the printed text.  Too often, he insisted in the preface to his text, mathematics was seen and valued ‘as the pure science of reason.’  In reality, he continued, mathematics was also ‘an essential tool for daily work.’  In view of the practical dimension of mathematics Sickenberger sought most of all to present basic propositions clearly rather than to arrive at formal conciseness.   Numerous examples took the place of long, complicated, and boring generalities.  In addition to the usual rules of arithmetic Sickenberger introduced diophantine equations.  To solve three linear, homogeneous, first-order equations with three unknowns he specified determinants and determinant algebra.  Then he went on to quadratic equations and logarithms.  In the second part of his book, Sickenberger treated plane geometry.
     According to a biography of Einstein written by his step-son-in-law, Rudolf Kayser– one that the theoretical physicist described as ‘duly accurate’– when he was twelve years old Einstein fell into possession of the ‘small geometry book’ used in the Luitpold Gymnasium before this subject was formally presented to him.  Einstein corroborated Kayser’s passage in autobiographical notes of 1949, when he described how at the age of twelve ‘a little book dealing with Euclidean plane geometry’ came into his hands ‘at the beginning of a school year.’  The ‘lucidity and certainty’ of plane geometry according to this ‘holy geometry booklet’ made, Einstein wrote, ‘an indescribable impression on me.’  Einstein saw here what he found in other texts that he enjoyed: it was ‘not too particular’ in logical rigour but ‘made up for this by permitting the main thoughts to stand out clearly and synoptically.’  Upon working his way through this text, Einstein was then presented with one of the many editions of Theodor Spieker’s geometry by Max Talmey, a medical student at the University of Munich who dined with the Einsteins and who was young Einstein’s friend when Einstein was between the ages of ten and fifteen.  We can only infer from Einstein’s retrospective judgment that the first geometry book exerted an impact greater than that produced by Spieker’s treatment, by the popular science expositions of Aaron Bernstein and Ludwig Büchner also given to him by Talmey, or by the texts of Heinrich Borchert Lübsen from which Einstein had by the age of fourteen taught himself differential and integral calculus.
     Which text constituted the ‘holy geometry booklet’?  In his will Einstein gave ‘all his books’ to his long-time secretary Helen Dukas.  Present in this collection are three bearing the signature ‘J Einstein’: a logarithmic and trigonometric handbook, a textbook on analysis, and an introduction to infinitesimal calculus.  The signature is that of Einstein’s father’s brother Jakob, a business partner and member of Einstein’s household in Ulm and Munich.  He presented the books to his nephew Albert.  A fourth book in Miss Dukas’s collection, which does not bear Jakob Einstein’s name, is the second part of a textbook on geometry, a work of astronomer Eduard Heis’s which was rewritten after his death by the Cologne schoolteacher Thomas Joseph Eschweiler.  Without offering reasons for his choice Banesh Hoffmann has recently identified Heis and Eschweiler’s text as the geometry book that made such an impression on Einstein.  Yet, assuming that Kayser’s unambiguous reporting is correct, it is far more likely that the geometrical part of Sickenberger’s text was what Einstein referred to in his autobiographical notes.  Sickenberger’s exposition was published seven years after that of Heis and Eschweiler, and unlike the latter it appeared with a Munich press.  Because it was used in the Luitpold Gymnasium, copies would have been readily available to Uncle Jakob or to whoever first acquainted Einstein with Euclidean geometry.”