1.10. Some historical notes 33 patron. But Gauss had an equal attraction to philology, the study of lan- guage. On October 15, 1795, Gauss entered the university of G¨ottingen. He had already proved several new theorems in mathematics but had not published any. He continued to study both mathematics and philology. Then, on March 30, 1796, came the point at which Gauss dedicated him- self to science and mathematics. The reason the date is known so precisely is that on that day Gauss began to keep a mathematical diary, which he called Notizenjournal, and which he wrote in Latin. The first entry in the diary described his discovery that the regular polygon of 17 sides is constructible by straightedge and compass alone. Gauss submitted a short note on June 1, 1796, announcing his discovery. In his first appearance in print, he wrote: Every beginner in geometry knows that it is possible to construct different regular polygons, for example triangles, pentagons, 15- gons, and those regular polygons that result from doubling the number of sides of these figures. One had already come this far in Euclid’s time, and it seems that since then one has generally be- lieved that the field for elementary geometry ended at that point, and in any case I do not know of any successful attempt to extend the boundaries beyond that line. Therefore it seems to me that this discovery possesses special interest, that besides these regular polygons a number of others are geometrically constructible, for example the 17-gon. This re- sult is really only a corollary of a theory with greater content, which is not complete yet, but which will be published as soon as it is complete. C. F. Gauss, Braunschweig mathematics student at G¨ottingen Gauss was never again to publish an advanced notice of his results. He took as his motto “Few but Ripe” he refused to publish partial results and always waited until he had a complete theory. Years after his death, the Notizenjournal was discovered. It contained various ideas and partial results which, had they been published during his lifetime, would have significantly accelerated the progress of mathematics. But these were not “Ripe” so he never shared them. In 1801, Gauss published his monumental work, Disquisitiones Arith- meticae (written in Latin, as was much of the scholarly work of the day). The English translation of this book is 465 pages long and is filled with mathematics — mostly the theory of numbers. At the end of the book is the theorem stating which regular polygons are constructible and that the 18-gon is not. But now something unfortunate happened. Gauss gave no proof of this theorem. He did prove that the 17-gon is constructible, but not that the 18-gon is not constructible. In fact, he never wrote down a proof.

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