34 1. Trisecting Angles Though some may have voiced skepticism over a claim that the 60◦ angle could not be trisected, one of the celebrated problems from antiquity, as Gauss’s career progressed and his stature in mathematics became the equal of Bach in music or Shakespeare in literature, the mathematical world accepted his claim as true and Gauss was credited with the solution of the trisection problem. Does Gauss deserve this credit? Never in his life did he write down a solution, and one was never found in his papers after his death. The spirit of modern mathematics is to not accept anything as true until a logically rigorous proof is produced. If one accepts this posture, then Gauss does not deserve the credit. But Gauss was Gauss if he said it was true, he had a proof. If not Gauss, then who first wrote out a proof? It seems to be a French bridge and highway engineer, Pierre Louis Wantzel, who first published a proof in 1837 that the 60◦ angle could not be trisected. Nevertheless, it is undoubtedly true that Gauss did prove the general theorem he had stated. Gauss’s notebook is filled with such unproven the- orems all true. Most of these entries are dated between 1795 and 1801, when Gauss was 18–24 years old. Of the 146 entries, 121 fall into this period. Gauss seems to have been overwhelmed in his youth with new ideas too many to fully explore. Gauss was a very complex human being. He seems to have had an intense dislike of controversy (who likes it?) and his motto, “Few but Ripe”, reflects his desire to only publish those theories that would completely exclude the possibility of controversy. If he had announced the 121 results he privately recorded between 1795 and 1801, he would have been making more than one such announcement a month. Undoubtedly this would have raised eyebrows, and controversy would have resulted. So Gauss guarded his results and waited for the time to fully develop them. Unfortunately, the time never came for most of them. Though he lived for 78 years, he published few of the results from his notebook. For a man who sought to avoid controversy, he also seems to have jumped with wild abandon into at least two. Later, as a professor at G¨ottingen and the acknowledged leading mathematician of his time, mathematicians freely communicated their ideas to him probably hoping for recognition and encouragement from the great man. On two occasions he told young mathematicians he had already made their discoveries though he had not published them. This had a devastating effect on their careers. One can’t help but form the picture of the older mathematician, receiving adulation from every corner, and so smug and complacent in his own position that he fails to
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