Hilbert - Alexander of the Mathematical World

Author: Rudolf
Publisher:
Publish Date: 2006-07-01
Features: During his college term, Hilbert attended three courses: calculus, matrix theory, and the theory of curvature of surfaces. According to custom, in the second term, he could transfer to another university to attend lectures. He chose Heidelberg University—the most charming and romantic university in Germany. At that time, a renowned scholar was teaching at Heidelberg, whose name, Lazarus Fuchs, had become synonymous with linear differential equations. Hilbert enrolled in his course. Fuchs's lectures were indeed unique and deeply impressive. He did not prepare much in advance for his lectures, as he was accustomed to putting himself in danger in class: he would derive the content on the spot. As one of his students later wrote, the students thus "gained an opportunity to witness the actual process of superb mathematical thinking." In the following term, it was originally allowed for Hilbert to transfer to Berlin to attend lectures. There, a group of brilliant scientists gathered, including Weierstrass, Kummer, Kronecker, and Helmholtz. However, he deeply missed his hometown—on this point of homesickness, Hilbert was very much like his father, so he resolutely returned to the University of K?nigsberg. At that time, K?nigsberg had only one full professor of mathematics: Heinrich Weber. This man was highly talented and versatile, truly the successor of Jacobi and Richard Dedekind. He made significant contributions in both number theory and mathematical physics. He also wrote many important works. Theory of Arithmetic Functions of a Single Variable was a masterpiece co-authored by him and Richard Dedekind. His works on algebra, including a monograph on mathematical physics co-authored with Riemann, were all classics in their respective fields. Hilbert studied number theory, function theory, and first became familiar with invariant theory—the fashionable mathematical theory of the time. He carefully preserved these notes from his first lectures. All other lecture notes from university were also well-maintained. We see that while the handwriting still shows some immaturity, with typical spelling errors of a young person, there is not a trace of carelessness. One set of notes was taken during his lectures on number theory with Weber, and it appears to be the only set that was thoroughly organized later. In the next term—spring of 1882—Hilbert again decided to stay at the university in his hometown. That same spring, Hermann Minkowski, after studying in Berlin for three terms, had returned to K?nigsberg. Minkowski was a chubby child, wearing a scholarly pair of pince-nez on his immature nose, which seemed somewhat out of place. While in Berlin, he had received a scholarship for his outstanding mathematical work. He gave this money to a classmate from a poor family. This story was unknown to anyone in K?nigsberg at the time (not even his family knew; it was only much later that his classmate's brother told this story to the Minkowski family). At the age of only 17, Minkowski, full of ambition, was completely immersed in a very profound research, hoping to win the mathematical science prize of the Paris Academy of Sciences with it. The Paris Academy of Sciences had announced a competition for solutions to the following problem: expressing a number as the sum of five squares. Minkowski's research results far exceeded the original problem. However, the deadline for submitting answers to the academy—June 1, 1882—had arrived. According to the competition rules, the article had to be translated into French, but Minkowski's article was not translated into French. With the situation as it was, he decided to submit his entry anyway. In the last minute, he followed his older brother Max's advice and wrote a short note to attach to the front of his article. In the note, Minkowski explained that the mathematical problem itself had so deeply attracted him that he had overlooked the competition rules; he also expressed hope that the academy would not think that "if I had missed something, in reality I had given more." As the motto at the beginning of the article, he quoted Boileau: "Nothing is more beautiful than truth, and nothing is more lovable than truth." P12-13