事实上, 20世纪产生了大量的新数学, especially with the 成长th of mathematical physics and the advent of computers. 随着专业化的发展, 然而, much of modern mathematics is simply inaccessible to the aver年龄 person. Imagine the whole edifice of mathematics as a giant tree with the ancients (such as the Pythagorean Theorem) forming the roots and the trunk of the tree, and modern mathematicians breaking off into specialities along different branches. An example of a twig sprouting off of a branch would be Topology (a sub-field of Geometry), 然而, 只有花了几个月时间的人才能理解, 也许是几年, 到那个特定的研究领域. 子领域的数量，小枝产卵小枝，越来越大. The sheer breadth of topics has been 成长ing exponentially and it continues to 成长, 使学习这些主题变得令人望而却步.
那么数学家到底在做什么呢? How do they eke out new twiglets on their little branch of this enormous tree? 数学家们玩. They test new ideas, search for generalities, look for beautiful relationships. In professor Paul Lockhart’s brilliant polemic “A Mathematician’s Lament,” he claims that “To do mathematics is to eng年龄 in an act of discovery and conjecture, 直觉和灵感, 处于混乱状态”(第8页). The process of mathematics begins with an observation or a question and then that notion is toyed with. 这个过程达到高潮, 如果数学家足够聪明或者幸运的话, 用无懈可击的证据证明了这个猜想. 虽然他的作品并不完全是现代的, an example from the life of famous mathematician Leonhard Euler (1707-1783) will help illustrate this.
传说在18世纪中期, the locals of Königsberg (now Russia) made a game of walking the seven bridges spanning the Pregel River and that good fortune would come to anyone who could traverse the bridges without backtracking or walking over the same bridge twice. See for yourself: attempt to trace a path with your finger but don’t go backwards or over the same bridge twice. 有趣,哈?
莱昂哈德·欧拉当时还不到30岁, 但他的名声是众所周知的, 13岁进入大学, 在青少年时期完成博士学位, 写不同的主题，比如导航, 声音传播, 和数学. He would eventually be regarded as one of the most brilliant and prolific mathematicians in history, 一直工作到76岁去世.
Euler likely treated this problem like most mathematicians would, playing with it just as you might. This brief video brings it to life and shows you how Euler was able to get to the heart of the problem (tracing the seven lines), 仔细分析它, 并最终解决它.
Euler's revelation provided the first result in a major branch of the tree of mathematics — that of Topology, a sub-field of Geometry — which has blossomed over the past 200+ years. While new developments in modern mathematics rarely produce such fertile results as Euler and his creation of Topology, 尽管如此, the fun is there and the inexorable moving forward of the subject continues.
Director of Studies Rick Tony is a member of 韦德娱乐app下载地址’s Math Department. 今年，他教大学先修课程微积分AB.