葬禮上的證明

Hilbert曾有一個學生，給了他一篇論文來證明Riemann猜想，儘管其中有個無法挽回的錯誤，Hilbert還是被深深的吸引了。第二年，這個學生不知道怎麼回事死了，Hilbert要求在葬禮上做一個演說。那天，風雨瑟瑟，這個學生的家屬們哀不勝收。Hilbert開始致詞，首先指出，這樣的天才這麼早離開我們實在是痛惜呀，眾人同感，哭得越來越凶。接下來，Hilbert說，儘管這個人的證明有錯，但是如果按照這條路走，應該有可能證明Riemann猜想，再接下來，Hilbert繼續熱烈的冒雨講道：「事實上，讓我們考慮一個單變數的複函數.....」眾人皆倒。

http://aleph0.clarku.edu/~djoyce/hilbert/
The Mathematical Problems of David Hilbert

About Hilbert's address and his 23 mathematical problems
Hilbert's address of 1900 to the International Congress of Mathematicians in Paris is perhaps the most influential speech ever given to mathematicians, given by a mathematician, or given about mathematics. In it, Hilbert outlined 23 major mathematical problems to be studied in the coming century. Some are broad, such as the axiomatization of physics (problem 6) and might never be considered completed. Others, such as problem 3, were much more specific and solved quickly. Some were resolved contrary to Hilbert's expectations, as the continuum hypothesis (problem 1).
Hilbert's address was more than a collection of problems. It outlined his philosophy of mathematics and proposed problems important to his philosophy.

Although almost a century old, Hilbert's address is still important and should be read (at least in part) by anyone interested in pursuing research in mathematics.

In 1974 a symposium was held at Northern Illinois University on the Mathematical developments arising from Hilbert problems. A major mathematician discussed progress on each problem and how work on the problem has influenced mathematics. Also, 23 new problems of importance were described. The two-volume proceedings of the symposium was edited by Felix Browder and published by the American mathematical Society in 1976. See also Irving Kaplansky's Hilbert's problems, University of Chicago, Chicago, 1977.

There is also a collection on Hilbert's Problems, edited by P. S. Alexandrov, Nauka, Moscow, 1969, in Russion, which has been translated into German.

中國的數學界精英們,  對著 David Hilbert 你們不感到害羞嗎?  你們是如何扶植新人的?