# Shangyoung Kwon

**email**

**Office Hours**

T/Th 3:00 pm - 4:00 pm (POT 718)

**Mathskeller**

F 3:00 - 4:00 pm

A great theorem should contribute substantial new information, and it should be unexpected! That is, it should reveal something which common sense would not naturally lead us to expect. We reach the conclusion - a conclusion we may have been skeptical about, but which is now established beyond a doubt - we feel a certain sense of awe not unlike our reaction to the ironic or tragic twist of a great story. - *Charles C. Pinter*

There is a great twist in the history of mathematics: the survival of the infinitesimal! Nonstandard analysis is very much the creation of one man, Abraham Robinson. It employs the methods of model theory (itself one of the important branches of mathematical logic) to embed the universe of mathematical discourse in a so-called "nonstandard universe" containing infinitesimals as well as infinite objects. It is a great historical irony that the very methods of mathematical logic that developed out of the drive toward absolute rigor in analysis have provided what is necessary to justify the once disreputable method of infinitesimals. Perhaps indeed, enthusiasm for nonstandard methods is not unrelated to the well-known pleasure of the illicit. But far more, this enthusiasm is the result of the mathematical simplicity, elegance, and beauty of these methods and their far-reaching application. - *Martin Davis*