Dr. Jonathan Rosenberg, Department of Mathematics
Mathematics is one of the greatest accomplishments of human civilization. This course will examine mathematics in a somewhat unusual way, not as a finished product to be studied out of a textbook, but as a process of discovery that has progressed for centuries and is still under development.
We will examine selected writings by great mathematicians from the past, such as Euclid, Newton, Gauss, and Hilbert. The course is not in any way intended as a substitute for more traditional math courses such as the calculus sequence. Instead, it will deal with questions which are rarely, if ever, treated in such courses, such as:
(1) What does it mean to do “research” in mathematics?
(2) What makes great mathematics and mathematicians great?
(3) How are mathematicians led to their ideas?
(4) How can mathematical ideas best be conveyed to an audience?
(5) How have ways of thinking about mathematics changed over the
centuries, and to what extent have they remained the same?
(6) In what way is the development of mathematics affected by its
cultural and historical milieu?
The only prerequisite is four years of high-school level mathematics and an interest in finding out what mathematics is about. An interest in history or literature will also be useful.
Students will be assigned works by famous mathematicians (short papers, letters, excepts from books, etc.) to read and present to the rest of the class for discussion. There will be no exams, but regular class participation is expected and at least one paper will be required. This is a discussion seminar, not a lecture course.
The following texts are collections of papers (all in English or translated into English). They will be supplemented by additional papers and letters extracted from various mathematicians’ collected works.
A Source Book in Mathematics, edited by D.E. Smith, Dover.
Mathematics Emerging: A Source Book, 1540-1900, edited by Jacqueline Stedall, Oxford.
In addition, it will be useful to look at a quick history of mathematics for orientation and overview. Here are two possibilities:
History of Mathematics: Brief Version, by Victor J. Katz, Pearson.
The History of Mathematics: A Very Short Introduction, by Jacqueline Stedall, Oxford.