This course is a novel introduction to mathematics and its history. It puts the difficulties of the subject upfront by enthusiastically tackling the most important ones: the seemingly impossible concepts of irrational and imaginary numbers, the fourth dimension, curved space, and infinity. Similar "impossibilities" arise in art, literature, philosophy, and physics - as we will see - but mathematics has the precision to separate actual impossibilities from those that are only apparent. By focusing reason and imagination on several apparent impossibilities, the course aims to show interesting math to students whose major may be in another field, and to widen horizons of math students whose other courses are necessarily rather narrowly focused.
John Stillwell was born and raised in Australia, where his favorite book as a child was Lewis Carroll’s Through the Looking Glass. This was his introduction to mathematics, logic, and impossibilities. He came to America to do a doctorate in mathematical logic at MIT, then returned to Australia for 30 years, where his interest in math broadened to embrace number theory, algebra, geometry, and their history. In 2002 he was drawn back to the U.S. and became a Professor of Mathematics at USF. He has written several books on mathematics, the best known of which is Mathematics and its History, and he hopes that the book on which this course is based will be his best yet.