Mathematics i s an incredibl y excitin g an d creativ e fiel d o f endeavor . Ye t
most peopl e neve r se e it that way . Nonmathematicians to o ofte n assum e
that w e mathematicians si t around talkin g about wha t Newto n di d thre e
hundred year s ag o o r calculatin g a coupl e o f extr a millio n digit s o f IT.
They do not realize that more new mathematics is being created now tha n
at any other time in the history of humankind .
Explaining th e fiel d o f kno t theor y i s a particularl y effectiv e wa y t o
dispel thi s misconception . Her e i s a field tha t i s over on e hundre d year s
old, and yet some of the most exciting results have occurred in the last fif-
teen years . Easil y state d ope n question s stil l abound , an d on e ca n ge t a
taste for wha t i t is like to do research very quickly. The other tremendou s
advantage tha t kno t theor y ha s over man y othe r fields o f mathematic s i s
that much of the theory can be explained at an elementary level. One does
not nee d t o understand th e complicated machiner y o f advance d area s of
mathematics to prove interesting results.
My hope is that this book will excite people about mathematics—tha t
it will motivate them t o continue to explore other relate d area s of mathe -