Geometric Aspects in the Development of Knot Theory

Derivation and Interpretation of the Gauss Linking Number

“…(Lk (2) = Lk (4) ). We recall that the degree of a (continuous) function restricted to the boundary of the manifold where it is defined is zero.…”

What Are Models For? Alexander Crum Brown’s Knitted Mathematical Surfaces

“…40 Tait wrote that Crum Brown's ''knowledge of mathematics'' is ''not merely better than that of most chemists, but is really good.'' 41 Crum Brown even inspired Tait's own practice of representation in knot theory: in an 1877 paper, Tait writes, ''we must now adopt something very much resembling Crum Brown's Graphical Formulae for chemical composition.…”

The Unknotting Problem and Normal Surface Q-Theory

“…In 1954 Wolfgang Haken surprised the mathematical community by announcing at the International Congress of Mathematicians that he had an algorithm to determine if a knot was unknotted or not. Not only was Haken an "outsider" of sorts, but his approach was radically different from the diagrammatic and group-theoretic techniques that preceded him [2].…”