Graph Theory III

"There are seven bridges. If the problem could be reduced to numbers, why couldn’t I find a mathematical approach to solving it? It’s nothing to do with mathematics - it’s a purely logical problem, but that’s what intrigued me about it." (Leonhard Euler, [letter to Carl Leonhard Gottlieb Ehler, mayor of Danzig] 1736)

"Thus, you see, most noble Sir, how this type of solution bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle. Because of this, I do not know why even questions which bear so little relationship to mathematics are solved more quickly by mathematicians than by others." (Leonhard Euler, [letter to Carl Leonhard Gottlieb Ehler, mayor of Danzig] 1736)

"A common objection to the use of mathematics in the social sciences is that the information available may only be qualitative, not quantitative. There are, however, several branches of mathematics that deal effectively with qualitative information. A very good example is graph theory." (John G Kemeny, "The Social Sciences Call on Mathematics", The Mathematical Sciences: A Collection of Essays, 1969)

"Graph theory, a special tool borrowed from topology, has now been used to reduce even quite complicated chemical structures to a chain of numbers so that a computer can analyze them." (George A W Boehm, "The Mathematical Sciences: A Collection of Essays", 1969)

"A graph is a good way to mathematically represent a physical situation in which there is a flow of something - materials, people, money, information – from one place to another." (John L Casti, "Five Golden Rules: Great Theories of 20th-Century Mathematics - and Why They Matter", 1995)

"Graph theory is typical of much modern mathematics. Its subject matter is not traditional, and it is not a development from traditional theories. Its applications are not traditional either. […] Graph theory is not concerned with continuous quantities. It often involves counting, but in integers, not measuring using fractions. Graph theory is an example of discrete mathematics. Graphs are put together in pieces, in chunks, rather like Meccano or Lego, or a jigsaw puzzle." (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)