Quotes from Richard J. Trudeau

Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub.

Geometric diagrams are to geometers what board and pieces are to chessmasters: visual aids, helpful but not indispensable.

It appears then that the essence of chess is its abstract structure. Names and shapes of pieces, colors of squares, whether the "squares" are in fact square, even the physical existence of board and pieces, are all irrelevant. What is relevant is the number and geometric arrangement of the "squares", the number of types of piece and the number of pieces of each type, the quantitative-geometric power of each piece, etc. Everything else is a visual aid or a fairy tale.

I use logic all the time in mathematics, and it seems to yield "correct" results, but in mathematics "correct" by and large means "logical", so I'm back where I started. I can't defend logic because I can't remove my glasses.

In particular the rules of logic tell us how to create, from the opening arrangement (the list of axioms), new arrangements (called "theorems").

Definition 20. If some new vertices of degree 2 are added to some of the edges of a graph G, the resulting graph H is called an expansion of G.

A statement that mathematicians believe but cannot as yet prove is called a "conjecture".

Map coloring problem. Find the smallest number m such that the faces of every planar graph can be colored with m or fewer colors in such a way that faces sharing a border have different colors.

It has been said that geometry is the art of applying good reasoning to bad diagrams.

Topology] is a purely qualitative subject where quantity is banned. In it two figures are always equivalent if it is possible to pass from one to the other by a continuous deformation, whose mathematical law can be of any sort whatsoever as long as continuity is respected.

The village barber shaves those and only those men who live in the village and do not shave themselves. The village barber is a man and he lives in the village. Consider the question "Who shaves the barber?

A topologist enters a coffee shop, orders coffee and a doughnut, and is served. Preoccupied with topological theorems, he takes a bite out of his coffee cup and has to finish his thoughts in a nearby emergency ward. His mistake is somewhat understandable as a doughnut and coffee cup are topologically equivalent

There has been a steady escalation of conditions since our first discussions in Chapter 2. Then we talked about plain old graphs. Subsequently we restricted our attention to planar graphs, then to planar connected graphs, then to planar connected graphs with each edge bordering two faces (polygonal graphs), and now to planar connected regular graphs with each edge bordering two faces and all faces bounded by the same number of edges (platonic graphs).

you should not allow yourself to be convinced by repeated failures,

But the pure mathematician's goal is to have a good time, not to be efficient; and machine-building is a lot more fun than problem-solving.

The Pythagoreans were mystics, and believed that the tetrahedron, cube, octahedron, and icosahedron respectively underlay the structure of the four elements of Greek science: fire, earth, air, and water. The dodecahedron they identified with the universe as a whole.