This story is somewhat convoluted, so please try to bear with me. George Sanders (1906 – 1972) was an English actor, known for his "extremely heavy English accent and bass voice." The latter led to his being cast often as a villan in his forty years of making films.
On April 23, 1972, George Sanders checked into a hotel near Barcelona, and was found dead two days later. He had committed suicide via a ton of barbiturates, but left behind this suicide note: Dear World, I am leaving because I am bored. I feel I have lived long enough. I am leaving you with your worries in this sweet cesspool. Good luck.
Still with me? The September, 1972, issue of the National Lampoon focused on boredom...and created the George Sanders Memorial Boredom Awards. Each "honored" item was mentioned as being able to bore one to death.
One category was "The Most Boring Mathematical Concept." Before revealing the winner, what would you suggest as possible candidates? I could list several, but found that I was listing them because of how they are taught/learned...not the concepts themselves!
Nonetheless, the winner in 1972 was "Tangent Bundles." What in the world are they?
Draw a circle and imagine all the tangents that can be drawn in the plane to that circle (see top right). Now, to prevent these tangents from intersecting, rotate them all out of the plane 90 degrees (see below right). The latter is a simplistic example (actually considered to be trivial) of a tangent bundle.
Tangent Bundles are a part of differential geometry. Their primary use is to provide a domain and range for the derivative of a smooth function. That is, imagine you have a function in a plane, with all of its tangent lines also rotated to be perpendicular to the plane.
Now, why is this boring? I do not know, especially since I have used Geometers SketchPad to draw a host of tangent bundles for various curves (unfortunately I could not rotate them out of the plane other than with imagination).
So, lets get back to the question. What is the most boring mathematical idea to you...and why? In turn, what is the most interesting mathematical idea to you...and why?
My guess is that one could respond with the same idea for both questions...and give appropriate answers as to why for both!