Monsters Among Us

The Weierstrass function was a remarkable function when introduced, being continuous EVERYwhere, yet differentiable NOwhere... a precursor to fractals. It was presented by Karl Weierstrass in 1872 to the horror of many mathematicians! Many called it Weierstrass's monster and since then many more "monster" mathematical functions have been introduced. R.J. Lipton has a new interesting post up on the monsters and non-monsters that lurk amongst us:

http://rjlipton.wordpress.com/2014/05/27/avoiding-monsters-and-non-monsters/

From the piece: "In analysis there are many strange and wonderful functions, for which it seems surprising that they even exist: space-filling curves, discontinuous additive functions, through to differentiable functions that are nowhere monotone...
"What we have learned in analysis—and the same lesson applies to many if not all parts of mathematics—is that monsters are often very common."