(November 6, 2018 at 8:37 am)Jehanne Wrote:(November 5, 2018 at 1:03 pm)polymath257 Wrote: Yes, research in math is hard.
The concept of a fractal dimension goes back to Hausdorff and is around a century old. Using various forms of iteration to produce rather complicated sets is even a bit older (the Cantor ternary set is, perhaps, the first example of a set now recognizable as a fractal).
All I can say is that a lot depends on your definitions. And there are several competing definitions for what constitutes a 'fractal'. But iterative methods involving self-similarity are widespread in math.
It is interesting because what is taught at the entire undergraduate level is mostly 19th-century math and science with some early 20th-century stuff tossed in for the junior and senior level students. I have read that PhD students in math start learning the 1950s material around their 2nd or 3rd year of graduate studies.
Actually, most of the undergraduate math is 18th century or before. The one exception at the 'lower' levels is linear algebra. If you get to the junior/senior classes, you get into the 19th century with groups and rings as well as some of the material on epsilon-delta proofs.
And yes, getting past 1950 or so is pretty much limited to PhD students, although some of the material relevant to theoretical computer science gets past that mark.