(November 5, 2018 at 1:03 pm)polymath257 Wrote:(November 5, 2018 at 9:55 am)Jehanne Wrote: Problem is that this stuff is really, really hard, not only to learn but to actually improve upon the work of others. My problem was that I had a love of physics and math; just was not particularly good at either subject. Still, got through 3-semesters of calculus and taught myself ordinary and partial differential equations with a little tensor calculus over the years. They are beautiful subjects, and I see no reason to believe that what modern science observes in the heavens and on earth is just the product of invisible angelic beings who are the true cause of particle motion, whether it be atomic, microscopic or macroscopic.
The Universe can be modeled just fine with higher math, although, just because something is correctly mathematically does not mean that such corresponds to physical reality.
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.
