Hopefully this thread can go back to its original focus. Sorry for the diversion. :sad: — jgill

We're the main show now.

Fair enough. When I speak of a topic being "beyond me" it's a cop-out for not having the mental energy at my age (83) to study it, or just a complete lack of interest. I appreciate your comment. — jgill

I figured out that you're excessively modest. I misunderstood you and drew false conclusions. You're a teacher and I learned something. Thank you.

Every so often, however, something a bit out of my purview will intrigue me and I will make an effort to understand it. For example, a couple of years ago the notion of a functional integral sparked my interest, having read of Feynman's Sum of All Paths concept. My brief exposure to the concept fifty years ago was shallow and uncompelling. — jgill

That's interesting stuff. I never studied formal physics but I watch a lot of Youtube videos.

That was a delightful exploration, starting with the basic Wikipedia definition, and I wrote a short math note about functional integrals in spaces of complex contours. I enjoy writing math programs, especially graphics, and I came up with some nice imagery. That was fun. — jgill

The modern computer tools like LaTeX and computer graphics are incredible. I wish they had those when I studied math. Especially because my handwriting was bad.

I should not be making dismissive comments about set theory. You, fdrake, Nagase, and a few others have clearly explained ideas in this subject, and it is a powerful link between math and philosophy, and a vital part of the mathematical galaxy. I apologize, and if I slip up in the future you should nail me! — jgill

I have it on good authority that you know a lot more set theory than you're letting on. Perhaps you mean some of the logic stuff, the incompleteness aspects of set theory. As far as my attempting to nail you, I also have it on good authority that you could kick my ass. I saw the videos :-) You dropped some clues, I hope you don't mind. I also found a lovely elementary survey article about infinitesimals in which you mentioned the ultrafilter construction. You are being modest. You know more set theory than most here.

Most of my research efforts have been in classical analysis, very basic dynamical systems in the complex plane, trying to determine convergence/divergence of certain sequences. At one time this was a popular topic, but modern analysis has moved the focus more toward algebraic systems and generalizations. — jgill

Interesting stuff.

But I remain attached to the old-fashioned, nuts and bolts, stuff. For example, my latest efforts concern the iteration of linear fractional transformations (f(z)=(az+b)/(cz+d)) when the attracting fixed points are functions of time and are no longer "fixed". — jgill

I do remember the linear fractional transformations from undergrad complex variables so at least I know what those are.

Like predator and prey, do the iterates "catch up" with the roving attractors? Modern theory dealing with LFTs is more geometrical and algebraic. — jgill

I remember predator/prey from diffEq. Volterra-Lotka equations.

OK. Enough rambling. Thank you for your comments. — jgill

In another life I wanted to be a professor of math. I envy you your obvious focus and discipline.

I'm but lately come to this discussion. Fact is, I've just confirmed my 'membership' in this forum. I've picked this as the first thread to read, primarily because Dr. Douglas Hofstadter's delightful book, Godel, Escher, Bach is one of my 'desert island choices.

That said, I sense a lack of clarification between mathematics qua mathematics -- that is, a system for dealing with the concepts known as numbers -- and the discussion of mathematics; metamathematics, if you wish.