One problem with the "slowness problem" is that our posts quickly sink to the bottom. So, I have brought the response to your post at
back to the top.
Your math experience sounds similar to mine. I, too, figured that it would be far more pleasurable to dabble in mathematics as an amateur rather than try to make a living at it. I guess that's the easy way out.
"but then one is faced with the question of what is going on behind the ...--->'s ?"
I'm not exactly sure what you are referring to by "...--->" but I'll make a guess. If I am wrong, please let me know what you mean. My guess is that you mean the limiting process. You say it is something "we do" and that it is "some repetitive operation". That is exactly how I see the limiting process. In conventional mathematics, it is assumed that this process -- of computing the next term in a series, or of defining the next integer in the foundations of Arithmetic -- just sort of proceeds unattended and in the process, grinds out infinite sets of things. That's the assumption I balk at. I think there is an implicit question here of exactly to what extent is some consciousness required to be involved in this process. It seems to me that the conventional view holds that consciousness can somehow disengage after a while and let the process proceed on its own in order to finally "reach infinity".
Since you still seem to be interested in this subject, you have prompted me to post an old essay to my web site which outlines my view of how we might dump the notion of infinity from math and yet not throw the baby out along with it. I would be honored if you would take a look at