What kind of truth about this whole issue do you think this has in common with category theory or perhaps this is sort of some kind of new logic at play? I mean, is there anything novel about this line of reasoning to the subject matter of mathematics?

I have no use for category theory, but it does attempt to generalize areas of math that have similarities. I fear your knowledge of mathematics is so minimal that we are not getting anywhere here. Since I have been a mathematician (over fifty years) the subject has grown so dramatically and is so complex now I understand little of it myself.

I have no use for category theory, but it does attempt to generalize areas of math that have similarities. I fear your knowledge of mathematics is so minimal that we are not getting anywhere here. Since I have been a mathematician (over fifty years) the subject has grown so dramatically and is so complex now I understand little of it myself. — jgill

Well, my knowledge doesn't seem to be a deterrent for some kind of discussion. All that I have concluded now is that there's no determined method to quantifying complexity in mathematics.

Is this thread intended to find something akin to the p vs np problem (related to complexity in computing)?

https://encyclopediaofmath.org/wiki/Complexity_theory

Interesting approach. What kind of general syntax applies to proof telling? — Shawn

Be it Gödel or Heisenberg, infinite variables can not be overcome by infinite description,
there must be a corner around which the pursuit changes velocity.

Theory of Nothingness
''Rather the starting point, the un-caused Cause, is Possibility which is both Something and Nothing and the basis of Probability.'' Marvin Glover

Is this thread intended to find something akin to the p vs np problem (related to complexity in computing)? — emancipate

Good question. I think there is confusion regarding complex in a technical sense and complicated in a more general sense. I know of no "scale" describing levels of complication in a mathematical proof, although when one conjectures a proof path it may be apparent that low or high levels of complication might ensue. And maybe there are practitioners who speculate "Why this looks to be about an eight on the scale of complexity!"

Again, a discussion of mathematics that mathematicians pay little attention to. But fun for amateur philosophers. :smile:

Connected with the ideas of "complex" and "complicated" in proofs is the word "elementary", which, when used by a mathematician, usually does not signify "simple" or "easy", but refers to the level of a mathematical argument, specifically that that argument involves only basic concepts in the specific subject area. Some elementary proofs are very complicated. Others, not so much.

"Non-elementary" usually means the argument involves more advanced concepts and results, and may actually be fairly straightforward and uncomplicated - or not. :cool: