Saturday, July 2, 2016

Do you feel competent to read mathematical proofs that are technically involved?

Probably not.  I don't really know.


  1. I don't know what "technically involved" means. I suppose that this question indicates that proofs lay on a spectrum of "difficulty" or "involvedness" or "technicality" or something. I have seen some proofs that I understood and some that I didn't. I don't remember a ratio. I don't know how far along the "difficulty" scale the proofs I've seen are. What if what I've seen is just 1% difficult, but to me some of it is impossibly hard? How could I possibly know what there is to know that I don't know yet? How could I know what exists that I haven't seen?

    However, if I had to guess, I'd say no, I am not competent to read proofs that are technically involved, because I think it is likely that I haven't seen the vast majority of the kinds of proofs that could exist. I think that because I have only taken undergraduate math classes and I've sucked at most of them, and there are more undergraduate math classes I haven't taken and there's graduate and Phd classes and people supposedly discovering/inventing new math all the time. And I think that given the fact that there's so much I haven't seen, the term "technically involved" couldn't possibly apply to the little bit of elementary math I've seen.

  2. Assuming that proofs fall on a spectrum of difficulty, I think that the ones I have seen are probably very near the easy end of the spectrum, because I have only had a few undergraduate math classes and I know that, not only are there more undergraduate math classes that I haven't taken, but there also are masters and Ph.D. level math classes, and people making new discoveries and inventions in math. I have seen proofs that I understood, for example, the proof that the square root of 2 is irrational, and the proof that there is an infinite number of irrational numbers. And though I can't think of a specific example, I know I have seen proofs that I didn't understand.

  3. There have also been proofs that I remember not understanding a few years ago, but now after taking more math classes at UALR I do understand them. So I know improvement is possible and that if I decide to study more math, I have a foundation.